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

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14 Dec 2012, 03:47

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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.

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.

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

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14 Dec 2012, 04:27

Bunuel wrote:

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 correct me if I am wrong, but I would also add that the only possibilities to be x not bigger than y is that:

- MAX/MIN of Set T are also MAX/MIN of Set S or - obviously, that Set T and Set S are equal (that is not excluded by the stem)

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: \(x\geq{y}\).

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

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27 Jun 2015, 13:12

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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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15 Jul 2016, 02:13

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

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24 Jan 2017, 20:39

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: \(x\geq{y}\).

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...
_________________

“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.” ― Henry Wadsworth Longfellow

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: \(x\geq{y}\).

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}.
_________________

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

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25 Jan 2017, 06:22

iMyself wrote:

Bunuel wrote:

MensaNumber wrote:

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

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}.[/quote] Does mathematics support/accept that {1, 2, 3} is a subset of {1, 2, 3}?, Bunuel? or is it possible to be {1, 2, 3} is a subset of {1, 2, 3} in mathematics? Thank you brother...
_________________

“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.” ― Henry Wadsworth Longfellow

[quote="iMyself" Does mathematics support/accept that {1, 2, 3} is a subset of {1, 2, 3}?, Bunuel? or is it possible to be {1, 2, 3} is a subset of {1, 2, 3} in mathematics? Thank you brother...[/quote]

As I said above, a set is a subset of itself.
_________________

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

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25 Jan 2017, 06:30

Bunuel wrote:

[quote="iMyself" Does mathematics support/accept that {1, 2, 3} is a subset of {1, 2, 3}?, Bunuel? or is it possible to be {1, 2, 3} is a subset of {1, 2, 3} in mathematics? Thank you brother...

As I said above, a set is a subset of itself.[/quote]

Actually, i did not get you. I don't have pure idea about subset! if set A contains value 1,2,3 and Set B contains value 1,2,3, then can can we say that A is subset of B? Thank you...
_________________

“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.” ― Henry Wadsworth Longfellow

Last edited by iMyself on 25 Jan 2017, 06:36, edited 1 time in total.

[quote="iMyself" Does mathematics support/accept that {1, 2, 3} is a subset of {1, 2, 3}?, Bunuel? or is it possible to be {1, 2, 3} is a subset of {1, 2, 3} in mathematics? Thank you brother...

As I said above, a set is a subset of itself.

Actually, i did not get you. I don't have pure idea about subset! if set A contains value 1,2,3 and Set B contains value 1,2,3, then can can we say that A is subset of B? Thank you...[/quote] _______________ YES.
_________________

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

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25 Jan 2017, 07:04

Bunuel wrote:

iMyself wrote:

iMyself wrote:

Does mathematics support/accept that {1, 2, 3} is a subset of {1, 2, 3}?, Bunuel? or is it possible to be {1, 2, 3} is a subset of {1, 2, 3} in mathematics? Thank you brother...

Actually, i did not get you. I don't have pure idea about subset! if set A contains value 1,2,3 and Set B contains value 1,2,3, then can can we say that A is subset of B? Thank you...

_______________ YES.

That means, in statement 1: T (y)=1,2,3,4,5,6,7 ----> Range: 6 S (x)=1,2,3,4,5,6,7 ----> Range: 6 In which both caries SAME values. Here, x=y. So, The answer is NO--->Sufficient.

or, if T=1,2,4,6,8,9,10 --->range: 9 S=1,2,4,6,8,9,10 --->range: 9 Here, x=y. So, the answer is NO--->Sufficient right? So, why do not we take the statement 1 sufficient? Thank you Brother for your help. But, I'm still in confusion. I'm sorry to bother you.
_________________

“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.” ― Henry Wadsworth Longfellow

[ That means, in statement 1: T (y)=1,2,3,4,5,6,7 ----> Range: 6 S (x)=1,2,3,4,5,6,7 ----> Range: 6 In which both caries SAME values. Here, x=y. So, The answer is NO--->Sufficient.

or, if T=1,2,4,6,8,9,10 --->range: 9 S=1,2,4,6,8,9,10 --->range: 9 Here, x=y. So, the answer is NO--->Sufficient right? So, why do not we take the statement 1 sufficient? Thank you Brother for your help. But, I'm still in confusion. I'm sorry to bother you.

In the solutions above there are several examples giving TWO different answers to the question. You are considering only cases which give a NO answer but there are examples giving an YES answer.

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.
_________________

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

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25 Jan 2017, 07:20

Bunuel wrote:

iMyself wrote:

That means, in statement 1: T (y)=1,2,3,4,5,6,7 ----> Range: 6 S (x)=1,2,3,4,5,6,7 ----> Range: 6 In which both caries SAME values. Here, x=y. So, The answer is NO--->Sufficient.

or, if T=1,2,4,6,8,9,10 --->range: 9 S=1,2,4,6,8,9,10 --->range: 9 Here, x=y. So, the answer is NO--->Sufficient right? So, why do not we take the statement 1 sufficient? Thank you Brother for your help. But, I'm still in confusion. I'm sorry to bother you.

In the solutions above there are several examples giving TWO different answers to the question. You are considering only cases which give a NO answer but there are examples giving an YES answer.

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.

The green part is my problem. Probably, the question does not say that S carries more number than T; it says: If all of the numbers in set T are also in set S ONLY. The italic part does not indicate that S carries more values than T. Here is my analogy, which is given in my previous post. If i say that all the members of gmatclub can sit in the chair of stadium S, should i assume or infer that there are more chair in this stadium 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 as it is 100% sure that there are more values in S than T? Thank you brother...
_________________

“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.” ― Henry Wadsworth Longfellow

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