Last Updated on May 9, 2023
GMAT OFFICIAL GUIDE DS
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.
Answer: E
