Data Sufficiency

AbeNeedsAnswers wrote:The range of the numbers in set S is X, and the range of the numbers in set T is y. If all of the numbers in set T are also in Set S, is x greater than y?

(1) Set S consists of 7 numbers
(2) Set T consists of 6 numbers

E

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.

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.

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 = {1,2,4,5,6,7}

y = range of set T = 7 - 1 = 6

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

x = range of set S = 7 - 1 = 6

In the above case, x = y.

Answer: E

AbeNeedsAnswers wrote:The range of the numbers in set S is X, and the range of the numbers in set T is y. If all of the numbers in set T are also in Set S, is x greater than y?

(1) Set S consists of 7 numbers
(2) Set T consists of 6 numbers

Target question: Is x greater than y?

Given: The range of the numbers in set S is X. The range of the numbers in set T is Y. All of the numbers in set T are also in Set S

Statement 1 contains no information about set T, so statement 1 is NOT SUFFICIENT
Statement 2 contains no information about set S, so statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are several conflicting scenarios that satisfy BOTH statements. Here are two:
Case a: set S = {1, 1, 1, 1, 1, 1, 4}, which means X = 3, and set T = {1, 1, 1, 1, 1, 1}, which means Y = 0. In this case, X IS greater than Y
Case b: set S = {1, 1, 1, 1, 1, 1, 1}, which means X = 0, and set T = {1, 1, 1, 1, 1, 1}, which means Y = 0. In this case, X is NOT greater than Y
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent