UPSC Prelims 2024 · CSAT
Question 50: Basic Numeracy
The total cost of 4 oranges, 6 mangoes and 8 apples is equal to twice the total cost of 1 orange, 2 mangoes and 5 apples. Consider the following statements :
- 1.The total cost of 3 oranges, 5 mangoes and 9 apples is equal to the total cost of 4 oranges, 6 mangoes and 8 apples.
- 2.The total cost of one orange and one mango is equal to the cost of one apple.
Which of the statements given above is/are correct?
AnswerUPSC’s answer is (c).
Write the first equation with o, m, a for the prices: 4o + 6m + 8a = 2(o + 2m + 5a) = 2o + 4m + 10a. Moving terms gives 2o + 2m = 2a, so o + m = a. That is statement 2. For statement 1: (3o + 5m + 9a) − (4o + 6m + 8a) = a − o − m = 0, so the two totals are equal. Both statements are correct.
- 1. The difference between the two totals is a − o − m, which is 0.
- 2. Simplifying the given equation gives o + m = a.
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 difference between the two totals is a − o − m, which is 0.
- Then, if you were sure statement 2 is correct, (a) goes: it leaves 2 out.
What you needed to know: Simplifying the given equation gives o + m = a.
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 correct.
- (b) Wrong. Statement 1 is also correct.
- (c) Right. Both follow from o + m = a.
- (d) Wrong. Both are correct.
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.