What is the number of integers that are common to both set

[BTGmoderatorDC]

What is the number of integers that are common to both set S and set T ?

(1) The number of integers in S is 7, and the number of integers in T is 6.
(2) U is the set of integers that are in S only or in T only or in both, and the number of integers in U is 10.


OA C

Source: Official Guide

[Jay@ManhattanReview]

What is the number of integers that are common to both set S and set T ?

(1) The number of integers in S is 7, and the number of integers in T is 6.
(2) U is the set of integers that are in S only or in T only or in both, and the number of integers in U is 10.

OA C

Source: Official Guide

Let's take each statement one by one.

(1) The number of integers in S is 7, and the number of integers in T is 6.

Certainly insufficient.

(2) U is the set of integers that are in S only or in T only or in both, and the number of integers in U is 10.

Certainly insufficient.

(1) and (2) together

Say the number of integers in Set U, Set S and Set T are u, s, and t, respectively. And the common integers between Set S and Set T is b. We have to get the value of b.

=> u = s + t - b
10 = 7 + 6 - b => b = 3. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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