DIRECTIONS for questions 1 to 4: Select the correct alternative from the given choices.
1. There are certain number of cookies with each of Payal, Richa and Sapna. If we add the number of cookies with anytwo girls at a time, the ratio is 3 : 4 : 5 (Payal+Richa : Richa+Sapna : Sapna+Payal respectively). Which of theollowing statements is/are true?
I. The number of cookies with Sapna is 50% of those with all three of them together.
II. Payal has twice as many cookies as Richa.
III. Richa and Sapna together have twice as many cookies as Payal.
(1) Only I and II (2) Only II and III (3) Only III and I (4) All three statements
2. Today, Susheel made a total of exactly one hundred calls from his cell phone to ten different people. He could only remember the fact that he had called each person at least four times. In how many ways could Susheel have distributed his calls among the ten different people today? Ignore the order in which the calls were made.
(1) 100C10 (2) 99C6 (3) 60C6 (4) 69C9
3. A boy starts to paint a fence on one day. On the second day two more boys join him and on the third day three more boys join the group and so on. If the fence is completely painted this way in exactly 20 days, then find the number of days in which 10 men painting together can paint the fence completely where every man can paint twice as fast as a boy can.
(1) 20 days (2) 40 days (3) 45 days (4) 77 days
4. On a certain sum, the difference between the compound interest and the simple interest for the second year is Rs.3,600 and the same for the third year is Rs.11,340. What is the sum?
(1) Rs.1,60,000 (2) Rs.1,20,000 (3) Rs.1,80,000 (4) Cannot be determined
DIRECTIONS for questions 5 and 6: These questions are based on the following data.
A box contains a certain number of red, green and blue balls. The number of balls of each colour is more than one. The ratio of the number of red balls to the number of green balls is the same as the ratio of the number of green balls to the number of blue balls.
5. If the total number of balls in the box is 61, how many green balls are there in the box?
(1) 16 (2) 20 (3) 25 (4) Cannot be determined
6. If the number of green balls in the box is 21, then the total number of balls in the box can be
(1) 63 (2) 89 (3) 101 (4) 117
DIRECTIONS for questions 7 to 43:
Select the correct alternative from the given choices.
7. Consider z = 22225555 + 55552222. Which of the following statements is/are true?
(1) z is a multiple of 7 but not 11. (2) z is a multiple of 11 but not 7.
(3) z is a multiple of both 7 and 11. (4) None of these
8. Two candles of equal length are lighted simultaneously. After 15 minutes of burning, the length of the first candlebears a ratio of 4 : 5 to that of the second candle. If the first candle burns out completely in 45 minutes how much more time does the second candle take to burn out completely?
(1) 30 minutes (2) 60 minutes (3) 45 minutes (4) None of these
9. The number of two-digit numbers [where neither digit is a zero] whose product of the digits is a square are
(1) 16 (2) 17 (3) 18 (4) None of these
10. Bakul and Manohar start from two points P and Q respectively on a river and head towards each other. Had theybeen travelling in still water, they would have met at a point R, which is twice as distant from P as it is from Q. If Bakul had been travelling along the current and Manohar against it, then they would have met in 24 minutes. Find the time they would take to meet, if Bakul were to travel against the current and Manohar along the current.
(1) 12 minutes (2) 24 minutes (3) 36 minutes (4) 48 minutes
11. If p + 7 > 0 and (25 - p2) < 0, how many integer solutions are possible for p given that it lies between -151/6 and 471/7?
(1) 41 (2) 42 (3) 43 (4) 45
12. If the sum of the first 10 terms of an arithmetic progression is 100 and the sum of the first 100 terms of
the sameprogression is 10, then the sum t101 + t102 + …..t110 is
(1) –90 (2) –100 (3) –110 (4) –120
13. A cuboidal box of dimensions 10 cm x 8 cm x 12 cm is partitioned completely into cubicles of dimensions 1 cm x1 cm x 1 cm. Amy the ant is in the top left corner cubicle towards the front of the box. If Amy can move only between any two cubicles that have a common face, then find the number of ways in which Amy can reach the bottom right corner cubicle that is towards the back of the box. Assume that Amy visits no cubicle more than once and that it is allowed to move only in downward, rightward and backward directions.
(1) 960 (2) 10!8!2!30! (3)9!7!11 !27 !(4)20C8 * 30C10
14. ABCD is a rhombus of side 12 cm. The diagonals of the rhombus meet at the point P. Line segments PX and PY are joined, where X and Y are the midpoints of the sides AD and CD respectively. If the length of the line segment PD is 10cm, find the length of the line segment XY.
(1) 2 11 (2) 3 11 (3) 4 11 (4) Cannot be determined
15. A group of new students whose total age is 221 years joins a class, because of which the strength of the class goes up by 50% but the average age of the class comes down by one year. What is the new average of the class if it is known to be a natural number after the new group of students have joined, given that the original strength of the class was a two digit number greater than 30?
(1) 15 yrs (2) 17 yrs (3) 19 yrs (4) 16 yrs
16. If x is an integer, then which of the following statements is true of z = (x + 1) (x + 2) (x + 3) (x + 4).
(1) z - 1 is a prime number. (2) z2 - 1 is a prime number.
(3) z + 1 is a perfect square (4) None of these
18. All Analysts are Engineers. One-third of all Engineers are Analysts. Half of all Technicians are Engineers. One Technician is an Analyst. Eight Technicians are Engineers. If the number of Engineers is 90, how many Engineers are neither Analysts nor Technicians?
(1) 65 (2) 79 (3) 82 (4) 53
19. If a is an integer greater than –7 but less than 5, b is an integer less than 7 but greater than –5 while c is an integer that is not greater than 6 and not less than –2, which of the following statements is/are always true?
I. –36 < (ab + bc + ca) < 84
II. –384 < a(b2 + c2) + b(c2 + a2) + c(a2 + b2) < 912
(1) I only (2) II only (3) Both I and II (4) None of these
20. Let S = 7A68G023535928. If S is divisible by 792, what is the value of A?
(1) 5 (2) 9 (3) 7 (4) 8
21. Amar and Ajeeth start simultaneously from the same point on a circular track, of length 5 km, and run in opposite directions. Their speeds are doubled every time they cross each other. Find the number of times that they will meet within the first hour, given that they started the race with respective speeds of 6 kmph and 4 kmph.
(1) 4 times (2) 6 times (3) 7 times (4) None of these
22. How many ordered pairs of integers (a, b), are there such that their product is a positive integer less than 100?
(1) 99 (2) 545 (3) 635 (4) 1090
23. Among four persons A, B, C and D, C works half as fast as A while D works a third as fast as B. If C and D, when working individually, complete the work in 24 and 54 days respectively more than the time in which they complete the work when working together, then find the time in which A and B, working together, will complete the work.
(1) 15 (2) 18 (3) 24 (4) 30
24. There are 51 coins in a bag. The coins are first divided into two separate bags after which the coins in one of the two bags are taken and again divided into two separate bags and so on until we are left with 51 bags containing one coin each. If after every division of the coins in a bag into two bags the product of the number of coins in the two bags is written down, what is the sum of all the numbers written down?
(1) 1020 (2) 1275 (3) 1551 (4) 1525
25. Train A leaves station X for station Z at 0800 hrs and travels at a constant speed of 36 kmph. Train B leaves station Z for station X at 0830 hrs and runs at a constant speed of 27 kmph. Both trains have a stop at station Y but train A stops for 10 minutes while train B stops for 15 min. If the distance between the stations X and Y is 300 km and that between Y and Z is 405 km, where do the two trains meet?
(1) 450 km from station X (2) 450 km from station Z
(3) 408 km from station X (4) 408 km from station Z
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