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A pie chart shows the percentage distribution of the total number of questions attempted by four students A, B, C, and D. The total number of questions attempted by all the students is 800. A = x%, B = 25%, C = y%, D = 24%. Find the value of \((x - y)\). Statement I: Among the four students, the number of questions attempted by B is the highest and that attempted by D is the lowest. The difference between the number of questions attempted by A and D is 20. Statement II: The number of questions attempted by B is greater than 220 and that attempted by D is less than 190. The values of x and y are distinct positive integers. If the number of questions attempted by D in the test is 160 and the number of questions attempted by E is 52 more than the number attempted by B, and if the number of questions attempted in History, Math, and English are in the ratio 7:6:2 respectively by E, find the difference between the number of questions attempted by E in History and English.

1. 170
2. 180
3. 150
4. 100

Correct answer: 100

Solution

D attempts 24% of 800, which is 192, but the later condition gives D = 160 for the second part of the question. Then B = 160 + 52 = 212. Since E's subject-wise attempts are in the ratio 7:6:2, the difference between History and English is \((7-2)\) parts out of 15; with total 300, one part is 20, so the difference is 5 × 20 = 100.

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