UPSC Prelims 2006 · General Studies
Question 96: Logical Reasoning and Mental Ability
Each of the persons A, B, C, D and E possesses unequal number (<10) of similar items. A, B and C possess 21 items in all, while C, D and E possess 7 items in all. How many items do A and B possess in all?
AnswerThe answer is (b).
Each person has some items (at least one), all different and below 10. C, D and E total 7 with three different numbers: the only possible set is 1, 2 and 4. A, B and C total 21, and since the largest A + B can be is 9 + 8 = 17, C must be at least 4, so C = 4 and A + B = 17 (9 and 8). So A and B together have 17.
How you could have got this
No shortcut here: in a “how many” question, ruling out options doesn’t help. Every statement has to be judged.
This follows an unofficial answer: UPSC has not published its key for this year, and if that answer is wrong, so is this path.
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) 15 would need C = 6, which is not in the set {1, 2, 4}.
- (b) Correct: C = 4, so A + B = 21 - 4 = 17.
- (c) 18 would need C = 3, which is not in the set {1, 2, 4}.
- (d) The data are enough to fix the answer.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2006, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.