Multiple choice

Directions: In the following problem, a question is followed by three statements numbered (I), (II), and (III). Read the statements carefully and determine which of the given statements is/are sufficient/necessary to answer the question. There are different numbers of students in classes A, B and C. How many are there in class B? I. If 30 students from class A are shifted to class C, then the number of students in class C becomes 180, which is 6 times that in class A. II. If 10 students are shifted from class C to class B, then number of students in both classes becomes the same. III. Ratio of numbers of students in classes C and A is 2 : 1.

  1. Only statements I and III

  2. Only statements II and III

  3. Only statements I and II

  4. Only statement II and either statement I or statement III

  5. All statements together
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

From I: A-30 = (C+30)/6. From III: C/A = 2/1. These two allow finding A and C. From II: C-10 = B+10. With C known from I and III, B can be found. Thus I and II are sufficient (or I, II, III). The question asks for the minimum sufficient set, which is I and II.

AI explanation

From statement one, shifting 30 students from A to C leaves C with 180 students and A with 30 students, establishing the original counts as A equals 60 and C equals 150. Statement two provides the necessary relationship for B by stating that shifting 10 students from C to B equalizes their numbers, leading to the equation B plus 10 equals 150 minus 10, which solves to B equals 130. Statement three only gives a ratio between C and A, so it cannot find B without more information. Therefore, only statements one and two together are necessary and sufficient to find the number of students in class B.

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