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

Question

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.

Bunuel · Accepted Answer

The range of the numbers in set S is x, and the range of the numbers in set Tis 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. Nothing about set T. Not sufficient.
(2) Set T consists of 6 numbers. Nothing about set S. Not sufficient.

(1)+(2) It's quite easy to get two different answers. For example, if S={1, 2, 3, 4, 5, 6, 7} and T={1, 2, 3, 4, 5, 6}, then x=6>5=y, but if S={1, 2, 3, 4, 5, 6, 7} and T={1, 2, 3, 4, 5,  7 }, then x=6=y. not sufficient.

Answer: E.

Bunuel · Answer

Good observation. We are told that all of the numbers in set T are also in set S, which means that set T is a subset of set S . As you corrected noted the range of a subset cannot be greater than the range of a whole set , thus y (the range of T) cannot be greater than x (the range of S), hence the following relationship must be true: x\geq{y} . Similar questions to practice: s-is-a-set-containing-9-different-numbers-t-is-a-set-contai-101912.html if-set-s-consists-of-the-numbers-w-x-y-z-is-the-range-of-158973.html r-is-a-set-containing-8-different-numbers-s-is-a-set-128119.html a-is-a-set-containing-7-different-numbers-b-is-a-set-contai-102809.html s-w-x-y-z-is-the-range-of-s-greater-than-101718.html set-a-contains-20-numbers-and-set-b-contains-40-numbers-is-132330.html if-s-is-a-set-of-four-numbers-w-x-y-and-z-is-the-range-o-166184.html Hope this helps.

NoHalfMeasures · Answer

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

NoHalfMeasures · Answer

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

JeffTargetTestPrep · Answer

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

GyanOne · Answer

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

TheUltimateWinner · Answer

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...

Bunuel · Answer

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}.

BrentGMATPrepNow · Answer

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

RELATED VIDEO
 https://www.youtube.com/watch?v=FbAlIjw2fwY

MHIKER · Answer

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

avigutman · Answer

Video solution from Quant Reasoning:
 https://www.youtube.com/watch?v=Ch3YzyvW4UI

sidchandan · Answer

If the range of subset T can never be larger than range of Set S -> then we have a definite YES to the question is x>y. Then why is the answer choice E, shouldn't it be C?

Bunuel · Answer

The range of a subset can never be larger than the range of the original set, but that doesn't mean the ranges can't be equal. If you check the solution, you'll see a clear example where the ranges are equal:

If S = {1, 2, 3, 4, 5, 6, 7} and T = {1, 2, 3, 4, 5,  7 }, then x = 6 = y. So, in this case the answer to the question whether x > y is NO.

Hope it's clear.

totaltestprepNick · Answer

E https://www.youtube.com/watch?v=MKC7WZlUNFo Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards