Directions : The charts given below represents data of number of students of…
2021
Directions : The charts given below represents data of number of students of four colleges P, Q, R and S. Based on the information given below, answer the questions that follow:
Note: 1. Number of girls in college Q is 10.
2. Difference between number of boys and girls in college P is 100. (Number of boys is greater than number of girls).
Which of the following is true statement?
- A.
Total number of students is least in college S
- B.
Total boys in college R is 360
- C.
Total girls in college P is 300
- D.
Difference between total number of boys in college P and that in S is 50
- E.
None of these
Show answer & explanation
Correct answer: B
Concept. In a two-pie data-interpretation set, each pie's slice percentage is taken on that pie's OWN total. Here pie 1 splits the 2500 students and pie 2 splits the 1200 boys, so for any college: students = (student-%) x 2500, boys = (boys-%) x 1200, and girls = students - boys. The two unknown student slices satisfy 100% - 20% - 25% = 55% (Q + R), and the two unknown boys slices satisfy 100% - 20% - 30% = 50% (P + S); the two textual notes pin them down.
Total girls = 2500 - 1200 = 1300. Known boys slices: Q = 20% x 1200 = 240, R = 30% x 1200 = 360.
Note 1 fixes Q: girls in Q = 10, so students in Q = 240 + 10 = 250, which is 250/2500 = 10% (this is x). Hence R's student share y = 55% - 10% = 45%, giving R = 45% x 2500 = 1125 students.
College P has 20% x 2500 = 500 students. Note 2 gives boys - girls = 100 with boys + girls = 500, so boys in P = 300 and girls in P = 200. Thus P's boys share a = 300/1200 = 25%, so S's boys share b = 50% - 25% = 25%, giving boys in S = 25% x 1200 = 300.
College S has 25% x 2500 = 625 students; girls in S = 625 - 300 = 325. College R: girls = 1125 - 360 = 765.
Statement | Computed value | True? |
|---|---|---|
Least students college | Q = 250 is least (P 500, S 625, R 1125) | No - it is Q, not S |
Boys in R | 30% x 1200 = 360 | Yes |
Girls in P | 500 - 300 = 200 | No - 200, not 300 |
Boys(P) - Boys(S) | 300 - 300 = 0 | No - 0, not 50 |
Result. Only the boys-in-R statement, 360, survives every check; the other three contradict the computed figures. Cross-check on the boys pie: P 300 + Q 240 + R 360 + S 300 = 1200, matching the stated total of 1200 boys, so the slice values are consistent.