A_Hundred_Math_Practice.pdf

A HUNDRED MATH PRACTICE #SMcxlvii

Contents TEST#01 ..........................................................................................................................................................4 TEST#02 ..........................................................................................................................................................5 TEST#03 ..........................................................................................................................................................6 TEST#04 ..........................................................................................................................................................7 TEST#05 ..........................................................................................................................................................8 TEST#06 ..........................................................................................................................................................9 TEST#07 ....................................................................................................................................................... 10 TEST#08 ....................................................................................................................................................... 11 TEST#09 ....................................................................................................................................................... 12 TEST#10 ....................................................................................................................................................... 13 Solution TO TEST#01 .................................................................................................................................. 15 Solution TO TEST#02 .................................................................................................................................. 18 Solution TO TEST#03 .................................................................................................................................. 21 Solution TO TEST#04 .................................................................................................................................. 24 Solution TO TEST#05 .................................................................................................................................. 27 Solution TO TEST#06 .................................................................................................................................. 30 Solution TO TEST#07 .................................................................................................................................. 33 Solution TO TEST#08 .................................................................................................................................. 36 Solution TO TEST#09 .................................................................................................................................. 39 Solution TO TEST#10 .................................................................................................................................. 42

Tests

TEST#01 01: In a triangular area the seats are arranged in rows so that the 1st, 2nd, 3rd, 4th etc. rows contain 1, 2, 3, 4 etc. seats and so on. 70 students take seats starting from the 1st row and filling up the rows in increasing order. How many rows are completely filled? a. 9 b. 10 c. 11 d. 12 e. None 02: 25 consecutive integers are given. If the sum of the 1st 3 integers is 24, what is the sum of the last 3? a. 27 b. 28 c. 29 d. 30 e. None 03: The average of all whole numbers between 1 and 100 that end in 3 = a. 44 b. 45 c. 46 d. 47 e. None 04: The average weight of three men is 53 kg. None of them weights less than 51 kg. What is the maximum possible weight (in kg) of a person in that group? a. 53 b. 55 c. 57 d. 59 e. None 05: (1/√2)7 times (1/√2)5 =? a. 1/8 b. 1/16

c. 1/32

d. 1/64

e. 1/128

06: Coffee A normally costs Tk. 100 per pound. It is mixed with Coffee B, which normally costs Tk. 70 per pound, to form a mixture which costs Tk. 88 per pound. If there are 10 pounds of the mix, how many pounds of Coffee A are used in the mix? a. 4 b. 5 c. 6 d. 7 e. None 07: In a survey in the City of Gotham, it was found that 70% of the people surveyed watched the news on TVs, 35% read newspapers, and 25% read newspapers and watched the news on TVs. What percentage of the total people surveyed neither watched the news on TVs nor read newspapers? a. 30% b. 0% c. 20% d. 15% e. 5% 08: 7 kg of mangoes cost as much as 10 kg of apples and 1 kg of oranges. 7 kg of oranges cost as much as 1 kg of mangoes and 2 kg of apples. How many kg of apples can be purchased by the amount of money required to purchase 12 kg of mangoes? a. 8 b. 14 c. 16 d. 18 e. 24 09: A jar contains 10 pencils. Some of them are sharpened, and some are not. Each of the following could be the ratio of sharpened to unsharpened pencils except...... a. 9:1 b. 5:1 c. 4:1 d. 3:2 e. 1:1 10: The angles of a triangle are in the proportion of 1:2:3 and the length of the smallest side is 1 meter. What is the length of the longest side of the triangle? a. 4 b. 5 c. 2 d. 3 e. None.

TEST#02 01: Smallest possible integer having only three different odd factors. a. 75 b. 90 c. 105 d. 120 e. none 02: The number of integers between 100 and 200 that are divisible by 3, but neither by 5 or 7 is: a. 23 b. 22 c. 21 d. 20 e. none 03: The smallest possible number which -when divided by 3, 6, or 9 leaves a remainder 2, but perfectly divisible by 8: a. 112 b. 152 c. 176 d. 192 e. 200 04: In the equation x = y/√z. Where x, y, and z each are non-zero positive integer. Is y/x an integer? a. Yes b. No c. Yes or No d. Never e. None 05: If x is between 0 and 1, which of the following increases as x increases? i. 1 - x2 ii. x-1 iii. 1/x2 a. i and ii

b. ii and iii

c. i and iii

d. ii only

e. i only

06: Four consecutive even integers are such that the sum of four times the first number and twice the last number is equal to sum of twice the second number and thrice the third number. Find the first number in the series. a. 4 b. 6 c. 8 d. 12 e. none 07: Which of the followings cannot be expressed as the sum of the squares of two integers? a. 13 b. 17 c. 21 d. 29 e. 34 08: Arif makes his first cup of coffee at 6am and then makes one cup of coffee every four hours after that. Asif makes his first cup of coffee at 8am and then makes one cup every 3 hours after that. At what time will they both be making coffee? a. 9am b. 11am c. 12noon d. 1pm e. 2pm 09: What must be subtracted from 3y/x to get x/y? a. {2y^2 + (y-x)(y+x)}/xy b. (x^2 - 3y^2)/xy c. (3y - x)/xy d. 2y/x e. none 10: One half of the female students enjoy watching movies and one third of the male students do not like to watch movies. What fractional part of the total students enjoys watching movies? a. 5/12 b. 2/5 c. 3/4 d. 1/6 e. cannot be determined.

TEST#03 01: After 30 years, Zaman will be four times as old as he is now. Find out his present age: a. 10 b. 11 c. 7.5 d. 30 e. none 02: Six years from now Sumi's age will be the square of her age six years ago. What is Sumi's age? a. 8 b. 10 c. 12 d. 15 e. none 03: Y is four times as old as X. After 6 years, the sum of half of X's age and a fourth of Y's age will be the same as three times the present age of X. How old will X be after 6 years? a. 3 b. 9 c. 10 d. 12 e. 15 04: Eight years ago Mr Karim was 1/3 the age he will be after 10 years. What is his age now? a. 16 b. 17 c. 18 d. 19 e. 20 05: If a>b and ab b, and a > c, which of the following must be greater than 0? a. [b-c]/[b+c] b. [c-b]/[a-b] c. [b-c]/[b-a] d. [b-a]/[c-a] e. none 06: If a > 0, b < 0, c > 1, and d < 1, which of the following must be true? a. ab > cd b. ab < cd c. ac > bd d. ac < db e. none 07: 10% of r is equal to 20% of s, and 20% of s is equal to 30% of t. if 100% of r is equal to x% of t, what is the value of x? a. 300 b. 40 c. 30 d. 20 e. none 08: written as a percent, 5 = ? a. 5% b. 50%

c. 500%

d. 0.05

e. 0.5

09: Sales of a company in 1994 was 5% higher than that of the previous year. It grew 4% in 1995, and in 1996. Which of the following is true? a. Sales was lowest in 1996 b. Sales was highest in 1994 c. Sales was same in 1995 and 1996 d. Sales was highest in 1995 e. none 10: Safia is paid Tk. 400 a month on her regular job. During February and March, in addition to her regular job, she earns Tk. 3000 per month from a second job. Approximately what percentage of her annual income does Safia make in March? Assume she has no other income except the income mentioned above. a. 5 b. 6.5 c. 13 d. 14 e. None

TEST#06 01: Mr. Tareq purchased 12 mangoes for Tk. 10 and sold 10 mangoes for Tk. 12. what is his profit margin? a. 20% b. 25% c. 32% d. 36% e. 44% 02: Of the total profit, A, B, C, D, and E get 50%, 20%, 15%, 10%, and 5% respectively. A's profit is what percentage of that of B? a. 150% b. 30% c. 20% d. 50% e. None 03: 3 packets have 250gm, 350gm, and 400gm of rice including 2%, 4% and 1.5% of dust respectively. The 3 packets are broken and all the rice re-mixed together. What is the overall percentage of dust in the new mixture? a. 2 b. 2.5 c. 3 d. 3.5 e. 3.75 04: A hammer and a screwdriver currently have the same price. If the price of a hammer rises by 6% and the price of a screwdriver goes up by 4%, how much more will it cost to buy 4 hammers and 4 screwdrivers? a. 5% b. 10% c. 24% d. 40% e. None 05: Ali's speed is 10% higher than that of Rahim, and Karim's speed is 10% lower than Ali's speed. Which of the following statements is true? a. Rahim's speed = Karim's speed b. Karim's speed is the highest c. Rahim's speed is the lowest d. Ali's speed is the lowest e. none 06: If the sales tax on appliance priced at Tk. 300 is between 5% and 8%, then the cost (price plus sales tax) of the appliance is a. 310 b. 312 c. 314 d. 318 e. 325 07: If a stock average was 500 points at the beginning of the week, and 400 points at the end of the same week, by what percentage has it decreased during the week? a. 20 b. 22 c. 25 d. 27 e. 30 08: A 4 litre oil can costs Tk. 200. If the price of oil increases by a half percent, how much will two 4-litre cans cost? a. Tk. 600 b. Tk. 420 c. Tk. 402 d. Tk. 300 e. none 09: Two banks offered interest rates of 6% and 7% respectively on savings account. Mr. SMcxlvii deposited a total amount of Tk. 4000 in the banks and in one year his interest income was Tk. 250. Find the investment in the bank with 7% interest. a. 3000 b. 2000 c. 3500 d. 2500 e. none 10: The average of a, b, and c is 6, and a-b = 4, and ab = 21. What is the value of c? a. 6 b. 7 c. 8 d. 3 e. none

TEST#07 Part A: Choose the correct option: 01: Two trains running on the same route travel at the rate of 25 and 30 mph. if the first train start out an hour earlier, how long will it take the second train to catch up with it? a. 2hr b. 3hr c. 4hr d. 5hr e. none 02: Bimal sprinted 100 meters in 10.61 seconds. Find his velocity in kmph rounded to the nearest km. a. 36 b. 34 c. 33 d. 3 e. none 03: A plane traveling at 600 mph is heading for Chittagong Airport. At 3:58 pm it is 30 miles from the airport. At what time will it arrive at the airport? a. 3:59 pm b. 4:00 pm c. 4:01 pm d. 4:02 pm e. 4:03 pm 04: In binary system, the number '93' is written by: a. 100011 b 1110011 c. 1001001

d. 1011101

e. 1011110

05: The cost of two liters of oil and its container is tk. 100. if the cost of the container is tk. 23 less than the cost of one liter oil, what is the cost of one liter of oil? a. 39 b. 41 c. 43 d. 47 e. none

Part B: Put the answer: 06: A and B can do a work in 8 days, B and C can do the same work in 12 days , A, B, and C together can finish it in 6 days. A n C together will do it in ____?___ days? 07: X can do a work in the same time in which y and z together can do it. if x and y together can do it in 10 days and z alone can do it in 50 days, how many days will y require to do the work alone? 08: If n = [7^9] - 6, what is the units digit of n? 09: Three friends eat together. First and second friends have 12 and 8 pieces of breads respectively. Third friend gives tk. 3 in lieu of bread. How much amount will 1st and 2nd friend get for bread? 10: 3 partners share the profit in a business in the ratio 5:7:8. They had partnership for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?

TEST#08 001: A train took 6 minutes to travel between two stations that are four miles apart. The speed of the train in mph was: a. 36 b. 30 c. 40 d. 20 e. 45 002: A cycle costs Tk2500 when it its new. At the end of each year it is worth 4/5th of its beginning of that year value. What is the cycle worth in Tk when it is 3 years old? a. 1280 b. 1350 c. 1820 d. 2180 e. 1500 003: The simple interest (in Taka) on Tk1800 at 6.5% in 6 years is: a. 702 b. 390 c. 3900 d. 7020

e. 1080

004: The length of a rectangular floor is one and a half times its breadth. What is the perimeter of the floor (in meters) if its area is 216 sq meters? a. 40 b. 50 c. 60 d. 44 e. 66 005: The rate of interest is reduced from 6% to 4%. What would be the difference (in Taka) in the total amount of simple interest for Tk500 in 3 years? a. 20 b. 30 c. 40 d. 50 e. 60 006: The cost of the carriage and the horse is Tk1500 and Tk2000 respectively. If the cost of carriage increases by 5% and the cost of horse increases by 8% the total cost of the carriage and the horse in Taka is : a. 3725 b. 3735 c. 3825 d. 3835 e. 3845 007: If x+y = 9, y+z = 7 and z+x = 9, what is the average of x, y, and z ? a. 11/3 b. 13(1/3) c. 25/6 d. 11 e. none 008: One day at a school, one-twelfth of the students were absent and twenty percent of those present went on a field trip. If the number of students staying back in the school that day was 660, how many students are enrolled in that school? a. 900 b. 960 c. 1000 d. 1220 e. none 009: A salesman usually makes 25% profit on every radio he sells. During a sale, he reduces his profit margin to 20%, while his sales increase by 10%. What is the ratio of his new profit to his usual profit? a. 10 : 25 b. 11 : 15 c. 22 : 25 d. 20 : 25 e. none 10: A tailor had a number of shirt pieces to cut from some large pieces of fabric. He cut each large piece into 10 smaller pieces. He cut at the rate of 45 cuts per minute. How many large pieces would be cut in 24 minutes? a. 32 b. 54 c. 108 d. 120 e. none

TEST#09 01) A club has 8 male and 8 female members; the club is choosing a committee of six members. The committee must have 3 male and 3 female members. In how many ways can the committees be chosen? a. 8C3 × 8C5 b. 8P3 × 8C3 c. 8C3 + 8C3 d. 2 × 8P3 e. none 02) If Lisa makes a box every five minutes and Nisa takes two minutes more to make a box, what will be the ratio of the number of boxes produced by Lisa to the number of boxes produced by Nisa if they work for 365 days continuously? a. 5 to 2 b. 2 to 5 c. 7 to 5 d. 3 to 5 e. none 03) How much interest will Tk2000 earn at an annual interest rate of 8% in one year if the interest is compounded semi-annually? a. 160.00 b. 163.20 c. 249.73 d. 332.80 e. none 04) A bought five hundred shares of company P at Tk600 and two months later another two hundred and fifty shares of the same company at Tk560. At which price should he purchase additional two hundred and fifty shares in order to have an average price of Tk580 per share? a. 600 b. 580 c. 560 d. 570 e. none 05) A wholesaler sells goods to a retailer at a profit of twenty percent. The retailer sells the goods to the customers who pay eighty percent more than the cost of the wholesaler. What is the retailer's profit? a. 30% b. 40% c. 50% d. 60% e. none 06) A certain sum of money consists of thirty coins, some of which are ten paisa coins, and the rest are five paisa coins. if the total value of the coins is Tk2, what is the ratio of the number of ten paisa coins to the number of five paisa coins ? a. 1 : 2 b. 1 : 3 c. 3 : 1 d. 2 : 1 e. none 07) A rectangular carpet measuring 16 meters by 12 meters, excluding the border, has a border of width 2 meters on each of its sides. What is the area of the border? a. 96 sq.m b. 112 sq.m c. 124 sq.m d. 128 sq.m e. 154 sq.m 08) A man has to go 10 km to catch a bus. He walks part of the way at 7 kmph and runs the rest of the way at 12 kmph. If he takes one hour and fifteen minutes to complete his journey, find how far he ran. a. 10 km b. 1 km c. 7 km d. 3 km e. none 09) What is the greatest number of apples not exceeding 460 that can be distributed among three persons in the proportions 5 : 6 : 7 ? a. 440 b. 432 c. 420 d. 450 e. none 10) In a class of 120 students, sixty percent can speak French and the rest can speak only English. If twenty-five percent of those in the class who can speak French can also speak English, how many of the students in the class can speak only French? a. 54 b. 60 c. 66 d. 84 e. none

TEST#10 01: If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 45. By how much do the two digits differ? a. 3 b. 4 c. 5 d. 6 e. 7 02: If n = 4p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n? a. 2 b. 3 c. 4 d. 6 e. 8 03: If (x-1)² = 400, which of the following could be the value of x-5? a. 15 b. 14 c. -24 d. -25 e. -26 04: If n is a prime factor of 7150, and n < 100. How many different values can n have? a. 1 b. 2 c. 3 d. 4 e. 5. 05: At present Finn is 14 years younger than Anderson. In 10 years, Anderson will be twice as old as Finn. In five years, how old will Anderson be? a. 9 b. 19 c. 21 d. 23 e. 33 06: A positive number x is multiplied by two and then the product divided by 3. the positive square root of the result is equal to x. what is the value of x? a. 9/4 b. 3/2 c. 4/3 d. 2/3 e. 1/2 07: If xφy = √(xy), then (5φ45)φ60 = ? a. 30 b. 60 c. 90

d. 30√15

e. 60√15

08: If aδb = (a-b)/(a+b), for all numbers a and b, such that a is not equal to -b. If a is not equal to -c, and aδc = 0, then, c = ? a. -a b. -1/a c. 0 d. 1/a e. a 09: if y/x < 1 where both x and y are positive integers, which of the following must be greater than 1? a. √(y/x) b. y/x² c. y/2x d. x/y² e. x/y 10: if (0.0015×10x) ÷ (0.03×10y) = 5×107, then x-y = ? a. 9 b. 8 c. 7

d. 6

e. 5

Solution to the Tests

Solution TO TEST#01 01: In a triangular area the seats are arranged in rows so that the 1st, 2nd, 3rd, 4th etc. rows contain 1, 2, 3, 4 etc. seats and so on. 70 students take seats starting from the 1st row and filling up the rows in increasing order. How many rows are completely filled? a. 9 b. 10 c. 11 d. 12 e. None Solution: If the number of rows is N, then there will be N(N+1)/2 students in the arrangement. Here, N(N+1)/2 ≤ 70; or, N(N+1) ≤ 140. The product of two consecutive numbers is less or equal to 140. We know, √140 ≈ 12. If the greater number is 12, then the smaller number is 11, and their product = 11×12 = 132. So, N = 11. Ans: c. 11. 02: 25 consecutive integers are given. If the sum of the 1st 3 integers is 24, what is the sum of the last 3? a. 27 b. 28 c. 29 d. 30 e. None Solution: Suppose, the first number is P. So, P + P+1 + P+2 = 24; or, P = 7. Sum of the last three numbers = Sum of the 23rd, 24th and 25th number = (P+22) + (P+23) + (P+24) = 3P+69 = 3×7 + 69 = 90 Ans: e. None 03: The average of all whole numbers between 1 and 100 that end in 3 = a. 44 b. 45 c. 46 d. 47 e. None Solution: The whole numbers between 1 and 100 that end in 3 are: 3, 13, 23, 33, .... 93. They are 10 in numbers and the difference between any two consecutive numbers is constant (10). So, average = (1st term + Last term)/2 = (3+93)/2 = 48. Ans: e. None 04: The average weight of three men is 53 kg. None of them weights less than 51 kg. What is the maximum possible weight (in kg) of a person in that group? a. 53 b. 55 c. 57 d. 59 e. None Solution: Minimum weight of two of them = 51×2 = 102. Maximum possible weight of a person in that group = 53×3 - 102 = 57. Ans: c. 57

05: (1/√2)7 times (1/√2)5 =? a. 1/8 b. 1/16

c. 1/32

d. 1/64

e. 1/128

Solution: 1/(√2)7 × 1/(√2)5 = 1/(√2)12 = 1/{(√2)²}6 = 1/26 = 1/64. Ans: d. 1/64 06: Coffee A normally costs Tk. 100 per pound. It is mixed with Coffee B, which normally costs Tk. 70 per pound, to form a mixture which costs Tk. 88 per pound. If there are 10 pounds of the mix, how many pounds of Coffee A are used in the mix? a. 4 b. 5 c. 6 d. 7 e. None Solution: Suppose, P pounds of coffee A is mixed with (10-P) pounds of coffee B to make P+(10-P) = 10 pounds of coffee mixture. According to the question: 100P + 70(10-P) = 10×88 100P + 700 - 70P = 880 30P = 180 P = 6. Ans: c. 6 07: In a survey in the City of Gotham, it was found that 70% of the people surveyed watched the news on TVs, 35% read newspapers, and 25% read newspapers and watched the news on TVs. What percentage of the total people surveyed neither watched the news on TVs nor read newspapers? a. 30% b. 0% c. 20% d. 15% e. 5% Solution: Watched TV only = 70% - 25% = 45% Read Newspapers only = 35-25 = 10% Took both of them = 25% So, the percentage of total people watching TV or reading newspaper or both = 45+10+25 = 80. The percentage of people surveyed neither watched TV, nor read books = (100 - 80)% = 20%. Ans: c. 20% 08: 7 kg of mangoes cost as much as 10 kg of apples and 1 kg of oranges. 7 kg of oranges cost as much as 1 kg of mangoes and 2 kg of apples. How many kg of apples can be purchased by the amount of money required to purchase 12 kg of mangoes? a. 8 b. 14 c. 16 d. 18 e. 24 Solution: Suppose, Cost of 1kg of mango is Tk A, 1 kg of apple is Tk B, and 1 kg of orange is Tk C.

According to the question: 7A = 10B + C ---------- (i) 7C = 1A + 2B ---------- (ii) Equation (i) × 7 = > 49A = 70B + 7C -------------- (iii) Equation (ii) => 1A = -2B + 7C ------------- (iv) (iii) - (iv) => 48A = 72B; or 12A = 18B. So, 18 kg of apples can be purchased by the amount of money required to purchase 12 kg of mangoes. Ans: d. 18 09: A jar contains 10 pencils. Some of them are sharpened, and some are not. Each of the following could be the ratio of sharpened to unsharpened pencils except...... a. 9:1 b. 5:1 c. 4:1 d. 3:2 e. 1:1 Solution: The sum of the ratio between these two types of pencils will be a factor of 10 (total number of pencil). Here, a. 9+1 = 10; b. 5+1 = 6; c. 4+1 = 5; d. 3+2 = 5; e. 1+1 = 2. All the ratios except b. are the possible ratios. Ans: b. 5:1 10: The angles of a triangle are in the proportion of 1:2:3 and the length of the smallest side is 1 meter. What is the length of the longest side of the triangle? a. 4 b. 5 c. 2 d. 3 e. None. Solution: rule: if the angles of a triangle are in the ratio 1 : 2 : 3, then the ratio of the sides of the triangle is 1 : √3 : 2. Here, length of the smallest side is 1 meter. So, the length of the longest side is 2 meters. Ans: c. 2

Solution TO TEST#02 01: Smallest possible integer having only three different odd factors. a. 75 b. 90 c. 105 d. 120 e. none Solution: The smallest possible integer having only three different odd factors is the product of smallest three positive odd integers. So, the integer is = 1×3×5 = 15. Ans: e. none 02: The number of integers between 100 and 200 that are divisible by 3, but neither by 5 or 7 is: a. 23 b. 22 c. 21 d. 20 e. none Solution: Range of the integers between p and q that are divisible by n = (smallest multiple of n that is greater or equal to p, greatest multiple of n that is less or equal to q). Range of the integers between 100 & 200 that are divisible by 3 = (102,198). Range of the integers between 100 & 200 that are divisible by 3&5 i.e.: 15 = (105, 195) Range of the integers between 100 & 200 that are divisible by 3&7 i.e.: 21 = (105, 189) Range of the integers between 100 & 200 that are divisible by 3,5&7 i.e.: 105 = (105,105) Required number of integers = {(198-102)/3 + 1} – {(195-105)/15 + 1} – {(189-105)/21 + 1} + {(105-105)/105 + 1} = 33 – 7 – 5 + 1 = 22 Ans: b. 22 03: The smallest possible number which -when divided by 3, 6, or 9 leaves a remainder 2, but perfectly divisible by 8: a. 112 b. 152 c. 176 d. 192 e. 200 Solution: The required number is (i) a multiple of the LCM of 3, 6, and 9 plus 2, and (ii) a multiple of 8. LCM of 3, 6, and 9 = 18. in the options, all the numbers are divisible by 8. Let's evaluate them for the first condition. a. (112-2) ÷ 18 = 6.something b. (152-2) ÷ 18 = 8.something c. (176-2) ÷ 18 = 9. something d. (192-2) ÷ 18 = 10.something e. (200-2) ÷ 18 = 11. Ans: e. 200

04: In the equation x = y/√z. Where x, y, and z each are non-zero positive integer. Is y/x an integer? a. Yes b. No c. Yes or No d. Never e. None Solution: Suppose, y = q√z, where q is an integer. So, x = q√z/√z = q. Therefore, y/z = q√z/q = √z. √z is an integer, if it is a perfect square number. We do not have any information about that. So, the answer can be Yes or No. Ans: c. Yes or No 05: If x is between 0 and 1, which of the following increases as x increases? i. 1 - x2 ii. x-1 iii. 1/x2 a. i and ii

b. ii and iii

c. i and iii

d. ii only

e. i only

Solution: Suppose, original value of x = 0.1, and increased value of x = 0.2. Test i: original value of 1-x² = 1 - 0.1² = 0.99, changed value = 1-0.2² = 0.96. [reduced] Test ii: original value of x-1 = 0.1 - 1 = -0.9, changed value = 0.2 - 1 = -0.8. [increased] Test iii: original value of 1/x² = 1/0.1² = 100, changed value = 1/0.2² = 25. [reduced] Ans: e. i only 06: Four consecutive even integers are such that the sum of four times the first number and twice the last number is equal to sum of twice the second number and thrice the third number. Find the first number in the series. a. 4 b. 6 c. 8 d. 12 e. none Solution: Suppose, the numbers are p, p+2, p+4, and p+6 According to the question: 4p+2(p+6) = 2(p+2)+3(p+4); => 4p+2p+12 = 2p+4+3p+12; => p = 4. Ans: a.4 07: Which of the followings cannot be expressed as the sum of the squares of two integers? a. 13 b. 17 c. 21 d. 29 e. 34 Solution: a. 13 = 2²+3² b. 17 = 1²+4² c. 21 = ? d. 29 = 2²+5² e. 34 = 3²+5² Ans: c. 21

08: Arif makes his first cup of coffee at 6am and then makes one cup of coffee every four hours after that. Asif makes his first cup of coffee at 8am and then makes one cup every 3 hours after that. At what time will they both be making coffee? a. 9am b. 11am c. 12noon d. 1pm e. 2pm Solution: Arif will be making coffee at : 6am - 10am - 2pm - 6pm Asif will be making coffee at : 8am - 11am - 2pm - 5pm From the above list we get, at 2pm, both of them will be making coffee. Ans: e. 2pm 09: What must be subtracted from 3y/x to get x/y? a. {2y^2 + (y-x)(y+x)}/xy b. (x^2 - 3y^2)/xy c. (3y - x)/xy d. 2y/x e. none Solution: Suppose, P must be subtracted from 3y/x to get x/y So, 3y/x - P= x/y; or, P = 3y/x - x/y = (3y²-x²)/xy = (2y²+y²-x²)/xy = {2y²+(y+x)(y-z)}/xy. Ans: a. {2y²+(y+x)(y-z)}/xy 10: One half of the female students enjoy watching movies and one third of the male students do not like to watch movies. What fractional part of the total students enjoys watching movies? a. 5/12 b. 2/5 c. 3/4 d. 1/6 e. cannot be determined. Solution: Total female student = P, Total male student = R Enjoy watching movie = P/2 + 2R/3 = (3P+4R)/6 Required fraction = (3P+4R)/6(P+R). The value of the fraction depends on the value of P and R. Without having any information regarding their values, we cannot determine the required fraction. Ans: e. cannot be determined.

Solution TO TEST#03 01: After 30 years, Zaman will be four times as old as he is now. Find out his present age: a. 10 b. 11 c. 7.5 d. 30 e. none Solution: Suppose, Zaman‟s present age = p years. According to the question: 4p = p+30 or, p = 10 Ans: a. 10 02: Six years from now Sumi's age will be the square of her age six years ago. What is Sumi's age? a. 8 b. 10 c. 12 d. 15 e. none Solution: Suppose, Sumi‟s present age = p years. According to the question: (p-6)² = p+6 or, p² - 12p + 36 – p – 6 = 0 or, p² - 13p + 30 = 0 or, (p-10)(p-3) = 0 or, p = 10 or 3. if p = 3, p-6 = -3 which is not acceptable as the age of someone cannot be a negative value. So, p = 10 Ans: b. 10 03: Y is four times as old as X. After 6 years, the sum of half of X's age and a fourth of Y's age will be the same as three times the present age of X. How old will X be after 6 years? a. 3 b. 9 c. 10 d. 12 e. 15 Solution: Suppose, the current age of X is = p years. So, the current age of Y is = 4p. According to the question: 3p = (p+6)/2 + (4p+6)/4 or, 12p = 2p+12+4p+6 or, 6p = 18 or, p = 3 or, p+6 = 3+6 = 9 Ans: b. 9

04: Eight years ago Mr Karim was 1/3 the age he will be after 10 years. What is his age now? a. 16 b. 17 c. 18 d. 19 e. 20 Solution: Suppose, his present age = p years. According to the question: 3(p-8) = p+10 or, 2p = 34 or, p = 17 Ans: b. 17 05: If a>b and ab |b|. the same rule is applicable for b²-a² (option a). Therefore, none of the given options is a “must true”. Ans: e. none of these 06: x, y, and Z are consecutive integers. If 0 k = (18×100×100)/(30×15) = 400. Ans: e. 400. 08: If Tk. 1000 is invested in an account that pays 10% p.a. compounded monthly, how much would be the nearest ending balance at the end of 10th year? a. 1104 b. 2594 c. 2840 d. 2208 e. 2708 Solution: Ending balance = 1000×(1 + 0.1/12)10×12 ≈ 2708. (using scientific calculator) Ans: e. 2708.

09: What is the width of a rectangular field whose length is 70 meters more than its width and the perimeter is 500 meters? a. 60 b. 70 c. 80 d. 90 e. 100 Solution: Suppose the width of the field is k meters. So, its length is (k+70) meters. According to the question: 2(k+70+k) = 500; => 2k+70 = 250; => k = 90. Ans: d. 90.

10: Due to reduction in the bus fare by 15%, the number of passengers on a certain route increased by 40%. What will be the percentage of increase in revenue? a. 17 b. 19 c. 20 d. 25 e. 21 Solution: Percentage of increase = -15% + 40% + (-15%×40%) = -15% + 40% - 6% = 19%. Ans: b. 19.

Solution TO TEST#05 01: If xyz < 0, and z < 0, then which of the following must always be true? a. xy > 0 b. xy < 0 c. xy > z d. xy < z e. none of these Solution: z is negative. Also the product xyz is negative. So, xy is positive. Hence, xy is greater than z. Ans: c. xy > z. 02: If a 1, which of the following decreases as x decreases? i. x + x^2 ii. 2x^2 - x iii. 1/[x^2 + 1] a. only i

b. both i & ii

c. only ii

d. only iii

e. none

Solution: i. x+x² = x(1+x) will decrease if x decreases. ii. 2x²-x = x(2x-1) will decrease if x decreases. iii. 1/(x²+1) = (x²+1)-1 will increase if x decreases. Ans: b. both i & ii. 04: What is the ratio of the circumference of a circle to its radius? a. π b. 2π c. π/2 d. 2/π

e. none

Solution: If the radius of a circle is r, then its circumference is 2πr. So, ratio = 2πr : r = 2π : 1 = 2π. Ans: b. 2π. 05: If a > b, and a > c, which of the following must be greater than 0? a. [b-c]/[b+c] b. [c-b]/[a-b] c. [b-c]/[b-a] d. [b-a]/[c-a] e. none Solution: We don‟t know the relationship between b and c. So, we have no comment for options a, b, and c. In case of option d both of the denominator and the numerator are positive. Hence, the value of option d is greater than zero. Ans: d. [b-a]/[c-a].

06: If a > 0, b < 0, c > 1, and d < 1, which of the following must be true? a. ab > cd b. ab < cd c. ac > bd d. ac < db e. none Solution: a. is false, if a = 1, b = -10, c = 2, and d = 0. (also for many other values of a,b,c, &d). b. is false, if a = 1, b = -1, c = 100, and d = -1. (also for many other values of a,b,c, &d). c. is false, if a = 1, b = -100, c = 2, and d = -100. (also for many other values of a,b,c, &d). d. is false, if a = 100, b = -10, c = 100, and d = 0. (also for many other values of a,b,c, &d). e. is true as the above four options are false. Ans: e. none. 07: 10% of r is equal to 20% of s, and 20% of s is equal to 30% of t. if 100% of r is equal to x% of t, what is the value of x? a. 300 b. 40 c. 30 d. 20 e. none Solution: 20s = 30t; => 10r = 30t; => r = 3t. According to the question: 100/100 of r = x/100 of t; => r = xt/100; => 3t = xt/100; => x = 300. Ans: a. 300. 08: written as a percent, 5 = ? a. 5% b. 50%

c. 500%

d. 0.05

e. 0.5

Solution: suppose, 5 = k%; => 5 = k/100, k = 500; => k% = 500% So, 5, written as a percent will be = 500%. Ans: c. 500% 09: Sales of a company in 1994 was 5% higher than that of the previous year. It grew 4% in 1995, and in 1996. Which of the following is true? a. Sales was lowest in 1996 b. Sales was highest in 1994 c. Sales was same in 1995 and 1996 d. Sales was highest in 1995 e. none Solution: Sale comparison of different years: 1993 < 1994 < 1995 < 1996 a. is wrong, sales was lowest in 1993 b. is wrong, sales was highest in 1996 c. is wrong, sales of 1995 was less than 1996 d. is wrong, sales of 1996 was highest e. says the truth about the above four options Ans: e. none

10: Safia is paid Tk. 400 a month on her regular job. During February and March, in addition to her regular job, she earns Tk. 3000 per month from a second job. Approximately what percentage of her annual income does Safia make in March? Assume she has no other income except the income mentioned above. a. 5 b. 6.5 c. 13 d. 14 e. None Solution: Total annual income = Tk. {(400×12) + (3000×2)} = Tk. 10800 Percentage of annual income in March = (400+3000)/10800 = 31.48%. Ans: e. None

Solution TO TEST#06 01: Mr. Tareq purchased 12 mangoes for Tk. 10 and sold 10 mangoes for Tk. 12. what is his profit margin? a. 20% b. 25% c. 32% d. 36% e. 44% Solution: Selling price of 12 mangoes = 12×12/10 = Tk. 14.40. Profit margin = (14.40 - 10)/10 = 44% Ans: e. 44% 02: Of the total profit, A, B, C, D, and E get 50%, 20%, 15%, 10%, and 5% respectively. A's profit is what percentage of that of B? a. 150% b. 30% c. 20% d. 50% e. None Solution: A‟s profit as a percentage of B‟s profit = (50/20)×100% = 250% Ans: e. None 03: 3 packets have 250gm, 350gm, and 400gm of rice including 2%, 4% and 1.5% of dust respectively. The 3 packets are broken and all the rice re-mixed together. What is the overall percentage of dust in the new mixture? a. 2 b. 2.5 c. 3 d. 3.5 e. 3.75 Solution: Total dust in the new mixture = 250×2% + 350×4% + 400×1.5% = 5+14+6 = 25gm. Total quantity of rice in the new mixture = 250+350+400 = 1000gm. Percentage of dust in the new mixture = 25/1000 = 2.5%. Ans: b. 2.5 04: A hammer and a screwdriver currently have the same price. If the price of a hammer rises by 6% and the price of a screwdriver goes up by 4%, how much more will it cost to buy 4 hammers and 4 screwdrivers? a. 5% b. 10% c. 24% d. 40% e. None Solution: Current price of a hammer = Current price of a screwdriver = k taka. So, Price of 4 hammers and 4 screw drivers = 4k+4k = 8k taka. After the increase, total price of 4 hammers and 4 screwdrivers = 4k×1.06 + 4k×1.04 = 4k×2.1 = 8.4k taka. Required percentage = (8.4k - 8k)/8k = 5%. Ans: a. 5%

05: Ali's speed is 10% higher than that of Rahim, and Karim's speed is 10% lower than Ali's speed. Which of the following statements is true? a. Rahim's speed = Karim's speed b. Karim's speed is the highest c. Rahim's speed is the lowest d. Ali's speed is the lowest e. none Solution: If Rahim‟s speed = 100k mps, then Ali‟s speed = 110k mps, and Karim‟s speed = .9×110k = 99k mps. Ans: e. none 06: If the sales tax on appliance priced at Tk. 300 is between 5% and 8%, then the cost (price plus sales tax) of the appliance is a. 310 b. 312 c. 314 d. 318 e. 325 Solution: Maximum tax inclusive price = 300×1.08 = 324 Minimum tax inclusive price = 300×1.05 = 315 Only Tk. 318 falls within this price range. Ans: d. 318 07: If a stock average was 500 points at the beginning of the week, and 400 points at the end of the same week, by what percentage has it decreased during the week? a. 20 b. 22 c. 25 d. 27 e. 30 Solution: Percentage of decrease = (500-400)/500 = 20%. Ans: a. 20% 08: A 4 litre oil can costs Tk. 200. If the price of oil increases by a half percent, how much will two 4-litre cans cost? a. Tk. 600 b. Tk. 420 c. Tk. 402 d. Tk. 300 e. none Solution: Cost of two 4-litre can = 2×200×1.005 = 402. Ans: c. Tk. 402. 09: Two banks offered interest rates of 6% and 7% respectively on savings account. Mr. SMcxlvii deposited a total amount of Tk. 4000 in the banks and in one year his interest income was Tk. 250. Find the investment in the bank with 7% interest. a. 3000 b. 2000 c. 3500 d. 2500 e. none Solution: Suppose, the investment in the bank with 7% rate of interest is Tk. k According to the question: 0.07k + 0.06(4000-k) = 250; => 0.01k = 10; => k = 1000. Ans: e. none

10: The average of a, b, and c is 6, and a-b = 4, and ab = 21. What is the value of c? a. 6 b. 7 c. 8 d. 3 e. none Solution: Quick Attack => => ab = 21, possible value set of a & b are (1, 21) and (3, 7). If a = 7 and b = 4, it will satisfy a-b = 4. Given, (a+b+c)/3 = 6; => (7+3+c) = 18; => c = 8. Ans: c. 8

Solution TO TEST#07 Part A: Choose the correct option: 01: Two trains running on the same route travel at the rate of 25 and 30 mph. if the first train start out an hour earlier, how long will it take the second train to catch up with it? a. 2hr b. 3hr c. 4hr d. 5hr e. none Solution: When the second train starts, the first train is 25 miles away. Relative speed of the second train over the first one = (30-25) mph = 5 mph. Required time to catch up = 25/5 = 5 hours. Ans: d. 5hr 02: Bimal sprinted 100 meters in 10.61 seconds. Find his velocity in kmph rounded to the nearest km. a. 36 b. 34 c. 33 d. 3 e. none Solution: Goes in 10.61 seconds = 100 meters Goes in 3600 seconds = 100×3600/10.61 = 33930 meters = 33.9 meters ≈ 34 meters. Ans: b. 34 meters 03: A plane traveling at 600 mph is heading for Chittagong Airport. At 3:58 pm it is 30 miles from the airport. At what time will it arrive at the airport? a. 3:59 pm b. 4:00 pm c. 4:01 pm d. 4:02 pm e. 4:03 pm Solution: Time to travel last 30 miles = 30/600 = 1/20 hours = 3 minutes. So, time to arrive = 3:58pm + 3 minutes = 4:01pm. Ans: c. 4:01pm 04: In binary system, the number '93' is written by: a. 100011 b 1110011 c. 1001001

d. 1011101

e. 1011110

Solution: … value of the above = Start from the left, mark those cells with „1‟ sum of who‟s above cells is 93. Fill up the remaining cells with „0‟

26 64

25 32

24 16

23 8

22 4

21 2

20 1

1

0

1

1

1

0

1

Binary of 93 = 1011101 Ans: d. 1011101

←

Alternative method: 93 = (2 × 46) + 1 46 = (2 × 23) + 0 23 = (2 × 11) + 1 11 = (2 × 5) + 1 5 = (2 × 2) + 1 2 = (2 × 1) + 0 1 = (2 × 0) + 1 Start from the bottom to the top, write the remainders: 1011101. Ans: d. 1011101 05: The cost of two liters of oil and its container is tk. 100. if the cost of the container is tk. 23 less than the cost of one liter oil, what is the cost of one liter of oil? a. 39 b. 41 c. 43 d. 47 e. none Solution: Suppose, the cost of one liter oil = tk. k. So, 2k + (k-23) = 100; => 3k = 123; => k = 41. Ans: b. 41

Part B: Put the answer: 06: A and B can do a work in 8 days, B and C can do the same work in 12 days , A, B, and C together can finish it in 6 days. A n C together will do it in ____?___ days? Solution: A+B+C s‟ work of 1 day = 1/6 ------------- (i) A+B s‟ work of 1 day = 1/8 --------------- (ii) B+C s‟ work of 1 day = 1/12 ---------------- (iii) (ii)+(iii) => A+2B+C = 1/8 + 1/12 = 5/24 ----------------- (iv) (iv)-(i) => B = 5/24 - 1/6 = 1/24 ------------------- (v) So, (i) - (v) => A+C = 1/6 - 1/24 = 3/24 = 1/8 Therefore, A and C can do in 1 day = 1/8 of the work. So, A and C can complete the work in 1/(1/8) = 8 days. Ans: 8 days. 07: X can do a work in the same time in which y and z together can do it. if x and y together can do it in 10 days and z alone can do it in 50 days, how many days will y require to do the work alone? Solution: z‟s work of 1 day = 1/50 work

x+y s‟ work of 1 day = 1/10 work x+y+z s‟ work of 1 day = 1/50 + 1/10 = 6/50 = 3/25 work. So, x can do the in 1 day = ½ × 3/25 = 3/50 work. Therefore, y can do in 1 day = 1/10 - 3/50 = 2/50 = 1/25 work. And y can do the complete work in 1/(1/25) = 25 days. Ans: 25 days. 08: If n = [79] - 6, what is the units digit of n? Solution: Consider the last digits only: 79= 7×7×7×7×7×7×7×7×7 = (7×7)×(7×7)×(7×7)×(7×7)×7 = 9×9×9×9×7 = (9×9)×(9×9)×7 = 1×1×7 = 7. So, unit digit of (79 - 6) = unit digit of 79 - 6 = 7-6 = 1. Ans: 1 09: Three friends eat together. First and second friends have 12 and 8 pieces of breads respectively. Third friend gives tk. 3 in lieu of bread. How much amount will 1st and 2nd friend get for bread? Solution: Total pieces of bread = 12+8 = 20. Number of pieces of bread ate by each of the friends = 20/3 = 6.67. First friend sold = (12 - 20/3) = 16/3 breads Second friend sold = (8 - 20/3) = 4/3 breads Total price of breads = Tk. 3. So, first friend will get = 3 × (16/3)/(20/3) = Tk. 2.40 and the second friend will get = Tk. (3 - 2.40) = Tk. 0.60 Ans: Tk. 2.40 and Tk. 0.60. 10: 3 partners share the profit in a business in the ratio 5:7:8. They had partnership for 14 months, 8 months and 7 months respectively. What was the ratio of their investments? Solution: Suppose, the amount of their respective investments is = a, b, and c. Ratio of profit = (duration of investment × amount of investment)1 : (duration of investment × amount of investment)2 : (duration of investment × amount of investment)3 So, 5 : 7 : 8 = (14a) : (8b) : (7c) From the above, we get 5/7 = 14a/8b; => a : b = 40 : 98 = 20 : 49 Again, 7/8 = 8b/7c; => b : c = 49 : 64 So, a : b : c = 20 : 49 : 64. Ans: 20 : 49 : 64

Solution TO TEST#08 001: A train took 6 minutes to travel between two stations that are four miles apart. The speed of the train in mph was: a. 36 b. 30 c. 40 d. 20 e. 45 Solution: 1 hour = 60 minutes. The train goes in 6 minutes = 4 miles So, the train can go in 60 minutes = 4×60/6 = 40 miles. Ans: c. 40 002: A cycle costs Tk2500 when it its new. At the end of each year it is worth 4/5th of its beginning of that year value. What is the cycle worth in Tk when it is 3 years old? a. 1280 b. 1350 c. 1820 d. 2180 e. 1500 Solution: Worth of the cycle = 2500 × 4/5 × 4/5 × 4/5 = 1280 Ans: a. 1280 003: The simple interest (in Taka) on Tk1800 at 6.5% in 6 years is: a. 702 b. 390 c. 3900 d. 7020

e. 1080

Solution: Simple interest = 1800 × 6.5/100 × 6 = 702 Ans: a. 702 004: The length of a rectangular floor is one and a half times its breadth. What is the perimeter of the floor (in meters) if its area is 216 sq meters? a. 40 b. 50 c. 60 d. 44 e. 66 Solution: Suppose, the breadth of the floor is p meters. So, the length of the floor is 1.5p = 3p/2. Therefore, its perimeter = 2(3p/2 + p) = 3p+2p = 5p. And, its area = 3p/2 × p = 3p²/2. According to the question: 3p²/2 = 216 or, p² = 144 or, p = 12 So, the perimeter = 5×12 = 60. Ans: c. 60

005: The rate of interest is reduced from 6% to 4%. What would be the difference (in Taka) in the total amount of simple interest for Tk500 in 3 years? a. 20 b. 30 c. 40 d. 50 e. 60 Solution: Required difference = (500×0.06×3) - (500×0.04×3) = 500×3×0.02 = 30 Ans: b. 30 006: The cost of the carriage and the horse is Tk1500 and Tk2000 respectively. If the cost of carriage increases by 5% and the cost of horse increases by 8% the total cost of the carriage and the horse in Taka is : a. 3725 b. 3735 c. 3825 d. 3835 e. 3845 Solution: Total cost = 1500×(1+0.05) + 2000×(1+0.08) = 3735 Ans: b. 3735 007: If x+y = 9, y+z = 7 and z+x = 9, what is the average of x, y, and z ? a. 11/3 b. 13(1/3) c. 25/6 d. 11 e. none Solution: Here, x+y + y+z + z+x = 9+7+9 or, 2(x+y+z) = 25 or, (x+y+z) = 25/2 i.e: the sum of x, y, and z is 25/2. Therefore, the average of x, y, and z =(25/2)/3 = 25/6. Ans: c. 25/6 008: One day at a school, one-twelfth of the students were absent and twenty percent of those present went on a field trip. If the number of students staying back in the school that day was 660, how many students are enrolled in that school? a. 900 b. 960 c. 1000 d. 1220 e. none Solution: 20% of the students present went on a field trip. So, 80% of the students present stayed back. Therefore, 80% of those present = 660 100% of those present = 660/0.8 = 825. Again, (1 - 1/12)th of the students = 825 11/12th of the students = 825 So, total number of students = 825×12/11 = 900. Ans: a. 900

009: A salesman usually makes 25% profit on every radio he sells. During a sale, he reduces his profit margin to 20%, while his sales increase by 10%. What is the ratio of his new profit to his usual profit? a. 10 : 25 b. 11 : 15 c. 22 : 25 d. 20 : 25 e. none Solution: Suppose, the cost of one unit of radio was Tk. 100p, and the number of units the seller usually sold was 100q units. So, his usual profit was = (100p×25%)×100q = 2500pq. If the change takes place, The amount of profit from each unit of radio sold = 100p×20% = 20p; and the number of units sold = 100q + 100q×10% = 110q. So, total profit now = 20p × 110q = 2200pq. Required ratio = 2200pq : 2500pq = 22 : 25 Ans: c. 22 : 25 10: A tailor had a number of shirt pieces to cut from some large pieces of fabric. He cut each large piece into 10 smaller pieces. He cut at the rate of 45 cuts per minute. How many large pieces would be cut in 24 minutes? a. 32 b. 54 c. 108 d. 120 e. none Solution: To cut 1 large piece into 10 smaller pieces, he needs to make 9 cuts. At 45 cuts per minute rate, he can make in 24 minutes = 24×45 cuts. Now, 9 cuts are required for 1 large piece. 24×45 cuts are required for 24×45/9 = 120 large pieces. Ans: d. 120

Solution TO TEST#09 01) A club has 8 male and 8 female members; the club is choosing a committee of six members. The committee must have 3 male and 3 female members. In how many ways can the committees be chosen? a. 8C3 × 8C5 b. 8P3 × 8C3 c. 8C3 + 8C3 d. 2 × 8P3 e. none Solution: 3 male members can be chosen from 8 male available in 8C3 ways. 3 female members can be chosen from 8 female available in 8C3 ways. Required number of ways = 8C3×8C3 = 8C3×8C5. 8C3 = 8!/3!(8-3)! = 8!/3!5! = 8!/5!3! = 8!/5!(8-5)! = 8C5. Ans: a. 8C3×8C5 02) If Lisa makes a box every five minutes and Nisa takes two minutes more to make a box, what will be the ratio of the number of boxes produced by Lisa to the number of boxes produced by Nisa if they work for 365 days continuously? a. 5 to 2 b. 2 to 5 c. 7 to 5 d. 3 to 5 e. none Solution: Lisa can make in 365 days = 365×24×60/5 boxes. Nisa can make in 365 days = 365×24×60/7 boxes. Required ratio = (365×24×60)/5 : (365×24×60)/7 = 7 : 5. Ans: c. 7 to 5 03) How much interest will Tk2000 earn at an annual interest rate of 8% in one year if the interest is compounded semi-annually? a. 160.00 b. 163.20 c. 249.73 d. 332.80 e. none Solution: Interest to be earned = Tk2000 × {(1+0.08/2)1×2 - 1} = Tk163.20 Ans: b. 163.20 04) A bought five hundred shares of company P at Tk600 and two months later another two hundred and fifty shares of the same company at Tk560. At which price should he purchase additional two hundred and fifty shares in order to have an average price of Tk580 per share? a. 600 b. 580 c. 560 d. 570 e. none Solution: Suppose, he should purchase 250 additional shares at Tk P per share So, (500×600 + 250×560 + 250P)/(500+250+250) = 580 or, (300000 + 140000 + 250P) = 580000

or, 250P + 440000 = 580000 or, P = 560 Ans: c. 560 05) A wholesaler sells goods to a retailer at a profit of twenty percent. The retailer sells the goods to the customers who pay eighty percent more than the cost of the wholesaler. What is the retailer's profit? a. 30% b. 40% c. 50% d. 60% e. none Solution: Suppose, the cost to the wholesaler = Tk P So, the cost to the retailer = Tk 1.2P So, the cost to the customer = Tk 1.8P Retailer's profit = (1.8P-1.2P)/1.2P = 0.6P/1.2P = 50% Ans: c. 50% 06) A certain sum of money consists of thirty coins, some of which are ten paisa coins, and the rest are five paisa coins. if the total value of the coins is Tk2, what is the ratio of the number of ten paisa coins to the number of five paisa coins ? a. 1 : 2 b. 1 : 3 c. 3 : 1 d. 2 : 1 e. none Solution: Total value = Tk2 = Ps200. Suppose, the number of ten paisa coins is P. According to the question: 10P + 5(30-P) = 200 10P + 150 - 5P = 200 P = 10 So, the number of five paisa coins = 30-10 = 20. Required ratio = 10 : 20 = 1 : 2. Ans: a. 1 : 2 07) A rectangular carpet measuring 16 meters by 12 meters, excluding the border, has a border of width 2 meters on each of its sides. what is the area of the border? a. 96 sq.m b. 112 sq.m c. 124 sq.m d. 128 sq.m e. 154 sq.m Solution: With the border, total area = (16+2×2)×(12+2×2) = 20×16 = 320 sq meters. Without the border, total area = 16×12 = 192 sq meters. Area of the border = 320 - 192 sq meters = 128 sq.m Ans: d. 128 sq.m

08) A man has to go 10 km to catch a bus. He walks part of the way at 7 kmph and runs the rest of the way at 12 kmph. If he takes one hour and fifteen minutes to complete his journey, find how far he ran. a. 10 km b. 1 km c. 7 km d. 3 km e. none Solution: Suppose, he ran a distance of P km So, he walked a distance of (10-P) km According to the question: P/12 + (10-P)/7 = 75/60 [we know, 1 hr 15 min = 60+15 min] (7P + 120 - 12P)/84 = 75/60 (120-5P)/84 = 5/4 120 - 5P = 105 P=3 Ans: d. 3 km 09) What is the greatest number of apples not exceeding 460 that can be distributed among three persons in the proportions 5 : 6 : 7 ? a. 440 b. 432 c. 420 d. 450 e. none Solution: Suppose, These three persons will get 5p, 6p and 7p apples. So, total number of apples distributed = 5p+6p+7p = 18p. So, the required number of apples is the greatest multiple of 18 for which 18p < 460. Now, 18p < 460; or, p < 460/18; or, p < 25.55 Greatest possible integer value of p is 25. So, the required number of apples = 18×25 = 450. Ans: d. 450 10) In a class of 120 students, sixty percent can speak French and the rest can speak only English. If twenty-five percent of those in the class who can speak French can also speak English, how many of the students in the class can speak only French? a. 54 b. 60 c. 66 d. 84 e. none Solution: Can speak only English = 40% Can speak both language = 60% × 25% = 15% Can speak only French = (100 - 40 - 15)% = 45%. Required number of students = 120 × 45% = 54. Ans: a. 54

Solution TO TEST#10 01: If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 45. By how much do the two digits differ? a. 3 b. 4 c. 5 d. 6 e. 7 Solution: Suppose, the unit digit of the number is R and the tens digit of number is P. According to the question: 10P+R - (10R+P) = 45; or, 9(P-R) = 45; or, P-R = 5. Ans: 5 02: If n = 4p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n? a. 2 b. 3 c. 4 d. 6 e. 8 Solution: if p = 3, then n = 4×3 = 12. Even divisors of 12 are 2, 4, 6 and 12. Number of divisors = 4. if p = 5, then n = 4×5 = 20. Even divisors of 20 are 2, 4, 10 and 20. Number of divisors = 4. if p = 7, then n = 4×7 = 28. Even divisors of 28 are 2, 4, 14, and 28. Number of divisors = 4. Ans: c. 4 03: If (x-1)² = 400, which of the following could be the value of x-5? a. 15 b. 14 c. -24 d. -25 e. -26 Solution: (x-1)² = 400; => x-1 = -20 or 20; => x = -19 or 21; => x-5 = -24 or 16. Ans: c. -24 04: If n is a prime factor of 7150, and n < 100. How many different values can n have? a. 1 b. 2 c. 3 d. 4 e. 5. Solution: 7150 = 2×5²×11×13. So, n can have 4 different values. Ans: d. 4 05: At present Finn is 14 years younger than Anderson. In 10 years, Anderson will be twice as old as Finn. In five years, how old will Anderson be? a. 9 b. 19 c. 21 d. 23 e. 33 Solution: Suppose, at present, the age of Anderson is P, and therefore, the age of Finn is (P-14). According to the question: (P+10)/(P-14+10) = 2; or, 2P-8 = P+10; or, P = 18. So, in 5 years, Anderson will be = 18+5 = 23 years old. Ans: d. 23

06: A positive number x is multiplied by two and then the product divided by 3. the positive square root of the result is equal to x. what is the value of x? a. 9/4 b. 3/2 c. 4/3 d. 2/3 e. 1/2 Solution: According to the question: √{(x×2)/3} = x; or, x² = 2x/3; or, 3x² = 2x; or, 3x²-2x = 0; or, x(3x-2) = 0; or, either x = 0, or x = 2/3. Ans: d. 2/3 07: If xφy = √(xy), then (5φ45)φ60 = ? a. 30 b. 60 c. 90

d. 30√15

e. 60√15

Solution: (5φ45)φ60 = √(5×45) φ 60 = 15φ60 = √(15×60) = 30. Ans: a. 30 08: If aδb = (a-b)/(a+b), for all numbers a and b, such that a is not equal to -b. If a is not equal to -c, and aδc = 0, then, c = ? a. -a b. -1/a c. 0 d. 1/a e. a Solution: aδc = 0; or, (a-c)/(a+c) = 0; or, a-c = 0; or, a = c. Ans: e. a 09: if y/x < 1 where both x and y are positive integers, which of the following must be greater than 1? a. √(y/x) b. y/x² c. y/2x d. x/y² e. x/y Solution: 0 < y/x < 1 where both x and y are positive integers. As y/x is between 0 and 1, we can say x > y. If x > y, we can say, x/y is always greater than 1. Ans: e. x/y 10: if (0.0015×10x) ÷ (0.03×10y) = 5×107, then x-y = ? a. 9 b. 8 c. 7 Solution: (0.0015×10x)/(0.03×10y) = 5×107 => (0.05×10(x-y)) = 5×107 => (5×100×10(x-y)) = 5×107; => 5×10(x-y+2) = 5×107 => x-y+2 = 7; => x-y = 5 Ans: e. 5

d. 6

e. 5