GMAT OFFICIAL GUIDE DS – The range of the numbers in set S…

Solution:

We are given that the range of the numbers in set S is x and that the range of the numbers in set T is y. We also know that all of the numbers in set T are included in set S. We must determine whether x is greater than y or, in other words, whether the range of set S is greater than the range of set T. Recall that the formula for the range of a set of numbers is: range = largest number – smallest number.

Statement One Alone:

Set S consists of 7 numbers.

Without knowing anything about the values of the numbers in set S or anything about set T, statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

Set T consists of 6 numbers.

Without knowing anything about the values of the numbers in set T or anything about set S, statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

From statements one and two we know that set S contains 7 numbers and that set T contains 6 numbers. We also know from the given information that all of the numbers in set T are also in set S. However, we still do not have enough information to determine whether the range of set S is greater than the range of set T. Let’s test a few cases to illustrate.

Case #1

set T = {1,2,3,4,5,6}

y = range of set T = 6 – 1 = 5

set S = {1,2,3,4,5,6,7}

x = range of set S = 7 – 1 = 6

In the above case, x is greater than y.

Case #2

set T = {1,2,3,4,5,6}

y = range of set T = 6 – 1 = 5

set S = {1,2,3,4,5,6,6}

x = range of set S = 6 – 1 = 5

In above case, x = y.