# Practice Question Set on Quantitative Ability for CMAT 2014

The question bank on Quantitative Ability provided here helps you prepare for the upcoming Common Management Admission Test. Solve these questions and be better prepared.  Practice Question Set on Quantitative Ability for CMAT 2014

The Question Bank on Quantitative Ability prepared for CMAT will help you test your knowledge on the subject matter thoroughly.

Quantitative Ability

Directions for questions (1 to 18) : Answer the question independently of each other

1. In the X- Y plane, the area of the region bounded by the graph |x + y| + |x - y| = 4 is

(a) 8

(b) 12

(c) 16

(d) 20

2. Let g(x) be a function such that g(x + I) + g(x - 1) = g(x) for every real x. Then for what value of p is the relation g(x + p) = g(x) necessarily true for every real x?

(a) 5

(b) 3

(c) 2

(d) 6

3. P, Q, S and R are points on the circumference of a circle of radius r, such that PQR is an equilateral triangle and PS is a diameter of the circle. What is the perimeter of the quadrilateral PQSR?

(a) 2r(1 + √3)

(b) 2r(2 + √3)

(c) r(1 + √5)

(d) 2r + √3

4. Let S be a set of positive integers such that every element n of S satisfies the conditions

1. 1000 < n < 1200

2. every digit of n is odd

Then how many elements of S are divisible by 3?

(a) 9

(b) 10

(c) 11

(d) 12

5. Letx= √4 + √4 - √4 + √4 - .... to infinity. Then x equals

(a) 3

(b) (√13 - 1/2)

(c) (√13 + 1/2)

(d) √13

6. A telecom service provider engages male and female operators for answering 1000 calls per day. Amale operator can handle 40 calls per day whereas a female operator can handle 50 calls per day. The male and the female operators get a fixed wages ofRs. 250 and Rs. 300 per day respectively. In addition, a male operator gets Rs. 15 per call he answers and a female operator gets Rs. 10 per call she answer. To minimize the total cost, how many male operators should the service provider employ assuming he has to employ more than 7 of the 12 female operators available for the job?

(a) 15

(b) 14

(c) 12

(d) 10

7. Three Englishmen and three Frenchmen work for the same company. Each of them knows a secret not known to others. They need to exchange these secrets over person-to-person phone calls so that eventually each person knows all six secrets. None of the Frenchmen knows English, and only one Englishman knows French. What is the minimum number of phone calls needed for the above purpose?

(a) 5

(b) 10

(c) 9

(d) 15

8. A rectangular floor is fully covered with square tiles of identical size. The tiles on the edges are white and the tiles in the interior are red. The number ofthe white tiles is the same as the number of red tiles. A possible value ofthe number of tiles along one edge of the floor is :

(a) 10

(b) 12

(c) 14

(d) 16

9. Let n! = 1 x 2 x 3 x ..... x n for integer n > 1. If p = 1 ! + (2 x 2!) + (3 x 3!) + ..... + (10 x 10!), then p + 2 when divided by 11 ! leaves a remainder of

(a) 10

(b) 0

(c) 7

(d) 1

10. Consider a triangle drawn on the X- Y plane with its three vertices at (41,0), (0,41) and (0, 0), each vertex being represented by its (X, Y) coordinates. The number of points with integer coordinates inside the triangle (excluding all the points on the boundary) is

(a) 780

(b) 800

(c) 820

(d) 741

11. The digits of a three-digit number A are written in the reverse order to form another three-digit number B. If B> A and B-A is perfectly divisible by 7, then which of the following is necessarily true?

(a) 100 < A < 299

(b) 106 < A < 305

(c) 112 < A < 311

(d) 118 < A < 317

12. If a1 = 1 and an + 1 - 3an + 2 = 4n for every positive integer n, then a100 equals

(a) 399 - 200

(b) 399 + 200

(c) 3100 - 200

(d) 3100 + 200

13. Let S be the set of five-digit numbers formed by the digits 1, 2, 3, 4 and 5, using each digit exactly once such that exactly two odd positions are occupied by odd digits. What is the sum of the digits in the rightmost position of the numbers in S?

(a) 228

(b) 216

(c) 294

(d) 192

14. The rightmost non-zero digit ofthe number 302720 is

(a) 1

(b) 3

(c) 7

(d) 9

15. Four points A, B, C and D lie on a straight line in the X- Y plane, such that AB = BC = CD and the length of AB is 1 meter. An ant at A wants to reach a sugar particle at D. But there are insect repellents kept at points Band C. The ant would not go within one meter of any insect repellent. The minimum distance in meters the ant must traverse to reach the sugar particle is

(a) 3√2

(b) 1 +  π

(c) 4π / 3

(d) 5

16. If x > y and y > 1, then the value of the expression logx (x/y) + logy (y/x) can never be

(a) -1

(b) -0.5

(c) 0

(d) 1

17. For a positive integer n, let Pn denote the product of the digits of n, and sn denote the sum of the digits of n. The number of integers between 10 and 1000 for which Pn + sn = n is

(a) 81

(b) 16

(c) 18

(d) 9

18. Rectangular tiles each of size 70 cm by 30 cm must be laid horizontally on a rectangular floor of size 110 ern by 130 cm, such that the tiles do not overlap. A tile can be placed in any orientation so long as its edges are parallel to the edges of the floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is

(a) 4

(b) 5

(c) 6

(d) 7

Directions for questions (19 & 20) : Answer the questions on the basis of the information given below

Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 krnlhr, reaches B and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed.

19. At what time do Ram and Shyam first meet each other?

(a) 10 a.m.

(b) 10 : 10a.m.

(c) 10 : 20 a.m.

(d) l0 : 30a.m.

20. At what time does Shyam overtake Ram?

(a) 10 : 20a.m.

(b) 10 : 30 a.m.

(c) 10 : 40a.m.

(d) 10 : 50a.m.

21. The price of Darjeeling tea (in rupees per kilogram) is 100 + 0.1 0n, on the nth day of 2007 (n = 1,2, ... , 100), and then remains constant. On the other hand, the price of Ooty tea (in rupees per kilogram) is 89 + 0.15n, on the nth day of 2007 (n = 1,2, ... , 365). On which date in 2007 will the prices of these two varieties of tea be equal?

(a) June 30

(b) May 21

(c) April 11

(d) May 20

(e) April 10

22. A quadratic function f (x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f (x) at x = 10?

(a) -105

(b) -119

(c) -159

(d) -110

(e) -180

23. Two circles with centres P and Q cut each other at two distinct points A and B. The circles have the same radii and neither P nor Q falls within the intersection of the circles. What is the smallest range that includes all possible values of the angle AQP in degrees?

(a) Between 0 and 45

(b) Between 0 and 90

(c) Between 0 and 30

(d) Between 0 and 60

(e) Between 0 and 75

Directions for questions (24 & 25) : Answer these questions on the basis of the information given below.

Let S be the set of all pairs (i,j) where 1 < i < j < n and n > 4. Any two distinct members of S are called "friends" if they have one constituent of the pairs in common and "enemies" otherwise. For example, if n = 4, then S = {(1, 2), (1,3), (1,4), (2, 3), (2,4), (3, 4)}. Here, (1, 2) and (1, 3) are friends, (1, 2) and (2, 3) are also friends, but (1, 4) and (2, 3) are enemies.

24. For general n, how many enemies will each member of Shave?

(a) 1/2 (n2 - 7n + 14)

(b) n - 3

(c) 1/2 (n2 - 3n - 2)

(d) 2n - 7

(e) 1/2 (n2 - 5n + 6)

25. For general n, consider any two members of S that are friends. How many other members of S will be common friends of both these members?

(a) 1/2 (n2 - 7n + 16)

(b) 1/2 (n2 - 5n + 8)

(c) 2n - 6

(d) 1/2n (n - 3)

(e) n - 2

Directions for questions (26 & 27) : Answer these questions on the basis of the information given below.

Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee maximum returns on her investment. She has three options, each of which cart be utilized fully or partially in conjunction with others.

Option A: Invest in a public sector bank. It promises a return of +0.10%.

Option B: Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a return of +5%, while a fall will entail a return of -3%,

Option C: Invest in mutual funds of CBALtd. Arise in the stock market will result in a return of-2.5%, while a fall will entail a return of +2%.

26. The maximum guaranteed return to Shabnam is

(a) 0.30%

(b) 0.25%

(c) 0.10%

(d) 0.20%

(e) 0.15%

27. What strategy will maximize the guaranteed return to Shabnam?

(a) 30% in option A, 32% in option B and 38% in option C

(b) 100% in option A

(c) 36% in option B and 64% in option C

(d) 64% in option B and 36% in option C

(e) 1/3 in each of the three options

Directions for questions (28 & 29) : Answer these questions on the basis of the information given below.

Cities A and B are in different time zones. A is located 3000 km east of B. The table below describes the schedule of an airline operating non-stop flights between A and B. All the times indicated are local and on the same day.

Departure Arrival
City Time City Time
B 8:00 AM A 3:00 PM
A 4:00 PM B 8:00 PM

Assume that planes cruise at the same speed in both directions. However, the effective speed is influenced by a steady wind blowing from east to west at 50 km per hour.

28. What is the time difference between A and B?

(a) 1 hour

(b) 1 hour and 30 minutes

(c) 2 hours

(d) 2 hours and 30 minutes

(e) Cannot be determined

29. What is the plane's cruising speed in km per hour?

(a) 500

(b) 700

(c) 550

(d) 600

(e) Cannot be determined.

30. Consider four digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares?

(a) 1

(b) 3

(c) 2

(d) 4

(e) 0

31. In a tournament, there are n teams T1, T2, ... , Tn, with n> 5. Each team consists of k players, k > 3. The following pairs of teams have one player in common:

T1 & T2, T2 & T3,..., T n-1 & Tn, and Tn & T1.

No other pair ofteams has any player in common. How many players are participating in the tournament, considering all the n teams together?

(a) (n-1) (k-1)

(b) n (k-1)

(c) k (n-1)

(d) n (k-2)

(e) k (n-2)

Directions for questions (32 & 33) : Answer these questions on the basis of the information given below.

Let a1 = p and b1 = q, where p and q are positive quantities. Define an = pbn-1, bn = qbn-1, for even n > 1, and an = pan-1, bn = qan-1, for odd n > 1.

32. Which of the following best describes an + bn for even n?

(a) q(pq)1/2n - 1 (p + q)1/2n

(b)  q(pq)1/2n - 1 (p + q)

(c) qp1/2n - 1 (p + q)

(d) q1/2n (p + q)

(e) q1/2n (p + q)1/2n

33. If p = 1/3 and q =2/3, then what is the smallest odd n such that an + bn < 0.01?

(a) 15

(b) 7

(c) 13

(d) 11

(e) 9

Directions for questions (34 to 37) : Answer these questions on the basis ofthe information given below.

Each question is followed by two statements A and B. Indicate your responses based on the following directives:

(a) if the question can be answered using A alone but not using B alone.

(b) if the question can be answered using B alone but not using A alone.

(c) if the question can be answered using A and B together, but not using either A or B alone.

(d) if the question cannot be answered even using A and B together.

34. The average weight of a class of 100 students is 45 kg. The class consists of two sections, I and II, each with 50 students. The average weight, WI, of Section I is smaller than the average weight, WII' of Section II. If the heaviest student, say Deepak, of Section II is moved to Section I, and the lightest student, say Poonam, of Section I is moved to Section II, then the average weights of the two sections are switched, i.e., the average weight of Section I becomes WII and that of Section II becomes WI. What is the weight of Poonam?

A: WII - WI = 1.0

B: Moving Deepak from Section II to I (without any move from I to II) makes the average weights of the two sections equal.

35. Consider integers x, y and z. What is the minimum possible value of x2 + y2 + z2?

A: x + y + z = 89

B: Among x, y, z two are equal.

36. Rahim plans to draw a square JKLM with a point a on the side JK but is not successful. Why is Rahim unable to draw the square?

A: The length of OM is twice that of OL.,

B: The length of OM is 4 cm,

37. ABC Corporation is required to maintain at least 400 Kilolitres of water at all times in its factory, in order to meet safety and regulatory requirements. ABC is considering the suitability of a spherical tank with uniform wall thickness for the purpose. The outer diameter of the tank is 10 meters. Is the tank capacity adequate to meet ABC's requirements?

A: The inner diameter of the tank is at least 8 meters.

B: The tank weights 30,000 kg when empty, and is made of a material with density of 3gm/cc.

38. Suppose you have a currency, named Miso, in three denominations: 1 Miso, 10 Misos and 50 Misos. In how many ways can you pay a bill of 107 Misos?

(a) 19

(b) 17

(c) 16

(d) 18

(e) 15

39. How many pairs of positive integers m, n satisfy

1/m + 4/n = 1/12 where n is an odd integer less than 60?

(a) 3

(b) 6

(c) 4

(d) 7

(e) 5

40. A confused bank teller transposed the rupees and paise when he cashed a cheque for Shailaja, giving her rupees instead of paise and paise instead of rupees. After buying a toffee for 50 paise, Shailaja noticed that she was left with exactly three times as much as the amount on the cheque. Which of the following is a valid statement about the cheque amount?

(a) Over Rupees 4 but less than Rupees 5

(b) Over Rupees 13 but less than Rupees 14

(c) Over Rupees 7 but less than Rupees 8

(d) Over Rupees 22 but less than Rupees 23

(e) Over Rupees 18 but less than Rupees 19

41. Consider the set S = {2, 3, 4, ... , 2n+ I}, where n is a positive integer larger than 2007. Define X as the average of the odd integers in S and Y as the average of the even integers in S. What is the value of X - Y?

(a) 2008

(b) 0

(c) I

(d) 1/2n

(e) n + 1/2n

42. Ten years ago, the ages of the members of a joint family of eight people added up to 231 years. Three years later, one member died at the age of 60 years and a child was born during the same year. After another three years, one more member died, again at 60, and a child was born during the same year. The current average age of this eight-member joint family is nearest to

(a) 24 years

(b) 23 years

(c) 22 years

(d) 21 years

(e) 25 years

43. A function f(x) satisfies f(l) = 3600 and f(l) + f(2) + ... + f(n) = n2 f(n), for all positive integers n > 1. What is the value of f(9)?

(a) 120

(b) 80

(c) 240

(d) 200

(e) 100

44. If mxm - nxn = 0, then what is the value of 1/xm + xn + 1/xm - xn in terms of xn ?

(a) 2mn/xn (n2 - m2)

(b) 2mn/xn (n2 + m2)

(c) 2mn/xn (m2 - n2)

(d) 2mn/xn (m2 + n2)

45. In a certain zoo, there are 42 animals in one sector, 34 in the second sector and 20 in the third sector. Out of this, 24 graze in sector one- and also in sector two. 10 graze in sector two and sector three, 12 graze in sector one and sector three. These figures also include four animals grazing in all the three seotors are now transported to another zoo, find the total number of animals.

(a) 38

(b) 56

(c) 54

(d) None of the above

46. The ratio of the roots of bx2 + nx + n = 0 is p : q, then

(a) √q/p + √p/q + √l/n = 0

(b) √p/q + √q/p + √n/l = 0

(c) √q/p + √p/q + √l/n = 0

(d) √p/q + √q/p + √n/l =0

47. The average age of a couple is 25 years. The average age of the family just after the birth of the first child was 18 years. The average age of the family just after the second child was born was 15 years. The average age of the family after the third and the fourth children (who are twins) were born was 12 years. If the present average age of the family of six persons is 16 years, how old is the eldest child?

(a) 6 years

(b) 7 years

(c) 8 years

(d) 9 years     .

48. 10% of the voters did not cast their vote in an election between two candidates. 10% of the votes polled were found invalid. The successful candidate got 54% of the valid votes and won by a majority of 1620 votes. The number of voters enrolled on the voters list was:

(a) 25000

(b) 33000

(c) 35000

(d) 40000

49. The resistance of a wire is proportional to its length and inversely proportional to the square of its radius. Two wires of the same material have the same resistance and their radii are in the ratio 9 : 8. lf the length of the first wire is 162 cms., find the length of the other.

(a) 64cm.

(b) 120cm.

(c) 128 em.

(d) 132cm.

50. If f (x + y/8, x - y/8) = xy, then f (m, n) + f (n, m) = 0

(a) only when m = n

(b) only when m ≠ n

(c) only when m = - n

(d) for all m and n

51. A person closes his account in an investment scheme by withdrawing Rs. 10,000. One year ago he had withdrawnRs. 6000. Two years ago he had withdrawn Rs. 5000 Three years ago he had not withdrawn any money. How much money had he deposited approximately at the time of opening the account 4 years ago, if the annual simple interest is 10% ?

(a) Rs. 15600

(b) Rs. 16500

(c) Rs. 17280

(d) None of these

52. It takes 6 technicians a total of 10 hours to build a new server from direct computer, with each working at the same rate. If six technicians start to build the server at 11:00 am, and one technician per hour is added beginning at 5:00 pm, at what time will the server be completed?

(a) 6:40pm

(b) 7:00pm

(c) 7:20pm

(d) 8:00pm

53. A ship 55 kms. from the shore springs a leak which admits 2 tones of water in 6 min ; 80 tones would suffer to sink her, but the pumps can throw out 12 tones an hour. Find the average rate of sailing that she may just reach the shore as she begins to sink.

(a) 5.5km/h

(b) 6.5km/h

(c) 7.5km/h

(d) 8.5km/h

54. In a 400 meter race around a circular stadium having a circumference of 1000 meters, the fastest runner and the slowest runner reach the same point at the end of the 5th minute, for the first time after the start of the race. All the runners have the same starting point and each runner maintains a uniform speed throughout the race. If the fastest runner runs at twice the speed of the slowest runner, what is the time taken by the fastest runner to finish the race?

(a) 20mins

(b) 15mins

(c) 10mins

(d) 5mins

55. A train crosses a platform 100 metres long in 60 seconds at a speed of 45 km per hour. The time taken by the train to cross an electric pole, is

(a) 8 seconds

(b) 1 minute

(c) 52 seconds

56. Two vertical lamp-posts of equal height stand on-either side of a road 50m wide. At a point P on the road between them, the elevation of the tops of the lamp-posts are 60° and 30°. Find the distance of P from the lamp post which makes angle of 60°.

(a) 25m

(b) 12.5m

(c) 16.5m

(d) 20.5m

57. There are three coplanar parallel lines. If any p points are taken on each ofthe lines, then find the maximum number of triangles with the vertices of these points.

(a) p2(4p - 3)

(b) p3(4p - 3)

(c) p(4p - 3)

(d) p3

58. A and B throw with one dice for a stake of Rs. 11 which is to be won by the player who first throws 6. If A has the first throw, what are their respective expectations

(a) Rs 7, Rs 4

(b) Rs 6, Rs 5

(c) Rs 4, Rs 7

(d) Rs 5, Rs 6

59. If r, s, and t are consecutive odd integers with r < s < t, which of the following must be true?

(a) rs = t

(b) r + t = 2t - s

(c) r + s = t - 2

(d) r + t = 2s

60. P, Q and R are three consecutive odd numbers in ascending order. If the value of three times P is three less than two times R, find the value of R.

(a) 5

(b) 7

(c) 9

(d) 11

61. Consider the following statements:

When two straight lines intersect, then:

I adjacent angles are complementary

II adjacent angles are supplementary

III opposite angles are equal

IV opposite angles are supplementary

Of these statements:

(a) (I) and (III) are correct

(b) (II) and (III) are correct

(c) (I) and (IV) are correct

(d) (II) and (IV) are correct

62. A pole has to be erected on the boundary of a circular park of diameter 13 metres in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. The distance of the pole from one of the gates is:

(a) 8 metres

(b) 8.25 metres

(c) 5 metres

(d) None these

63. From a square piece of card-board measuring 2a on each side of a box with no top is to be formed by cutting out from each comer a square with sides b and bending up the flaps. The value of b for which the box has the greatest volume is

(a) b = a/5

(b) b = a/4

(c) b = 2a/3

(d) b = a/2

64. The sum of the areas of two circles which touch each other externally is 153π. If the sum of their radii is 15, find the ratio of the larger to the smaller radius

(a) 4

(b) 2

(c) 3

(d) None of these

65. Consider the following statements:

I If ax = b, by = c, cz = a, then xyz = 1

II If P = ax, q = ay, (py qy)z = a2, then xyz = 1

III If xa = yb = zc and ab + bc + ca = 0 then xyz = 1

Of these statements:

(a) I and II are correct

(b) II and III are correct

(c) Only I is correct

(d) All I , II and III are correct

66. If a, b and c are three real numbers, then which of the following is not true?

(a) |a + b| < |a| + |b|

(b) |a - b| < |a| + |b|

(c) |a - b| < |a| - |b|

(d) |a - c| < |a - b| + |b - c|

67. Let S denote the infinite sum

2 + 5x + 9x2 + 14x3 + 20x4 + ........ , where |x| < 1 and the coefficient of xn-1 is 1/2n(n + 3), (n = 1, 2,.....) . Then S equals

(a) 2 - x/(1 - x)3

(b) 2 - x/(1 + x)3

(c) 2 + x/(1 - x)3

(d) 2 + x/(1 + x)3

68. ABCD is a rectangle. The points p and Q lie on AD and AB respectively. If the triangles PAQ, QBC and PCD all have the same areas and BQ = 2, then AQ =

(a) 1 + √5

(b) 1 - √5

(c) √7

(d) 2√7

69. For which value of k does the following pair of equations yield a unique solution for x such that the solution is positive?
x2 - y2 = 0
(x - k)2 + y2 = 1

(a) 2

(b) 0

(c) √2

(d) -√2

70. In an examination, the average marks obtained by students who passed was x %, while the average of those who failed was y %. The average marks of all students taking the exam was z %. Find in terms of x, y and z, the percentage of students taking the exam who failed.

(a) (z - x) / (y - x)

(b) (x - z) / (y - z)

(c) (y - x) / (z - y)

(d) (y - z) / (x - z)

1. (c) 36. (b)
2. (d) 37. (b)
3. (a) 38. (d)
4. (a)
39. (a)
5. (c) 40. (e)
6. (d) 41. (c)
7. (c) 42. (a)
8. (b) 43. (b)
9. (d) 44. (a)
10. (a) 45. (c)
11. (b) 46. (b)
12. (c) 47. (d)
13. (b) 48. (a)
14. (a) 49. (c)
15. (b) 50. (d)
16. (d) 51. (a)
17. (d) 52. (d)
18. (c) 53. (a)
19. (b) 54. (c)
20. (b) 55. (c)
21. (d) 56. (b)
22. (c) 57 (a)
23. (d) 58. (b)
24. (e) 59. (d)
25. (e) 60. (c)
26. (d) 61. (b)
27. (c) 62. (c)
28. (a) 63. (c)
29. (c) 64. (a)
30. (a) 65. (d)
31. (b) 66. (c)
32. (b) 67. (a)
33. (e) 68. (a)
34. (c) 69. (c)
35. (a) 70. (a)

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