Mental Ability, Analytical and Logical Reasoning (UPSC) Part-VIII

Total Questions: 28

11. The calendar for the year 2025 is same for [2024-II]

(a) 2029
(b) 2030
(c) 2031
(d) 2033

Solution:Year 2025 is a non-leap year. Number of odd days between year 2025 and year 2031 = 7 days

And year 2031 is also a non-leap year.

∴ year 2025 will be same and year 2031.

12. Consider the sequence [2024-II]

A_BCD_BBCDABCDABC_D that follows a certain pattern. Which one of the following completes the sequence?

(a) B, A, D, C
(b) B, A, C, D
(c) A, A, C, D
(d) A, A, D, C

Correct Answer: (c) A, A, C, D

Solution:Total number of letters = 20.

On Dividing by 4, we get 5 group of letters.

Pattern : A A B, C D, A B B C D, A B C C D, A B C D D.

13. A father said to his son, "n years back I was as old as you are now. My present age is four times your age n years back". If the sum of the present ages of the father and the son is 130 years, what is the difference of their ages? [2024-II]

(a) 30 years
(b) 32 years
(c) 34 years
(d) 36 years

Correct Answer: (a) 30 years

Solution:Let the age of father be X and the age of son be Y.

According to the question.

(X – n) = Y

or X – Y = n (i)

and X = 4 (Y – n)

or X = 4Y – 4n

or (4Y – X)/4 = n (ii)

From equation (i) and (ii), we get:

X – Y = (4Y – X)/4

or 4X – 4Y = 4Y – X

or 5X = 8Y

or X/Y = 8/5

or we can say that, X = 8k and Y = 5k

Given that, X + Y = 130

or 8k + 5k = 130

or 13k = 130

or k = 10

Hence, age of father (X) = 8k = 80 years

and age of son (Y) = 5k = 50 years

Difference in their ages = 80 – 50 = 30 years

14. Consider the following [2024-II]

1. 1000 litres = 1 m³

2. 1 metric ton = 1000 kg

3. 1 hectare = 10000 m²

Which of the above are correct?

(a) 1 and 2 only
(b) 2 and 3 only
(c) 1 and 3 only
(d) 1, 2 and 3

Correct Answer: (d) 1, 2 and 3

Solution:All three statement are correct

15. In the expression 5 * 4 * 3 * 1 * is chosen from +,-, x each at most two times. What is the smallest non-negative value of the expression? [2024-II]

(a) 3
(b) 2
(c) 1
(d) 0

Correct Answer: (d) 0

Solution:5 * 4 * 3 * 2 * 1

5 - 4 - 3 + 2 × 1

5 - 7 + 2 = 0

16. A Main Statement is followed by four Statements P, Q, R and S. Choose the ordered pair of the Statements where the first Statement implies the second, and the two Statements are logically consistent with the Main Statement. [2024-II]

Main Statement:

Pradeep becomes either a Director or a Producer

Statement P: Pradeep is a Director

Statement Q: Pradeep is a Producer

Statement R: Pradeep is not a Director

Statement S: Pradeep is not a Producer

Select the correct answer

(a) SP only
(b) RQ only
(c) Both SP and RQ
(d) Neither SP and RQ

Correct Answer: (c) Both SP and RQ

Solution:If Pradeep is not a producer (S), he must be a Director (P).

If Pradeep is not a Director (R), he must be a Producer (Q). Both pairs are logically consistent with the main statement.

Hence, logically consistent with main statement are both SP and RQ.

17. If a + b means a - b; a - b means a x b; a x b means a / b; a / b means a + b, then what is the value of 10 + 30 - 100 x 50 / 25? (Operations are to be replaced simultaneously) [2024-II]

(a) 15
(b) 0
(c) -15
(d) -25

Correct Answer: (d) -25

Solution:a + b ⇒ a – b ; a – b ⇒ a × b

a × b ⇒ a ÷ b ; a ÷ b ⇒ a + b

Then, 10 + 30 – 100 × 50 ÷ 25

⇒ 10 – 30 × 100 ÷ 50 + 25

⇒ 10 – 30 × 2 + 25 = – 25

18. IfP means 'greater than (>)'; Q means 'less than (<)'; R means 'not greater than (<̷); S means 'not less than (<̷)' and T means 'equal to (=)', then consider the following statements: [2024-II]

1. If 2x (S) 3y and 3x (T) 4z, then 9y (P) 8z.
2. If x (Q) 2y and y (R) z, then x (R) z.
Which of the statements given above is/are correct?

(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2

Correct Answer: (d) Neither 1 nor 2

Solution:

1. 2x ≥ 3y and 3x = 4z

⇒ 4x ≥ 9y and 6x = 8z

⇒ 8z > 9y ∴ 9y(p)8z is wrong.

2. x < 2y and y ≤ z ⇒ 2y ≤ 2z.

∴ x < 2z. so, x ≤ z may be correct or wrong.

Hence, both statement is wrong.

19. If in a certain code, 'ABCD' is written as 24 and 'EFGH' is written as 1680, then how is 'IJKL written in that code? [2024-II]

(a) 11880
(b) 11240
(c) 7920
(d) 5940

Correct Answer: (a) 11880