UPSC Prelims 2005 Q118: Science & Technology – Quantitative Aptitude
- (a) 41
- (b) 47
- (c) 53
- (d) 58
Answer: (d) 58
Explanation
> Note for students: As printed, every option is impossible (the total is 6x + 21). The published key is (d) 58, which is correct only if clue (ii) means 'D has 4 items less than B'. Choose (d) 58 or skip it to avoid a negative mark.
Items held by six persons
| Person | Items in terms of E = x |
|---|---|
| E | x |
| C | x + 2 (C has 2 more than E) |
| A | x + 5 (A has 3 more than C) |
| F | x + 6 (E has 6 less than F) |
| D | x + 3 (F has 3 more than D) |
| B | x + 5 (D has 2 less than B) |
| Total | 6x + 21 |
With the clues exactly as printed, the total is 6x + 21, which is always 3 more than a multiple of 6. None of 41, 47, 53 and 58 has that form, so every option 'cannot' be the total and the question has no unique answer. The published key is (d) 58; it is the unique answer only if clue (ii) is read as 'D has 4 items less than B', which gives 6x + 23, and then 41, 47 and 53 are possible while 58 is not.
Answer: (d) 58 (published key; as printed, all four totals are impossible).
Why each option is right or wrong
- (a) Incorrect. As printed it is impossible too, but under the likely intended clue it is possible.
- (b) Incorrect. As printed it is impossible too, but under the likely intended clue it is possible.
- (c) Incorrect. As printed it is impossible too, but under the likely intended clue it is possible.
- (d) CORRECT. This is the published key and the only total impossible under the likely intended clue.
Key point
Express everyone in one variable, sum, then test each option for divisibility.
Remember
As printed, the total is of the form 6x + 21.
Common mistakes
- Mis-reading D less than B by 2 instead of 4.
- Not expressing all six in terms of one person.
- Testing options without finding the form of the total.
Exam tip
Total = 6x + 21 as printed (or 6x + 23 with 'four less').
Sources
- Arun Sharma — How to Prepare for Quantitative Aptitude for the CAT (Algebra)
- NCERT Class VIII Mathematics — Linear Equations in One Variable