Kryteax Aptitude
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Aptitude
01. A bag contains an equal number of one rupee, 50 paisa and 25 paisa coins. If the total value is ₨ 35 then the number of coins of each type are (a) 10 (b) 40 (c) 20 (d) 18 02. ‘A’ lent Rs 5000 to ‘B’ for 2 years and Rs 3000 to ‘C’ for 4 years on simple interest at the same rate of interest and received Rs 2200, in all from both them as interest. Then the rate of interest per annum is (a) 10% (b) 20% (c) 8% (d) 4%
03. A Father’s age is three times the sum of the age of his two children, after 20 years his age will be equal to the sum of their ages. Then the Father’s age (in years) is (a) 30 (b) 40 (c) 35 (d) 45
04. 8 : 81 : : 64 : ______________ (a) 125 (c) 625
(b) 137 (d) 525
th th 05. In a row of Boys, where A is 10 from left and B is 9 from the right. On interchanging
th their positions, A becomes 15 from the left. The number of Boys in the row are:
(a) 23 (c) 25
(b) 24 (d) 31
06. QIOK : MMKO :: YAWC : _______________ (a) UESG (c) VUES
(b) USGA (d) SUEG
n n 07. 7 4 is divisible by 11 for
(a) odd values of n (c) both odd and even values of n © Kreatryx. All Rights Reserved.
(b) even values of n (d) None of these 1
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08. From the diagram, the value of x is
16 13 14 15
28 12 10 30
29 16 15 x
(a) 60 (c) 20
(b) 30 (d) 45
09. The side of a square is 22 m. The radius (in m) of the circle, whose circumference is equal to the perimeter of square, is (a) 28 (b) 3.5 (c) 14 (d) 7
10. Two stations A and B are 110 km apart on a straight line. One train starts from A at 7:00 AM and travels towards B at 20 km/hr speed. Another train starts from B at 8:00 AM and travels towards A at 25 km/hr speed. The time at which they will meet is (a) 10:30 AM (b) 11:00 AM (c) 10:00 AM (d) 11:30 AM 11. Four examiners can examine certain number of answer papers in 10 days by working 5 hours a day. The number of working hours in a day would 2 examiners take have to work in order to examine twice the number of answer papers in 20 days is (a) 8 hours (b) 10 hours (c) 9 hours (d) 11 hours 12. Which of the following statements is incorrect? (a) log10 10 1
(c) log 2 3 log 2 3
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(b) log10 1 0 (d) log6 log1 log2 log3
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13. A reduction of 20%, in the price of rice enables a person to buy 3.5 kg more rice for Rs 385. The original price (in Rs) of rice per kg is (a) 20 (c) 25
(b) 22.50 (d) 27.50
14. The mean marks of 10 Boys in a class is 70%, whereas the mean marks of 15 girls is 60%. The mean (in %) marks of all 25 students is (a) 64 (c) 55
(b) 60 (d) 52
15. If N 1! 3! 5! 7!........................................99! then remainder obtained when N is divided by 24 is (a) 7 (b) 6 (c) 3 (d) 5 16. The unit’s digit in the product of
197
443
296
1076
273
4513
2379
2194
3125
773
(a) 7 (c) 3
is (b) 6 (d) 0
17. Red light flashes 3 times per minute and Green light flashes 5 times in every 2 minutes. If both light start flashing at the same time, then how many times do they flash together in each hour? (a) 30 (b) 24 (c) 20 (d) 60
18. From a beaker full of pure cola, Mohit withdraws 25% of cola and replaces it with water. He again withdraws 25% of mixture of cola and again replaces with water and the process was repeated two more times till he finds 567 ml of pure cola left in the mixture. Then the actual initial quantity (in ml) of cola was (a) 1792 (c) 1296
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(b) 1000 (d) None of these
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19. The numbers that can be made with digits 0, 7, 8 which are greater than 0 and less than a million are (a) 496 (c) 728
(b) 486 (d) 1084
6n 6n 20. 7 6 , where ‘n’ is an integer greater than 0, is divisible by
(a) 13 (c) 559
(b) 127 (d) All of these
21. Two third of a consignment was sold at a profit of 5% and remainder was sold at a profit of 2%. If total profit was Rs 800, then the value (in Rs) of the consignment is (a) 20000 (c) 16000
(b) 18000 (d) 24000
22. If N a1a2a3a1a2a3a1a2a3 ................................,N is a repeating nor terminating decimal number, then the natural number by which N can be multiplied so that the resultant is a natural number is (a) 495 (b) 1001 (c) 891 (d) 4995 23. A and B decided to meet on 14th February, 2014 between 6 and 7 pm. The probability that they will meet provided one cannot wait for the other for more than 12 minutes is 5 9 9 (c) 25
7 16 11 (d) 36
(a)
(b)
24. If petrol becomes cheaper by 25%. The percentage by which Ashish can drive his bike more, so that his budget for petrol remains unaltered, is (a) 22.2% (c) 33.3%
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(b) 11.2% (d) 10.2%
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25. The maximum number of students, among whom 429 mangoes and 715 oranges can be equally distributed, are (a) 143 (b) 173 (c) 133 (d) 193 1 1 1 of his income on food, of the rest on house rent and on cloth. He 5 3 4 still has Rs 1760 left with him. Then his income (in Rs) is
26. A man spends
(a) 4400 (c) 5800
(b) 4800 (d) 5400
27. Sectoral growth rate (in %) of major industry groups (2006-2007) are given as Sec tor Weight 2006 2007 Mining 11.46 2.9 Manufacturing 77.11 8.7 Electricity 11.43 7.1
From table, the weighted average growth rate (in %) of all the industries in 2006-2007 was (a) 7.85 (b) 6.85 (c) 4.85 (d) 9.85
28. The angle of elevation of the top of a tower 30 m high, from two points on the level ground on its opposite sides are 45° and 60°. The distance (in m) between the two points is
(d) 30 3 3
(c) 15 3 3 (a) 20 3 3
(b) 10 3 3
29. Two coins are tossed 4 times then the probability that there will be equal number of ‘heads’ and ‘tails’ is 1 35 (a) (b) 7 64 2 1 35 (c) (d) 8 128 2
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30. A trader marked his goods at 20% above the cost price. He sold half the stock at the marked price, one quarter at a discount of 20% on the marked price and the rest at a discount of 40% on the marked price. Then his total gain (in %) is (a) 4 (b) 6 (c) 8 (d) 2 31. 10 men and 15 women together can complete a work in 6 days. It takes 100 days for the man alone to complete the same work. The number of days required for one woman to complete the same work are (a) 225 (c) 125
(b) 325 (d) 425
32. A man can row at a speed of 4.5 km/hr is still water to a certain upstream point and back to the starting point in a river which flows at 1.5 km/hr. his average speed (in km/hr) for total journey is (a) 4 (b) 8 (c) 10 (d) 12
33. If x 1 a a2 ............. and y 1 b b2 ........... then 1 ab a2b2 a3b3 ........ is given by (where a and b are less than 1) (a) xy (c)
xy x y 1
(b)
xy x y 1
(d)
xy x y 1
34. The probability that January of a leap year should have 5 Sundays is 2 7 6 (d) 7
1 7 3 (c) 7
(a)
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(b)
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35. If 2 3 is a root of the equation x2 px 6 0 and the equation x2 px q has equal roots, then value of Q is 1 4 5 (c) 4
(a)
(b) (d)
3 4
3 4
36. The term that comes next in the series YEB, WFD, UHG, SKI is (a) QOL (c) TOL
(b) QGL (d) QNL
37. If a, b, c, d and e are positive real numbers, then the minimum value of
a b c d e 1a b1 1c 1d 1e
(a) 25
(b) 5
(c) 125
(d) cannot be determined
38. A man can do a piece of work in 91 days. In order to complete the work faster, he starts increasing his efficiency by 20% everyday (100% on day 1, 120% on day 2, 140% on day 3 and so on). How many days (minimum) would be required to complete the work now? (a) 14
(b) 25
(c) 13
(d) 61
39. 10 men and their wives participate in a corporate mixed-doubles tennis championship. What is the probability that no couple play in the same game? (a) 0.6222
(b) 0.3111
(c) 0.4285
(d) 0.2777
40. How many ways can 9! be expressed as a product of two co-primes? (a) 6
(b) 8
(c) 10
(d) 12
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41. Study the following graph and answer the question below
Average annual exports during the period 1994-1997 for company P is what percent of the average annual exports for company Q? ________ (a) 113.33
(b) 123.25
(c) 145.65
(d) 135.61
42. If |x|+y+z=15, then find the number of possible integral solutions? (a) 250
(b) 254
(c) 286
(d) 290
43. Study the following pie-diagrams and answer the question below.
If the total weight of the human body were to be shown in a single pie chart, the weight of water present in hormones and enzymes should be shown as an arc of the circle subtended at an angle of (a) 54° (c) 108°
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(b) 126° (d) 252°
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44. Study the graph and answer the question that follows. Income and expenditure (in crore Rs.) of four companies in the year 2014.
If the income of company Q in 2014 was 20% more than its income in 2013 and the company had earned a profit of 10% in 2013, then its expenditure in 2013 (in crore Rs.) was _________(2 decimal places) (a) 25.61 (b) 22.77 (c) 15.65
(d) 35.68
2 log16 0.5 2 , then x (a) 4log4 x 7
(b) 2log4 x 7
(c) 2log16 x 7
(d) log16 x 7
45. If log4
46. The sum of all possible two digit numbers formed from three different one digit natural numbers when divided by sum of the original three numbers is (a) 36 (c) 22
(b) 28 (d) 15
47. In a city, Star sports, ESPN and ZEE sports are three sports channel watched by 56%, 80% and 45% of the population respectively. 40% watch exactly two of the three channels and 10% watch none. What percent of the people watch all three channels? (a) 36.5
(b) 56.41
(c) 45.65
(d) 25.5
48. In an examination, there are 5 subjects and each has the same maximum. A boy’s marks are in the ratio 3:4:5:6:7 and his aggregate is 3/5th of the full marks. In how many subjects did he get more than 50% marks? (a) 1
(b) 2
(c) 3
(d) 4
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49. Two pipes A and B can separately fill a cistern in 15 and 20 minutes respectively and the waste pipe C can carry off 10 litters per minute. If the three pipes are opened when the cistern is full, it is emptied in 2 hours. How many litters does the cistern hold? (a) 40
(b) 80
(c) 60
(d) 120
50. The three interior angles of a quadrilateral are in AP such that the difference between the largest and the second largest angle is equal to the smallest angle considering the same three angles. Also the fourth angle is equal to one of the three angles that are in AP. At least one of the angles of the quadrilateral is 900. The least angle of the quadrilateral can be (a) 40
(b) 45
(c) 51.3
(d) Data insufficient
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Answer Key 1 c
2 a
3 a
4 c
5 a
6 a
7 a
8 b
9 c
10 c
11 b
12 c
13 d
14 a
15 a
16 d
17 a
18 a
19 c
20 d
21 a
22 d
23 c
24 c
25 a
26 b
27 a
28 b
29 c
30 D
31 a
32 a
33 b
34 c
35 d
36 a
37 a
38 d
39 a
40 b
41 a
42 d
43 c
44 b
45 a
46 c
47 d
48 c
49 b
50 b
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Solutions 01. Ans: (c) Solution: Let there are ‘X’ number of coins of each type
Total value 35 1 0.5 0.25 x
x 20
02. Ans: (a) Solution: Let the rate of interest be r% Total int erest Interest from B Interest from C 5000 r 2 3000 r 4 2200 100 100
2200 100r 120r r 10%
03. Ans: (a) Solution: Let the current sum of ages of two children be ‘x’ Let the current Father’s age be ‘y’ ...(i) y 3x After 20 years y 20 x 20 20
(Because he has two children)
....(ii) y x 20 Equating value of ‘x’ from equation (ii) in equation (i) y
y 20 3
y 30 years 04. Ans: (c) Solution: 8 : 81 : : 64 : ______________ 23 :34 :: 43 :54 ∴ Answer is 625
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05. Ans: (a) Solution: | | | | | | | | | A | | | | B| | | | | | | | Total boys A’s new position B’s old position 1 23
06. Ans: (a) Solution: Sum of the position of the first number and next two add upto 26 Q is 17, I is 9 and O is 15, K is 11 M is 13, M is 13 and K is 11, O is 15 Y is 25, A is 1 and W is 23, C is 3 So, term satisfying this relation is UESG. Alternate Logic: The difference between first letters of the 2 given ratios is -4, +4, -4, +4. Q (17) – M (13) = +4 I (9) – M (13) = -4 O (15) – K (11) = +4 K (11) – O (15) = -4 Following the same pattern, the correct answer is UESG. 07. Ans: (a) Solution:
a
n
bn is divisible by a b , when n is odd.
You can also follow a hit and trial method. Substitute n= 0, 1, 2, 3 and see if the value is divisible by 11. You’ll find that the value is only divisible by 11 when n= 1 and 3, which gives you (a) as the correct answer. 08. Ans: (b) Solution: In a column, sum of top two numbers is equal to sum of bottom two numbers. Column 1 16 13 14 15
Column 2 28 12 10 30 Column 3 29 16 15 x
x 30
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09. Ans: (c) Solution: Let the radius be ‘r’ m
4 22 2r r 14m
10. Ans: (c) Solution: A
B
110 km
Let train B has travelled for ‘x’ has after its starting time till trains from A and B meet Total distance 110 = speed of train from A × time taken by train from A + speed of train from B × time taken by train from B
110 20 x 1 25 x
90 45x x 2hrs
∴ at 10:00 hrs they will meet.
11. Ans: (b) Solution: Let ‘X’ number of answer paper are examined by four examiners in 10 days by workings 5 hours x ∴ Paper examined by 1 examiner in 1 day by working 1 hour 4 10 5 Let ‘H’ number of hours in a day are taken by 2 examiners to examine ‘2x’ answer papers in 20 days. x 2 20 H 2x 4 10 5 H 10hours
12. Ans: (c) Solution: log 2 3 log2 log3 © Kreatryx. All Rights Reserved.
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13. Ans: (d) Solution: Let the original price be Rs x and the buys ‘y’ kg of rice with Rs 385 xy 385 on 20% reduction of price, person can buy 3.5 kg more rice 4 x y 3.5 385 5 4 4 xy x 3.5 385 5 5 4 385 2.8x 385 5 385 2.8 x 77 5 x Rs27.5
14. Ans: (a) Solution: Mean of 25 students
70% 10 60% 15 64% 25
15. Ans: (a) Solution: 4! Onwards every factorial will be a multiple of 24. As 4! 24 5! 4! 5
6! 4! 5 6 and so on So, remainder will be 1! 3! 7 16. Ans: (d) Solution: In the given number there is an even number (296) as well as a multiple of 5 i.e. (3125). So, the product will surely end in a zero. 17. Ans: (a) Solution: Red light flashes after every 20 second and Green light flashes after every 24 second. They will flash together after LCM (20, 24)=120 seconds or 2 minutes Hence, they will flash together 30 times in an hour.
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18. Ans: (a) Solution:
1 Quantity of cola left after 4th operation initial quantity 1 4 3 567 initial quantity 4
4
4
4
4 So, initial quantity 567 1792 ml 3 19. Ans: (c) Solution: Numbers less than a million will be 36 1 728 (as zero has to be excluded)
20. Ans: (d) Solution:
an bn will always be divisible by a b , if n is even
6n 6n ab So, 7 6 is divisible by i.e. 7 6 13
6
76n 66n 73
2n
3
2n
will always be divisible by 73 63
and 73 63
(as power is even). So, the number is divisible by 127 and 559 as well. 21. Ans: (a) Solution: Let ‘x’ be the value of consignment 2x 5 x 2 800 3 100 3 100 x Rs20000
profit
22. Ans: (d) Solution:
N a1a2a3
…(i)
10 N a1a2a3 a1a2a3 3
…(ii)
(i)-(ii) 999N a1a2a3 © Kreatryx. All Rights Reserved.
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So, N have to be multiplied by 999 or any multiple of 999. Hence, 999 5 4995 is the answer. 23. Ans: (c) Solution: If A arrives at time ‘x’ and B arrives at time ‘y’ then for them to meet the range of y will be ‘x-12’ to ‘x+12’ so the favourable area is the area bounded between these two lines. favourable area 48 48 9 Required probability 1 total area 60 60 25
24. Ans: (c) Solution: If prices becomes cheaper by 25%, 25 1 then consumption can be increased by 100 100% 33.3% 3 100 25
25. Ans: (a) Solution: H.C.F. of 429 and 715 is 143 26. Ans: (b) Solution: Let the income of man is Rs. ‘P’ P 1 P 1 P P P 1760 P 3 4 3 5 3 P P 2P 1760 P 3 6 15 P P 2P 1760 P 3 6 15 30 10 5 4 P 1760 30 P Rs 4800
27. Ans: (a) Solution: Weighted average growth
11.46 2.9 77.11 8.7 11.43 7.1 33.234 670.857 81.153 11.46 77.11 11.43
7.85%
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28. Ans: (b) Solution: Distance between two points AB BC
35 30 10 3 3 m tan 45 tan60
29. Ans: (c) Solution: If coin 1 gets 4 heads, then coin 2 must get 4 tails for required condition 4 P 4P Permutation for this case 4 4 1 4! 4! If coin 1 gets 3 heads, then coin 2 must get 3 tails for required condition 4 P3 4 P3 Permutation for this case 16 3! 3! If coin 1 gets 2 heads, then coin 2 must get 2 tails for required condition 4 P 4P Permutation for this case 2 2 36 2! 2! If coin 1 gets 1 heads, then coin 2 must get 1 tails for required condition Permutation for this case 4 P1 4 P1 16 If coin 1 gets 0 heads, then coin 2 must get 0 tails for required condition Permutation for this case 4 P0 4 P0 1 Total possible cases 1 16 36 16 1 70 70 35 ∴ Pr obability 8 128 2 30. Ans: (d) Solution: Let the C.P be ‘x’ ∴ Marked price of good is
6 x 5
6 6 6 80 60 x x x x x x 1 5 15 1 100 100 Total profit 100 100 5 100 2 x 4 x 4 x
1 6 1 20 1 140 100 100 100 10 1 7 2% 2 5 4 500 4 500
31. Ans: (a) Solution: A man takes 100 days to complete the work © Kreatryx. All Rights Reserved.
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1 100 Let the woman require ‘x’ days to complete the same work 1 Work done by a single woman in a day x 1 1 10 15 6 1 100 x
Work done by a single man in 1 day
1 15 1 10 x 6 15 1 1 10 6 4 1 x 6 10 60 60 15 x 225 days
32. Ans: (a) Solution: Speed in still water 4.5 km / hr Speed of river 1.5 km / hr w While going upstream river will flow against the man Hence, Upstream speed 3 per hour While going downstream river will flow with the man Hence, Downstream speed 6 per hour d hr 3 d Time taken while going downstream hr 6 Total dis tance 2d Average speed 4 km / hr d d Total time 3 6
Time taken while going upstream
33. Ans: (b) Solution: x 1 a a2 ............. G.P. with r a 1 x 1a x 1 a x y 1 Similarly, b y Now, a, b are less than 1 ab 1 © Kreatryx. All Rights Reserved.
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∴ 1 ab ab2 ........ 1 1 ab
1 1 ab
(G.P. with r=ab)
xy xy 1 x 1 y 1 xy xy x y 1 x y 1 1 x y
34. Ans: (c) Solution: January has 31 days So, apart from 4 full weeks we have 3 days left. To have a 5th Sunday we have 3 possible chances Out of the 7 total chances 3 Pr obability 7 35. Ans: (d) Solution:
2 3 is a root of x2 px 6 0
2 3
p
2
p 2 3 6 0
6
3 2 3 2 For x px q 0 p q 2
2
2
3 3 q 2 4
36. Ans: (a) Solution: Y W 2 U 2 S 2 Q 2
E F 1 H 2 K 3 O 4
B D 2 G 3 I 2 L 3
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37. Ans: (a) Solution: For positive real numbers a1 ,a2 ,a3 ...............an ,
a
1
1 1 1 1 a2 a3 ............... an .............. n2 an a1 a2 a3
1 1 1 1 1 Hence the minimum value of a b c d e is 52 25 a b c d e
38. Ans: (d) Solution: In first day he would complete
1 of the work 91
Second day (20% more) 120%of Third day
1 1.2 91 91
1.4 and so on 91
1 1.2 1.4 x ........... 1 91 91 91 91 1 1 x 1 1.2 1.4 .......... x 1 x 1 1 x x 1 182 x 13 91 91 2
Here, x is the nth term, but we need to find ‘n’ 13=1+ (n-1) (0.2)
[ (an=a+(n-1)d)]
n 61
39. Ans: (a) Solution: A game can be played without selecting couples Total number of games that can be played The required probability=
10 10
10
C2 8 C2 2
C2 C2 2
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10
10
C2 8 C2 2 ways
C2 10 C2 2 ways
28 0.6222 45
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40. Ans: (b) Solution 9! 27 34 51 71
co-prime numbers are called coprime if only positive integer that evenly divides both of them is 1 So, Factors can be selected in 24 16 ways; hence, 8 pairs are possible. Alternate Solution: If N ap bq .........., where a, b, - - - - are prime numbers, then N can be written as a product of two co primes in 2n-1 ways, where n is the number of prime factors to N. Here, n=4 (Since the prime factors are 2, 3, 5, 7) Hence the number of ways 9! Can be expressed as a product of two prime factors =24-1=8
41. Ans: (a) Solution: Average annual exports of P (during 1994-97) =
30 20 36 50 34crores 4
Average annual exports of Q (during 1994-97) =
20 30 30 40 30crores 4
Percentage of P’s exports with respect to that of Q=
34 100 113.33% 30
42. Ans: (d) Solution: Given x y z 15 The following three cases exist. Case (1): x 0 y z 15 y, z 0
Number of solutions= 1521 C21
C1 16
16
Case (2): x 15 y z 0
Number of solutions 21 2 x 15
Case (3): x y z 15 x, y, z 0 x y z 15
1531
Cr 1
Number of solutions
17
17
C2
C2 21 272
Hence, 272+16+2=290
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43. Ans: (c) Solution: Let total weight of body be x 1 1 1 18 2x Weight of hormones and enzymes x x x x 3 6 10 30 5
Weight of water present in hormones and enzymes=
75 2 30 x x 100 5 100
30 x Angle of subtended arc= 100 360 1080 x
44. Ans: (b) Solution: Profit%=
Income Expenditure 100 Expenditure
Let income of company Q in 2013 = Rs. x crore 120 Then income of Q in 2014= crore 100 120 30 x 100
x 25 Income of Q in 2013 = Rs.25 crore Let expenditure of Q in 2013 be Rs.E crore 25 E Then, 10 100 E 25 10 1 100 E 10 22.77 11 Expenditure of Q in 2013 = Rs.22.77 crore E 25
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45. Ans: (a) Solution: log4
2 log16 0.5 2 x 2
2 1 log16 log16 2 2 x 2 2 1 log16 2 x 2 log16
2 2 x2
log16 2 log16 x 2 2 log16 x 2
1 2 4
2log16 x
7 4
log4 x
1 log16 2 4
7 4
46. Ans: (c) Solution: Let the one digit numbers be x, y, z Sum of all possible two digit number
10x y 10x z 10y x 10y z 10z x 10z y 22 x y z
Therefore sum of all possible two digit numbers when divided by sum of one digit numbers gives 22.
47. Ans: (d) Solution:
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As 10% do not watch any of the channels, so 90% watch at least one of the channels
56 a b x 80 a c x 45 b c x a b c x 90 90 56 80 45 a b c 3x x 2x 51
a b c 40
x 25.5% 48. Ans: (c) Solution: If the maximum of each paper is 100x, total marks = 500x 3 The boy’s aggregate = 500x 300x , which when divided in the given ratio gives marks: 5 36x, 48x, 60x, 72x and 84x
He scored more than 50 % in three subjects 49. Ans: (b) Solution: Let V be the volume In one minute, A and B can fill
V V and of the cistern respectively. 15 20
Also, C can carry off 10 litters in one minute. V V We have, V 120 10 0 15 20
V 8V 6V 1200 0 15V 1200 V 80litters
50. Ans: (b) Solution: Let the three angles (in A.P) be x, x a, x 2a
Given that x 2a x a x , i.e. 2a a x a x Hence the angles are in the form x, 2x, 3x. Let the 4th angle be P Three cases exist when P is equal to one of x, 2x and 3x respectively. Case1: P=x
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x 2x 3x x 360 7x 360 x 51.4
Angles are 51.4,51.4; 51.4 2; 51.4 3 Since no angle is 90; we reject this possibility Case 2: P=3x x 2x 3x 3x 360 9x x 40
Angles are 40; 80;120;120 (Rejected) Case 3: P=2x x 2x 3x 2x 8x 360 x 450
Angles are 450 ,900 ,1350 ,900. Thus the smallest angle= 450 .
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