ACET 2017 Answer Key (Jun)

Institute of Actuaries of India
Solutions for ACET June 2017

Mathematics
1. B. or, (y). Thus

2. C. Thus .

3. D. . Thus,
. It follows that and .

4. A. . But Hence the result.

5. B. Let and . So Further,
If is the angle between and , we have . Thus, .

6. D. . Therefore,

7. C. .

8. B. The given matrix contains 3 columns of and Hence rank = 3.

9. C. The expression is an identity if
hold at the same time. Thus

10. C. = Thus

11. D. Note that . Thus maximum value = 20.

12. A. Clearly for any real or, or,
.

13. B. or, as Thus .

14. A. Put so given integral as

15. D. Let the requisite sum be . Hence, , or, , assuming

16. B. Let so and As per given
condition so that
Thus

17. D. Thus =1 and which contradict each
other. Hence is non-existent.

18. C. Limit of as tends to zero is

Statistics
19. A. It is generally known that A.M. G.M. H.M. The three means are equal only when
all the numbers are equal, but they are said to be distinct. Thus, B is not correct.

20. B. As 77 corresponds to the highest frequency 21.

21. C. Variance = Now cannot hold for any integer .
Options A, B and D are possible for different values of .

22. A. Note that . The transformation does not change or but changes by the
multiplying factor Hence the answer.

23. C. total number of matches = 30, even. Median =
=

24. B. Required probability = [
as and are mutually
exclusive events.

25. C. Nine distinct and ordered digits can be chosen from 10 (0 to 9) numbers in
ways, out of which 0 will appear in the first place in ways. Thus the number
of numbers with distinct digits = 10! – 9! = . The total number of 9 digit numbers is
. Therefore, the probability that the selected number has distinct digits is
.

26. B. event that the sum is 7 and : event that 2 appears at least once. So
, and Required probability
=

27. D. Sample space = Clearly,
Mean = = 2.

28. C. The probability of correct answer ; so the probability of wrong answer
Clearly where is the number of correct answers and

Required probability =

29. D

30. B

31. D.

Data Interpretation
32. A. City T contributes the largest summand to the sum in Problem 31. The number is
10500.

33. B. City P has the same second lowest number of movie watchers which is 4000.

4000= 2000/(1-50%)

34. D. The total number is

35. A. The average sales cannot be as small as Rs. 642 lakh, as there are many large values to
offset the few marginally smaller values. For the same reason, Rs. 383 lakh is too small a
value for average cost.

36. C. 4%. 4% = 20% of 20% .

37. D. Cannot be determined. Only percentage or occurrence of proteins in bones is provided
but not the overall percentage of bones in the body.

38. B. 10 lakhs. Let the total production in 2001 be .

English
39. D
40. D
41. C
42. B
43. B
44. A
45. B
46. B
47. C
48. A
49. A
50. B
51. B
52. D
53. C
54. A
55. C
56. D
57. C
58. A
59. B
60. D
61. B
62. A

Logical Reasoning

63. A

64. A. Diagram A has a black dot inside a triangle, which is inside a circle, which in turn is
inside a rectangle. In diagram B, the black dot is intact, the order of containment between
the second and third items (triangle and circle) is reversed and the outermost rectangle is
missing.

In diagram C, the second and third items, in order of containment, are a square and a
triangle. By reversing their order and dropping the outermost rectangle, we have the
shape given in option (1).

65. D. Drizzle is weaker/slower than rain; walking is slower than running.

66. B. In a normal year the first day and the last day of the year is the same. In a leap year the
last day is one day more than the first day. In this question it is a leap year. So 16(Jan)+
29(Feb) + 15(March) = 60 days.

67. D. The lady is the wife of grandson of Amit's mother i.e., the lady is the wife of son of
Amit. Hence, Amit is the father-in-law of the lady.

68. B. .

20 60 12
M P

69. B. A is sitting next to B, while A and C are sitting together. Therefore, A is sitting in between
B and C.

(The given facts imply that the seated persons from left to right are E B A C D, but this is
not needed to answer the question.)

70. A. The number of hours from 8:00 p.m. on Thursday to 8:00 a.m. on Monday is 84. In 84
hours, the watch lost 12 minutes. But to show the correct time, the watch has to lose 5
minutes. This would happen in hours. 35 hours from 8:00 p.m. on Thursday
is 7:00 a.m. on Saturday.