ACET 2018 Answer Key (Jan)

Institute of Actuaries of India
ACET January 2018 Solutions
Mathematics

1. C. is the sum of the squares of n positive integers. Hence,
is a multiple of 6. The other choices are not always true.

2. A. .

3. A. The following information given.
F(x)

2.5 0.3554
3.5 0.5221

Using linear interpolation, we have , giving
approximately.
Alternative method: Since 3 is the mid-point of 2.5 and 3.5,

4. D. implies , giving .
This implies that either or

Thus for the inequality to hold

5. A. If are the roots of the quadratic equation the sum of
the roots is and product of the roots is 1.Thus, if are the roots of an equation, then
the sum of the roots is and the product of the roots is = 1. The only
quadratic equation satisfying these conditions is choice A.

6. B. In the expansion of , the general term is

The coefficient of is the coefficient of when , which is .

7. D. . By L’ Hospitals rule we have the given limit equal
to =

8. C. For the curve , and . Equating
gives . Since , it is a minima of .

9. A. The maximum/minimum value of the function

in the interval
is obtained by equating the first derivative of

=0.

Or

Or

Or giving .
The second derivative is hard to compute, but it can be seen that has the same
sign as , which is negative in the interval
. Therefore, is decreasing over this interval and has a minimum at
.

10. B. , Then ( =

Similarly , ( =

Hence, = = .

11. C If , then ;

12. A. .

13. B. . This implies . Putting
and putting .

14. B. .

15. D. The resultant has same magnitude as , and therefore the three vectors
form an isosceles triangle. By considering half-base and one side of the triangle, we
have angle between and as .

16. C. The inverse of the matrix is

17. A. .

18. B. . The rank of this matrix is 1.

Statistics
19. B. Arrangement: BBBBGGG or GGGBBBB. The number of ways the boys can sit
together and so can all the girls is . Required probability
.

20. A.
= (Since is subset of )
=
This implies
(Alternatively, since , . Therefore, .)

21. C. Let M: Male, F: Female, C: Colorblind.

Find

22. B. Median So Hence mean is
.
23. D. Standard deviation of new observations is |-4| .
24. C. Accident cost over a year would be Rs. Rs. .
25. B.

26. A. Suppose is the median of . Then .
This implies .
So . This implies .

27. C. = 0 (because the integrand is an odd function).

28. A. .

This implies

29. D. . This implies or

30. B. .

31. C. Least squares estimate of is obtained by minimizing .

This gives .

Data Interpretation

32. A. ,
.

33. D. It is clear from the frequency distribution.

34. A. The percentage of people below 30 years age = 7 +14 +7+7+7 = 42.

35. C. The percentage of people 55 and above = 10+6+6 =22. The percentage of people
above 65 = 6+6 = 12. The percentage of people above 55 years will lie between 12 and
22.

36. A. The percentage of people 65 and above is 6+6 =12. The percentage of people in the
age group [45, 65) = 14+10 =24. So the ratio is 12:24 = 1:2.

37. D. Inspecting the graph, it can be easily obtained.

38. B. By inspecting the graph, it can be easily obtained that maximum fall occurred in the
year 1990.

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

Logical Reasoning
63. B
64. A
65. C 17 June 2017 (day of this ACET exam) is a Saturday. The number of years in between
17-6-2006 and 17-6-2017 is 11. Number of odd days = 11 + 3 =14 (3 leap years among
the 11 years). Since 14 is a multiple of 7, 17 June 2006 must have been a Saturday too.

66. C. M, I, R, A, C, L and E are mapped to N, K, U, E, H, R and L, respectively. Therefore,
in this code, RECLAIM would be coded as ULHREKN.
67. C. The correct order is :
Plant Cotton Yarn Cloth Saree
2 4 1 5 3

68. B. An ounce measures weight; the other choices measure length.
69. C.
Cricket
Football
18 7 9
3
5 6
12
Basketball

Number of players who play only one game = 18 + 9 +12 = 39

70. C. The set of all terrorists is a subset of the intersection of the set of guilty and
criminals. Hence, some guilty are criminals.