UPSC Prelims 2024 · CSAT
Question 76: Logical Reasoning and Mental Ability
If P 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 :
- 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?
AnswerUPSC’s answer is (d).
The codes mean: P is greater than, Q is less than, R is not greater than (so at most), S is not less than (so at least), T is equal to. Statement 1: 2x ≥ 3y and 3x = 4z give 6x ≥ 9y and 6x = 8z, so 8z ≥ 9y, which contradicts 9y > 8z. Statement 2: x < 2y and y ≤ z give x < 2z, not x ≤ z; for example y = z = 10 and x = 15. Both are incorrect.
- 1. 6x is at least 9y and equals 8z, so 8z ≥ 9y, not 9y > 8z.
- 2. x < 2z does not guarantee x ≤ z; x = 15, y = z = 10 is a counter-example.
How you could have got this
- If you were sure statement 1 is not correct, (a) and (c) go: each of them includes 1.
What you needed to know: 6x is at least 9y and equals 8z, so 8z ≥ 9y, not 9y > 8z.
- Then, if you were sure statement 2 is not correct, (b) goes: it includes 2.
What you needed to know: x < 2z does not guarantee x ≤ z; x = 15, y = z = 10 is a counter-example.
Only (d) is left. This one needs every statement.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) Wrong. Statement 1 gives 8z ≥ 9y, not 9y > 8z.
- (b) Wrong. A counter-example with y = z = 10 and x = 15 breaks statement 2.
- (c) Wrong. Both statements fail.
- (d) Right. Both conclusions fail.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2024, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.