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# Set A consists of five positive numbers. Set B consists of the square

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Math Expert
Joined: 02 Sep 2009
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Set A consists of five positive numbers. Set B consists of the square  [#permalink]

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27 Jul 2017, 01:33
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Difficulty:

95% (hard)

Question Stats:

36% (02:00) correct 64% (02:03) wrong based on 123 sessions

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Set A consists of five positive numbers. Set B consists of the square roots of each of the five numbers from Set A. If the standard deviation of Set B > standard deviation of Set A, which of the following must be true?

I. The range of the numbers in Set A is greater than 1
II. At least one of the numbers in Set A is less than 1
III. The range of Set A > Set B

(A) I only
(B) III only
(C) I and III
(D) I and II
(E) II only

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Re: Set A consists of five positive numbers. Set B consists of the square  [#permalink]

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28 Jul 2017, 05:05
Bunuel wrote:
Set A consists of five positive numbers. Set B consists of the square roots of each of the five numbers from Set A. If the standard deviation of Set B > standard deviation of Set A, which of the following must be true?

I. The range of the numbers in Set A is greater than 1
II. At least one of the numbers in Set A is less than 1
III. The range of Set A > Set B

(A) I only
(B) III only
(C) I and III
(D) I and II
(E) II only

Answer of the question is D.
Range cant not be negative. So option A is correct.
For standard deviation of A less than B, at least one number should be negative.

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Joined: 11 Feb 2017
Posts: 188
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01 Aug 2017, 09:41
Bunuel wrote:
Set A consists of five positive numbers. Set B consists of the square roots of each of the five numbers from Set A. If the standard deviation of Set B > standard deviation of Set A, which of the following must be true?

I. The range of the numbers in Set A is greater than 1
II. At least one of the numbers in Set A is less than 1
III. The range of Set A > Set B

(A) I only
(B) III only
(C) I and III
(D) I and II
(E) II only

I tried in this way

Set A = [1,4,144,144,144]
Set B = [1,2,12,12,12]

I. The range of the numbers in Set A is greater than 1

If all numbers are positive integers then range must be greater than 1.
Even if all numbers in set A are equal then range will be 0 and so it will be of B and hence it will contradict the statement [standard deviation of Set B > standard deviation of Set A]

hence not must be true

II. At least one of the numbers in Set A is less than 1

Not possible as its given that Set A consists of All positive integers

III. The range of Set A > Set B

I find this statement only to be true as None of the Above option is not given
I will go for (B)

Still i dont get it that if its true then according to the set i took , it will contradict the statement [standard deviation of Set B > standard deviation of Set A]

any kind of help will be appreciated

But my vote for B
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Joined: 09 Mar 2017
Posts: 36
Set A consists of five positive numbers. Set B consists of the square  [#permalink]

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21 Aug 2017, 14:16
This is how I answered it, although I'm sure there is a better way.

if set A was (9,16,25) and set b was (3,4,5). Then range and st. dev of A is greater than that of set B. Thus I realized for set B to have greater range and st. dev than that of set a, and for set b to be the square root of set a, then the numbers would probably look something more like set a: [1/9,1/16,1/25] and set b [1/3,1/4,1/5]. This would satisfy the 2 conditions, and only statement 2 is true of this set.

kudos if this makes sense. thanks.
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Re: Set A consists of five positive numbers. Set B consists of the square  [#permalink]

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22 Aug 2017, 00:09
2
SD is directly proportional to Range.

So, in above scenario, Range of SetB is greater than SetA.

Now, There is only one condition in which Range of a set with positive numbers [SetA] is smaller than Range of their square roots [SetB]:
That is, if both a1 and a5 are less than 1.

Eg.
SetA: a1=0.04 and a5=0.16
Range= 0.12

SetB: a1=0.2 and a5=0.4
Range= 0.2

Therefore, Range of SetA is greater than Range of Set B.

Basis, only Must be True condition is Condition 2.

Hence, Ans E.

Posted from my mobile device
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Posts: 27
Re: Set A consists of five positive numbers. Set B consists of the square  [#permalink]

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02 Oct 2017, 08:26
1
Bunuel wrote:
Set A consists of five positive numbers. Set B consists of the square roots of each of the five numbers from Set A. If the standard deviation of Set B > standard deviation of Set A, which of the following must be true?

I. The range of the numbers in Set A is greater than 1
II. At least one of the numbers in Set A is less than 1
III. The range of Set A > Set B

(A) I only
(B) III only
(C) I and III
(D) I and II
(E) II only

Consider below set:
Set A = 0.04, 0.25, 0.36, ....
Set B = 0.2, 0.5, 0.6, ....

I - False
II - True
III - False
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Re: Set A consists of five positive numbers. Set B consists of the square  [#permalink]

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11 Mar 2018, 02:50
First thing to note, after taking the square roots, the S.D of new set increases, it means, some of the numbers are 0 < x < 1,
as only for values, 0 < x < 1, square root x > x.

So statement 2 is definitely true.
This eliminates option A,B,C as none of them as statement 2

Now left with option D and E.
Statement 1 says, range must be greater than 1, This need not be true always, say set = {0.25,0.04,0.16}, new set = {0.5,0.2,0.4} , S.D of new set > S.D of set before square roots.

so option D is out. left with (E)
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Re: Set A consists of five positive numbers. Set B consists of the square  [#permalink]

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18 May 2019, 23:09
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Set A consists of five positive numbers. Set B consists of the square   [#permalink] 18 May 2019, 23:09
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