The range of the numbers in set S is x, and the range of the

Hi Bunuel, So 'y' can never be larger than 'x', can it? Thanks!

Thanks for validating that observation. Thanks also for providing additional practice questions. Really appreciated!

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

Statement (1):
Set S consists of 7 numbers. We do not know how many numbers are in set T, other than they can at most be 7. If the range of set S is x, is is possible to define set T in such a way that it has less elements than set S, and the lowest and highest of these elements in set T is higher and lower respectively than the highest and lowest in set S. It is also possible to define set T in such a way that it is exactly similar to set S, in which case the ranges are equal. Therefore this statement alone is insufficient.

Statement (2):
This is similar to statement (1), except here we are given the number of elements in set T. So we know the number of elements in set S is six or greater, and includes all the elements in set T. Using similar logic as in statement (1), we can see that this statement too is insufficient.

Combining both the statements:
Set S has 7 elements and set T has six. We can still have the following two cases:
The lowest of set T is higher than that of set S and all other elements of set T are same as those of set S. In this case the range of set S is higher than that of set T.
The lowest and highest of set T and set S are the same. In this case the ranges are the same.

Therefore even combining both the statements is insufficient.

The answer is therefore E

Another similar question for practice: https://gmatclub.com/forum/set-a-contain ... l#p1083950

But, how do we be sure that set S consists more numbers than set T? If i say that all the members of gmatclub can sit in the chair of stedium S, should i assume or infer that there are more chair in this stedium than the number of the members of gmat club? MAY be yes ( more chair than member)or may not be (equal number of chair and member of gmat club). If something is used as MAY, why do we take it seriously or exactly? Thank you...

If I understood you correctly, then answer to your question is that a set can be considered to be a subset of itself. For example, {1, 2, 3} is a subset of {1, 2, 3}.

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:
RELATED VIDEO

T is a subset of S and the range of a subset cannot be greater than the range of a whole set. x≥y is a must.

(1) No information about T; Insufficient.

(2) No Information about S; Insufficient.

Let S= 1,2,3,4,5,6,7 and T = 1,2,3,4,5,6 then x>y, Yes
but if S = 1,2,3,4,5,6,7 then the range is x = 6, while if T = 1,2,3,4,5,7 then the range y = 6, then x = y NO

The answer is E.
So

Video solution from Quant Reasoning:

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