2019 CSAT, all questions
UPSC Prelims 2019 · CSAT
Question 50: Basic Numeracy
If the numerator and denominator of a proper fraction are increased by the same positive quantity which is greater than zero, the resulting fraction is
aalways less than the original fraction
balways greater than the original fraction
calways equal to the original fraction
dsuch that nothing can be claimed definitely
AnswerUPSC’s answer is (b).
Take a proper fraction a/b with a < b and add x > 0 to both. Compare (a + x)/(b + x) with a/b by cross-multiplying: b(a + x) - a(b + x) = x(b - a), which is positive because b > a. So the new fraction is always greater. Example: 1/2 becomes 2/3, which is larger. The result is reversed for improper fractions.
Why each option is right or wrong
- (a) Wrong: the fraction increases for a proper fraction.
- (b) Right: the difference x(b - a) is positive.
- (c) Wrong: equality would need a = b.
- (d) Wrong: a definite claim can be made.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2019, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.