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

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The range of the numbers in set S is x, and the range of the  [#permalink]

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New post 14 Dec 2012, 02:47
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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.
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Re: The range of the numbers in set S is x, and the range of the  [#permalink]

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New post 14 Dec 2012, 02:50
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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.
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Re: The range of the numbers in set S is x, and the range of the  [#permalink]

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New post 07 Apr 2014, 00:55
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Hi Bunuel, So 'y' can never be larger than 'x', can it? Thanks!
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Re: The range of the numbers in set S is x, and the range of the  [#permalink]

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New post 07 Apr 2014, 01:11
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MensaNumber wrote:
Hi Bunuel, So 'y' can never be larger than 'x', can it? Thanks!


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
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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

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Re: The range of the numbers in set S is x, and the range of the  [#permalink]

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New post 07 Apr 2014, 02:10
Thanks for validating that observation. Thanks also for providing additional practice questions. Really appreciated!
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Re: The range of the numbers in set S is x, and the range of the  [#permalink]

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New post 29 Sep 2016, 06:08
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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
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The range of the numbers in set S is x, and the range of the  [#permalink]

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New post 22 Dec 2016, 12:01
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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: http://gmatclub.com/forum/set-a-contain ... l#p1083950
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Re: The range of the numbers in set S is x, and the range of the  [#permalink]

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New post 24 Jan 2017, 19:39
Bunuel wrote:
MensaNumber wrote:
Hi Bunuel, So 'y' can never be larger than 'x', can it? Thanks!


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.

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...
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Re: The range of the numbers in set S is x, and the range of the  [#permalink]

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New post 25 Jan 2017, 05:15
iMyself wrote:
Bunuel wrote:
MensaNumber wrote:
Hi Bunuel, So 'y' can never be larger than 'x', can it? Thanks!


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.

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}.
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Re: The range of the numbers in set S is x, and the range of the  [#permalink]

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New post 30 Aug 2017, 14:05
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Walkabout 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:

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Re: The range of the numbers in set S is x, and the range of the   [#permalink] 03 May 2020, 10:22

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