\(Q\) is a set of 7 integers, \(m\) and \(n\) are two of the

[BTGmoderatorLU]

Source: Economist GMAT Tutor

\(Q\) is a set of 7 integers, \(m\) and \(n\) are two of the numbers in \(Q\). Excluding \(m\) and \(n\), the largest integer in \(Q\) is 21 and the smallest integer is 1. What is the range of \(Q\)?

1) \(m > n > 1\)
2) \(n < m < 20\)

The OA is C

[Jay@ManhattanReview]

Source: Economist GMAT Tutor

\(Q\) is a set of 7 integers, \(m\) and \(n\) are two of the numbers in \(Q\). Excluding \(m\) and \(n\), the largest integer in \(Q\) is 21 and the smallest integer is 1. What is the range of \(Q\)?

1) \(m > n > 1\)
2) \(n < m < 20\)

The OA is C

Range of a set = Largest number - Smallest number

We need to determine whether m or/and n is one of the largest number and the smallest number.

Let's take each statement one by one.

1) \(m > n > 1\)

=> Smallest number = 1 (neither m nor m is smallest; however, m can still be the largest number. Insufficient.

2) \(n < m < 20\)

=> Largest number = 21 (neither m nor m is largest; however, n can still be the smallest number. Insufficient.

(1) and (2) together

From (1), we get Smallest number = 1 and from (2), we get Largest number = 21; thus, range = 21 - 1 = 20. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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