Mrs. Brown is dividing 50 students into 3 groups for a class project.

Question

Mrs. Brown is dividing 50 students into 3 groups for a class project. How many children are in the largest group?

(1) The total number of children in the two smaller groups is equal to the number of children in the largest group.

(2) The smallest group contains 6 children.

Archit3110 · Answer

given 
a+b+c=50
#1
 The total number of children in the two smaller groups is equal to the number of children in the largest group
a+b= c
we get 2c=50
c=25
sufficient
#2
The smallest group contains 6 children
insufficient
IMO A

divyadna · Answer

A+B+C=50
A+B=C
C+C=50
C=25
Statement I alone is sufficient.

Statement II: A=6

6+B+C=50

Value of C cannot be derived.
Statement II alone is not sufficient.
Answer is option A

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ScottTargetTestPrep · Answer

Question Stem Analysis:

We are told that 50 students are being divided into three groups. We must determine the number of students in the largest group.

Statement One Alone:

\Rightarrow  The total number of children in the two smaller groups is equal to the number of children in the largest group.

Let L be the number of children in the largest group and let A and B denote the number of children in the remaining two groups. Thus, A + B + L = 50.

We are told that the combined number of children in the two smaller groups is equal to the number of children in the largest group, which means A + B = L. Substituting L = A + B in the equation, we get:

A + B + L = 50

L + L = 50

2L = 50

L = 25

Statement one alone is sufficent.

Eliminate answer choices B, C, and E.

Statement Two Alone:

\Rightarrow  The smallest group contains 6 children.

If one of the groups contain 7 children, then the largest group contains 50 - (6 + 7) = 37 children.

If one of the groups contain 8 children, then the largest group contains 50 - (6 + 8) = 36 children.

Since there are more than one possible values for the number of children in the largest group, statement two alone is not sufficient.

Answer: A

Mrs. Brown is dividing 50 students into 3 groups for a class project.

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Mrs. Brown is dividing 50 students into 3 groups for a class project.

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