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# Set S and Set T both contain x elements. The average of Set S is 40.

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Math Expert
Joined: 02 Sep 2009
Posts: 54369
Set S and Set T both contain x elements. The average of Set S is 40.  [#permalink]

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28 Jul 2017, 09:12
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25% (medium)

Question Stats:

71% (01:48) correct 29% (01:53) wrong based on 107 sessions

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Set S and Set T both contain x elements. The average of Set S is 40. If the average of Set S and Set T combined is 50, which of the following must be true?

I. The average of Set T is 60.

II. The range of Set T is greater than that of Set S.

III. x is an even number

(A) I only

(B) I & II

(C) II only

(D) I & III

(E) All of the above

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Re: Set S and Set T both contain x elements. The average of Set S is 40.  [#permalink]

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28 Jul 2017, 09:32
Bunuel wrote:
Set S and Set T both contain x elements. The average of Set S is 40. If the average of Set S and Set T combined is 50, which of the following must be true?

I. The average of Set T is 60.

II. The range of Set T is greater than that of Set S.

III. x is an even number

(A) I only

(B) I & II

(C) II only

(D) I & III

(E) All of the above

Sum of all numbers of set S = $$40*x$$
Sum of all numbers of set S & set T = $$50*2x$$ (as both set S & set T contains $$x$$ elements)
Therefore sum of all elements of set T = $$100x - 40x = 60x$$
Hence average of set T = $$60x/x = 60$$. Hence $$I$$ must be true

Suppose set S contain two elements {-20,100}, then the average will be 40 but the range will be 120
and suppose set T contains two elements {60,60}, then the average will be 60 but the range will be 0. Hence $$II$$ may or may not be true

from the question stem we cannot say anything about $$x$$ and to arrive at the average for set T we do not require the value of $$x$$. Hence $$III$$ may or may not be true

Hence Option A
Manager
Joined: 03 May 2017
Posts: 91
Re: Set S and Set T both contain x elements. The average of Set S is 40.  [#permalink]

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28 Jul 2017, 18:40
Bunuel wrote:
Set S and Set T both contain x elements. The average of Set S is 40. If the average of Set S and Set T combined is 50, which of the following must be true?

I. The average of Set T is 60.

II. The range of Set T is greater than that of Set S.

III. x is an even number

(A) I only

(B) I & II

(C) II only

(D) I & III

(E) All of the above

I. Average (S+T)= 100, Average S =40, Average T= 60.. MBT
II. No idea of contents of sets; no idea of range...MNBT
III. No idea of contents of sets nor value of x;...MNBT

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Re: Set S and Set T both contain x elements. The average of Set S is 40.  [#permalink]

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29 Jul 2017, 03:38
Bunuel wrote:
Set S and Set T both contain x elements. The average of Set S is 40. If the average of Set S and Set T combined is 50, which of the following must be true?

I. The average of Set T is 60.

II. The range of Set T is greater than that of Set S.

III. x is an even number

(A) I only

(B) I & II

(C) II only

(D) I & III

(E) All of the above

S & T both contains x elements.
Av.(Set S) = 40
Sum (Set S) = 40x

Av.(Set S & T) = 50
Sum (Set S & T) = 100x

So Sum of Set T = 60x
Av(Set T) = 60

I. CORRECT

II. The Least and highest numbers in set S may be ( -30, 90) and Set T may be (60,60). SO we can't comment on the value of range.
INCORRECT

III. Since x has no role in finding the average values etc. So, we can't say x is even or not.
INCORRECT

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Posts: 7556
Re: Set S and Set T both contain x elements. The average of Set S is 40.  [#permalink]

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29 Jul 2017, 05:48
shashankism wrote:
Bunuel wrote:
Set S and Set T both contain x elements. The average of Set S is 40. If the average of Set S and Set T combined is 50, which of the following must be true?

I. The average of Set T is 60.

II. The range of Set T is greater than that of Set S.

III. x is an even number

(A) I only

(B) I & II

(C) II only

(D) I & III

(E) All of the above

S & T both contains x elements.
Av.(Set S) = 40
Sum (Set S) = 40x

Av.(Set S & T) = 50
Sum (Set S & T) = 100x

So Sum of Set T = 60x
Av(Set T) = 60

I. CORRECT

II. The Least and highest numbers in set S may be ( -30, 90) and Set T may be (60,60). SO we can't comment on the value of range.
INCORRECT

III. Since x has no role in finding the average values etc. So, we can't say x is even or not.
INCORRECT

hi,

just on a lighter side..

your signature says " Appreciate by clicking +1 kudos (lets be generous, friends)"
so instinctively thought of looking at your $$\frac{kudos.given}{kudos.recieved}$$..
it is less than $$\frac{1}{2}$$.. remembered a proverb -- " Charity begins at home" :wink:
On the lighter side. will remove it if offended
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Posts: 2803
Re: Set S and Set T both contain x elements. The average of Set S is 40.  [#permalink]

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29 Jul 2017, 10:16
Bunuel wrote:
Set S and Set T both contain x elements. The average of Set S is 40. If the average of Set S and Set T combined is 50, which of the following must be true?

I. The average of Set T is 60.

II. The range of Set T is greater than that of Set S.

III. x is an even number

(A) I only

(B) I & II

(C) II only

(D) I & III

(E) All of the above

• Let the average be Set T be “T”.
o Average of S and T $$= \frac{(Tx + 40x)}{2x}$$
o $$100 = T + 40$$
o Thus, $$T = 60$$
o Statement I is correct.

• Let us now focus on the Range.
o Set S average is 40.
o A possible scenario could be {40,40,40….x terms), the range is 0 in this case.
o Set T average is 60.
o A possible scenario could be {60, 60,60….x terms), the range is 0 in this case.
• Thus, we cannot say for sure if the range of Set T is greater than Set S.
o Statement II is not always true.
• Finally, we do not know the value of x, it could be even or odd.

Thus, the correct answer is Option A.

Thanks,
Saquib
Quant Expert
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Re: Set S and Set T both contain x elements. The average of Set S is 40.  [#permalink]

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29 Jul 2017, 20:11
chetan2u wrote:
shashankism wrote:
Bunuel wrote:
Set S and Set T both contain x elements. The average of Set S is 40. If the average of Set S and Set T combined is 50, which of the following must be true?

I. The average of Set T is 60.

II. The range of Set T is greater than that of Set S.

III. x is an even number

(A) I only

(B) I & II

(C) II only

(D) I & III

(E) All of the above

S & T both contains x elements.
Av.(Set S) = 40
Sum (Set S) = 40x

Av.(Set S & T) = 50
Sum (Set S & T) = 100x

So Sum of Set T = 60x
Av(Set T) = 60

I. CORRECT

II. The Least and highest numbers in set S may be ( -30, 90) and Set T may be (60,60). SO we can't comment on the value of range.
INCORRECT

III. Since x has no role in finding the average values etc. So, we can't say x is even or not.
INCORRECT

hi,

just on a lighter side..

your signature says " Appreciate by clicking +1 kudos (lets be generous, friends)"
so instinctively thought of looking at your $$\frac{kudos.given}{kudos.recieved}$$..
it is less than $$\frac{1}{2}$$.. remembered a proverb -- " Charity begins at home" :wink:
On the lighter side. will remove it if offended

Hahahaha... chetan2u Yes you are correct but presently I am continuously in Kudos collection mode and trying to provide solution of as many questions as possible. So if you can see I am working very hard to solve & provide better solution to quant questions which is my strong area. Meanwhile when I get a good solution I too provide kudos. Once I will start solving VA section, in which I am weaker than QA section, I will surely provide kudos to good answers. But for last 1 month I am just solving and providing solution.. Anyway your comments are always welcome, it will increase bond between us and will help gmatclub to be more interactive. Even my moto is to interact with as many nice people here as possible
_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

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Re: Set S and Set T both contain x elements. The average of Set S is 40.  [#permalink]

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29 Jul 2017, 23:51
Bunuel wrote:
Set S and Set T both contain x elements. The average of Set S is 40. If the average of Set S and Set T combined is 50, which of the following must be true?

I. The average of Set T is 60.

II. The range of Set T is greater than that of Set S.

III. x is an even number

(A) I only

(B) I & II

(C) II only

(D) I & III

(E) All of the above

Total of S = 40x
Total of S & T combined = 100x (50*2x)
Total of T = 60x
Average in T = 60x/x = 60

I must be true

Let x be odd
S = 30,40,50
Range of S = 20
T = 60,60,60
Average of S & T combined = 50
Range of T = 0

II and III not necessarily be true
Hence A
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Re: Set S and Set T both contain x elements. The average of Set S is 40.   [#permalink] 29 Jul 2017, 23:51
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