UPSC Prelims 2023 · CSAT
Question 69: Basic Numeracy
There are large number of silver coins weighing 2 gm, 5 gm, 10 gm, 25 gm, 50 gm each. Consider the following statements :
- 1.To buy 78 gm of coins one must buy at least 7 coins.
- 2.To weigh 78 gm using these coins one can use less than 7 coins.
Which of the statements given above is/are correct ?
AnswerUPSC’s answer is (c).
Statement 1 (buying, coins on one side): 78 is even, so the number of odd coins (5, 25) used must be even. With only 2, 10 and 50: 50 + 10 + 10 + 2 + 2 + 2 + 2 = 78 uses 7 coins, and no other combination uses fewer. Statement 2 (weighing on a balance, coins on both pans): the 78 g object plus a 2 g coin balances 50 + 25 + 5 = 80, using 4 coins, fewer than 7. Both statements are true.
- 1. The smallest way to make 78 by buying uses 7 coins.
- 2. Weighing with coins on both pans, 78 + 2 = 50 + 25 + 5 uses 4 coins.
How you could have got this
- If you were sure statement 1 is correct, (b) and (d) go: each of them leaves 1 out.
What you needed to know: The smallest way to make 78 by buying uses 7 coins.
- Then, if you were sure statement 2 is correct, (a) goes: it leaves 2 out.
What you needed to know: Weighing with coins on both pans, 78 + 2 = 50 + 25 + 5 uses 4 coins.
Only (c) 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 2 is also true, using a balance with coins on both pans.
- (b) Wrong: statement 1 is also true; 7 is the minimum for buying.
- (c) Right: buying needs at least 7 coins, but weighing needs only 4.
- (d) Wrong: both statements are true.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2023, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.