Anita's mathematics test had 70 problems carrying equal marks i.e., 10 arithmetic, 30 algebra and 30 geometry. Although she answered 70% of the arithmetic, 40% of the algebra and 60% of the geometry problems correctly, she did not pass the test because she got less than 60% marks. The number of more questions she would have to answer correctly to earn a 60% passing marks is :
- (a) 1
- (b) 5 ✓ UPSC's answer
- (c) 7
- (d) 9
Why the answer is (b)
• Total marks available are 700 (70 problems × 10 marks each), and the passing threshold is 60%, which equals 420 marks.
• Anita answered 70% of 10 arithmetic problems correctly, scoring 7 × 10 = 70 marks.
• She answered 40% of 30 algebra problems correctly, scoring 12 × 10 = 120 marks.
• She answered 60% of 30 geometry problems correctly, scoring 18 × 10 = 180 marks.
• Her total score is 70 + 120 + 180 = 370 marks, which is 50 marks short of the required 420 marks.
• Since each problem carries 10 marks, she needs to answer 50 / 10 = 5 more questions correctly to reach the passing mark.
Why the other options are wrong
- (a) 1
- Answering only 1 more question would add 10 marks, bringing her total to 380, which is still below the 420 passing mark.
- (c) 7
- Answering 7 more questions would add 70 marks, bringing her total to 440, which exceeds the minimum required 420 marks.
- (d) 9
- Answering 9 more questions would add 90 marks, bringing her total to 460, which is significantly higher than the minimum required 420 marks.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2016, held on 7 August 2016. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.