Test--1 EDIT

1.

The left most digit of an integer of length 2000 digits is 3. In this integer, any two consecutive digits must be divisible by 17 or 23. The 2000th digit may be either x or y. What is the value of x + y? 1)6 2)7 3)8 4)12 5)5

2.

A number has exactly 15 composite factors. What can be the minimum number of prime factors of this number? 1)2 2)3 3)4 4)5 5) 1

3.

How many numbers of zeros will be there at the end of 12! expressed in base 6? 1)4 2)5 3)6 4)7 5)8

4.

How many positive integers not exceeding 2001 are multiples of 3 or 4 but not 5? 1)812 2)788 3)476 4)312 5)801

5.

Let S be the prime numbers greater than or equal to 2 and less than 1000. Multiply all elements of S. With how many consecutive zeros will the product end? 1)1 2)4 3)5 4)10 5)None of these

6.

Direction for questions 6 to 9: Answer the questions based on the following information. Ten coins are distributed among four people P, Q, R and S such that one of them gets one coin, another gets two coins, the third gets three coins and the fourth gets four coins. It is known that Q gets more coins than P, and gets fewer coins than R. If the number of coins distributed to Q is twice the number distributed to P, then which one of the following is necessarily true? 1) R gets an even number of coins. 2) R gets and odd number of coins. 3) S gets an even number of coins. 4) S gets an odd number of coins. 5) None of these.

7.

If R gets at least two more coins than S, then which one of the following is necessarily true? 1) Q gets at least two more coins. 2) Q gets more coins than S 3) P gets more coins than S. 4) P and Q together get at least five coins. 5) None of these.

8.

If Q gets fewer coins than R, then which one of the following is not necessarily true? 1) P and Q together get at least four coins. 2) Q and S together get at least four coins. 3) R and S together get at least five coins. 4) P and R together get at least five coins. 5) None of these.

9.

In a four-digit Number the sum of the first 2 digits is equal to that of the last 2 digits. The sum of the first and last digits is equal to the third digit. Finally, the sum of the second and fourth digit is twice the sum of the other 2 digits. What is the third digit of the number? 1) 5 2) 8 3) 1 4) 4 5) 3

10. 10007-17 is written in decimal notation. What is the sum of its digits? 1) 181 2) 182 3) 183 4) 1

5) None of these

11. In a system of writing of N digits, 4×6 = 30 and 5×6 = 36. What will be the value of N = 3×4×5 in the same system writing? 1) 62 2) 74 3) 56 4) 66 5) 54 12. f(n) = sum of digits of n until single digit is obtained. Find f(19101). 1) 0 2) 3 3) 6 4) 8

5) 1

13. What is the tens place digit of 12626 +12525? 1) 0 2) 3 3) 7

5) 1

4) 9

14. If n2 is a cube, then which of the following statements is always true? 1) n is odd 2) n is even 3) n3 is square 4) n is cube

5) None of these

15. (1721 +1921) is not divisible by 1) 36 2) 8

5) 2

3) 9

4) 18

16. What is the remainder when 1044 × 1047 × 1050 × 1053 is divided by 33? 1) 13 2) 22 3) 30 4) 8 5) 20 17. The average weight of 5 apples is 100g and the average weight of 4 oranges is 80g. If 2 apples and 2 oranges are picked from them then average weight is found to be 85g. What is the average weight of the remaining apples and oranges? 1) 88g 2)90g 3)96g 4)95g 5)92g 18. A person bought 20kg of rice at RS 10.50 per Kg and 30 Kg at Rs 12 per Kg. He mixed the two and sold the mixture at Rs 11.40 per Kg. What was the gain in the deal (in Rs)? 1)0 2)20 3)100 4)75 5)5 19. Rs. 4000 is divided into two parts such that one part is put out at 3% and the other at 5%. If the annual interest earned from both the investments be Rs 144, find the first part. 1) Rs 4000 2)Rs 2800 3) Rs 3800 4) Rs 3500 5)Rs 2600 20. A vessel of 70 litres is filled with milk and water. 75 percent of milk and 25 percent of water is taken out of the vessel. It is found that the vessel is vacated by 60 percent. Find the initial quantity of water. 1)21 litres 2)25 litres 3)27 litres 4)32 litres 5)None of these 21. A reduction of 20% in the price of sugar enables a person to obtain 40Kg more for Rs 210. What is the reduced price per Kg? 1)Rs 1 2)Rs1.10 3)Rs 1.150 4)Rs1.75 5)None of these. 22. Find the difference between the compound interest and the simple interest for the sum Rs 1200 at 15% per annum for 2 years. 1) Rs 22.50 2)Rs 23.70 3) Rs27 4)Rs 30.60 5) Rs None of these. 23. The profit earned by selling a watch for Rs 820 is as much as loss incurred when it is sold for Rs 650. What is the cost price of the watch? 1) Rs 735 2) Rs835 3) Rs750 4)Rs700 5)Rs 690 24. The Length and breadth of a rectangle are increased by 30% and 20% respectively. Which of the following can be the percentage increase in its perimeter? 1) 20% 2)16% 3)15% 4)28% 5)18% 25. A cat takes 5 leaps for every 4 leaps of a dog, but 3 leaps of the dog are equal to 4 leaps of the cat. What is the ratio of the speed of the dog to that of the cat? 1)11:15 2)15:11 3)16:15 4)15:16 5)None of these 26.

Directions for Q 26 and 27 . Read the passage given below and solve the Q based on it. Three different faces of a cube are colored in three different colors----black, green and blue. This cube is now cut into 216 smaller but identical cubes. 27. What is the least number of the smaller cubes that will have exactly three faces colored? 1)0 2)6 3)2 4)12 5) Cannot be determined 28. How many smaller cubes have exactly two faces colored? 1)32 2)45 3)56 4)18

5) Cannot be determined

29. How many runs did Rahul score in his 32nd match? A For the first 30 matches his average was 36. B His average run score is 32 till 31st match. C The average till 31st match is greater than his score in 32nd match. 1) A and B together are sufficient. 2) A and C together are sufficient 3) B and C together are sufficient. 4) All A, B and C together are necessary. 5) All A, B and C even together are not sufficient. 30. Mohit was conducting an experiment in which the average of 11 observations came to be 90. Average of first five observations was 87, and that of the last five was 84. What was the measure of the 6 th observation? 1)165 2)150 3)145 4)135 5)125 31. From the top of a cliff 25m high, the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. Find the height of the tower. 1)40m 2)48m 3)50m 4)52m 5)45m 32. When the length of the shadow of a pole is equal to the height of the pole, then the elevation of source of light is 1)300 2)450 3)600 4)750 5)150 33. The angle of elevation of a moon when the length of the shadow is equal to its height is 1)300 2)600 3)450 4)750 5)150

34. Every element of S1 is made greater than or equal to every of S2 by adding to each element of S1an integer X, than x cannot be less than 1) 210 2) the smallest value of S2 3) the largest value of S2 4) (G-L) 5)2