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

21. In the sequence 1, 5, 7, 3, 5, 7, 4, 3, 5, 7, how many such 5s are there which are not immediately preceded by 3 but are immediately followed by 7? [2019-II]

(a) 1
(b) 2
(c) 3
(d) None

Correct Answer: (a) 1

Solution:According to the question,

1, 5, 7, 3, 5, 7, 4, 3, 5, 7.

Option (a) is correct.

22. A joint family consists of seven members A, B, C, D, E, F and G with three females. G is a widow and sister-in-law of D's father F, B and D are siblings and A is daughter of B. C is cousin of B. Who is E? [2019-II]

(1) Wife of F

(2) Grandmother of A

(3) Aunt of C

Select the correct answer using the code given below:

(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:According to the question,

So, E may be wife of F; Grandmother of A and Aunt of C

∴ Option (d) is correct.

23. If $ means 'divided by'; @ means 'multiplied by'; # means 'minus'; then the value of 10#5@1$5 is [2019-II]

(a) 0
(b) 1
(c) 2
(d) 9

Correct Answer: (d) 9

Solution:10 # 5 @ 1 $ 5

= 10 - 5 × 1 / 5 = 10 - 5 × 1/5 = 10 - 1 = 9 .

24. If F stands second in the ranking, then the position of B is [2019-II]

Six students A, B, C, D, E and F appeared in several tests. Either C or F scores the highest. Whenever C scores the highest, then E scores the least, Whenever F scores the highest, B scores the least, In all the tests they got different marks; D scores higher than A, but they are close competitors; A scores higher than B; C scores higher than A.

(a) Third
(b) Fourth
(c) Fifth
(d) Sixth

Correct Answer: (c) Fifth

Solution:From case I (iii), When F stand second B is fifth.

Case - I: When C gets highest marks,
(i) E < F < B < A < D < C or,
(ii) E < B < F < A < D < C or,
(iii) E < B < A < D < F < C.
Case - II: When F Scores highest,
(i) B < A < D < C < E < F. or,
(ii) B < A < D < E < C < F.

25. If B scores the least, the rank of C will be [2019-II]

Six students A, B, C, D, E and F appeared in several tests. Either C or F scores the highest. Whenever C scores the highest, then E scores the least, Whenever F scores the highest, B scores the least, In all the tests they got different marks; D scores higher than A, but they are close competitors; A scores higher than B; C scores higher than A.

(a) Second
(b) Third
(c) Fourth
(d) Second or third

Correct Answer: (d) Second or third

Solution:From case II, When B score the least then C stand either second or third.

Case - I: When C gets highest marks,
(i) E < F < B < A < D < C or,
(ii) E < B < F < A < D < C or,
(iii) E < B < A < D < F < C.
Case - II: When F Scores highest,
(i) B < A < D < C < E < F. or,
(ii) B < A < D < E < C < F.

26. If E is ranked third, then which one of the following is correct? [2019-II]

Six students A, B, C, D, E and F appeared in several tests. Either C or F scores the highest. Whenever C scores the highest, then E scores the least, Whenever F scores the highest, B scores the least, In all the tests they got different marks; D scores higher than A, but they are close competitors; A scores higher than B; C scores higher than A.

(a) E gets more marks than C
(b) C gets more marks than E
(c) A is ranked fourth
(d) D is ranked fifth

Correct Answer: (b) C gets more marks than E

Solution:From case - II (ii), When E ranked third, then C score more then E.

Case - I: When C gets highest marks,
(i) E < F < B < A < D < C or,
(ii) E < B < F < A < D < C or,
(iii) E < B < A < D < F < C.
Case - II: When F Scores highest,
(i) B < A < D < C < E < F. or,
(ii) B < A < D < E < C < F.

27. Which one of the following statements is correct? [2019-II]

S1: Twice the weight of Sohan is less than the weight of Mohan or that of Rohan.

S2: Twice the weight of Rohan is greater than the weight of Mohan or that of Sohan.

(a) Weight of Mohan is greatest
(b) Weight of Sohan is greatest
(c) Weight of Rohan is greatest
(d) 'Whose weight is greatest' cannot be determined

Correct Answer: (d) 'Whose weight is greatest' cannot be determined

Solution:From S1 and S2, either Rohan or Mohan's weight is greatest but we can't determined whose weight is greatest.

S1 → 2 × (Sohan's weight) < {(Mohan's weight) or (Rohan's weight)}
S2 → 2 × (Rohan's weight) > {(Mohan's weight) or (Sohan's weight)}

28. Which one of the following statements is correct? [2019-II]

S1: Twice the weight of Sohan is less than the weight of Mohan or that of Rohan.

S2: Twice the weight of Rohan is greater than the weight of Mohan or that of Sohan.

(a) Weight of Mohan is least
(b) Weight of Sohan is least
(c) Weight of Rohan is least
(d) 'Whose weight is least' cannot be determined

Correct Answer: (b) Weight of Sohan is least

Solution:From S1, weight of Sohan is least.

S1 → 2 × (Sohan's weight) < {(Mohan's weight) or (Rohan's weight)}
S2 → 2 × (Rohan's weight) > {(Mohan's weight) or (Sohan's weight)}

29. What is X in the sequence [2019-II]

132, 129, 124, 117, 106, 93, X?

(a) 74
(b) 75
(c) 76
(d) 77

Correct Answer: (c) 76

Solution:

30. If the numerator and denominator of a proper fraction are increased by the same positive quantity which is greater than zero, the resulting fraction is [2019-II]

(a) always less than the original fraction
(b) always greater than the original fraction
(c) always equal to the original fraction
(d) such that nothing can be claimed definitely

Correct Answer: (b) always greater than the original fraction

Solution:A proper fraction is one which is less than 1.
when same positive number is added in numerator and de-nominator then, fraction value increases from original value.
For example, when 1 is added to both numerator and denominator of 3/7, then 3 + 1/7 + 1 = 4/8

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

21. In the sequence 1, 5, 7, 3, 5, 7, 4, 3, 5, 7, how many such 5s are there which are not immediately preceded by 3 but are immediately followed by 7? [2019-II]

22. A joint family consists of seven members A, B, C, D, E, F and G with three females. G is a widow and sister-in-law of D's father F, B and D are siblings and A is daughter of B. C is cousin of B. Who is E? [2019-II]

23. If $ means 'divided by'; @ means 'multiplied by'; # means 'minus'; then the value of 10#5@1$5 is [2019-II]

24. If F stands second in the ranking, then the position of B is [2019-II]

25. If B scores the least, the rank of C will be [2019-II]

26. If E is ranked third, then which one of the following is correct? [2019-II]

27. Which one of the following statements is correct? [2019-II]

28. Which one of the following statements is correct? [2019-II]

29. What is X in the sequence [2019-II]

30. If the numerator and denominator of a proper fraction are increased by the same positive quantity which is greater than zero, the resulting fraction is [2019-II]

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