The difference between John's and Paul's heights is twice : GMAT Data Sufficiency (DS)
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# The difference between John's and Paul's heights is twice

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The difference between John's and Paul's heights is twice [#permalink]

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06 Apr 2012, 11:35
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The difference between John's and Paul's heights is twice the difference between John's and Thom's heights. If John is the tallest, what is the average (arithmetic mean) height of the three?

(1) Paul is 163 centimeters tall.

(2) Thom is 173 centimeters tall.
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Re: The difference between John's and Paul's heights is twice [#permalink]

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06 Apr 2012, 11:47
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The difference between John's and Paul's heights is twice the difference between John's and Thom's heights. If John is the tallest, what is the average (arithmetic mean) height of the three?

J-P=2(J-T) --> J-P=2J-2T --> 2T=J+P. Question: (J+P+T)/3=? --> (2T+T)/3=T=?

(1) Paul is 163 centimeters tall --> P=163. Not sufficient.

(2) Thom is 173 centimeters tall --> directly gives the value of T. Sufficient.

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Re: The difference between John's and Paul's heights is twice [#permalink]

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14 Sep 2012, 06:53
Bunuel wrote:
The difference between John's and Paul's heights is twice the difference between John's and Thom's heights. If John is the tallest, what is the average (arithmetic mean) height of the three?

J-P=2(J-T) --> J-P=2J-2T --> 2T=J+P. Question: (J+P+T)/3=? --> (2T+T)/3=T=?

(1) Paul is 163 centimeters tall --> P=163. Not sufficient.

(2) Thom is 173 centimeters tall --> directly gives the value of T. Sufficient.

Hi Bunuel,

I have a doubt in this question. Kindly correct me if i am wrong.

Let the height of John Paul Tom
5x 3x 4x
John - Paul = 2(John - Tom)
5x-3x = 2 (5x-4x)
LHS = RHS
Average height of 3 = 12x/3 = 4x

(1) 3x = 163----> we can find the value of 4x as there is no restriction on the value x can take.---> Sufficient
(2) 4x = 173 ----> Sufficient

Can you tell me WHY i am wrong wrt OA

Waiting for response.
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Re: The difference between John's and Paul's heights is twice [#permalink]

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14 Sep 2012, 06:59
fameatop wrote:
Bunuel wrote:
The difference between John's and Paul's heights is twice the difference between John's and Thom's heights. If John is the tallest, what is the average (arithmetic mean) height of the three?

J-P=2(J-T) --> J-P=2J-2T --> 2T=J+P. Question: (J+P+T)/3=? --> (2T+T)/3=T=?

(1) Paul is 163 centimeters tall --> P=163. Not sufficient.

(2) Thom is 173 centimeters tall --> directly gives the value of T. Sufficient.

Hi Bunuel,

I have a doubt in this question. Kindly correct me if i am wrong.

Let the height of John Paul Tom
5x 3x 4x
John - Paul = 2(John - Tom)
5x-3x = 2 (5x-4x)
LHS = RHS
Average height of 3 = 12x/3 = 4x

(1) 3x = 163----> we can find the value of 4x as there is no restriction on the value x can take.---> Sufficient
(2) 4x = 173 ----> Sufficient

Can you tell me WHY i am wrong wrt OA

Waiting for response.

You cannot arbitrary assume that the heights are 5x, 3x and 4x. Why not 10x, 6x, and 8x?
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Re: The difference between John's and Paul's heights is twice [#permalink]

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14 Sep 2012, 07:33
rovshan85 wrote:
The difference between John's and Paul's heights is twice the difference between John's and Thom's heights. If John is the tallest, what is the average (arithmetic mean) height of the three?

(1) Paul is 163 centimeters tall.

(2) Thom is 173 centimeters tall.

If we denote the heights by J, P and T, we can write J = P + 2x and J = T + x for some positive integer x.
Then, P + 2x = T + x, or P = T - x.
So, the three heights are T - x, T, and T + x. Obviously, their average is T.

We can immediately see that (1) is not sufficient, but (2) is.

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Re: The difference between John's and Paul's heights is twice [#permalink]

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14 Sep 2012, 07:54
Bunuel wrote:
fameatop wrote:
Bunuel wrote:
The difference between John's and Paul's heights is twice the difference between John's and Thom's heights. If John is the tallest, what is the average (arithmetic mean) height of the three?

J-P=2(J-T) --> J-P=2J-2T --> 2T=J+P. Question: (J+P+T)/3=? --> (2T+T)/3=T=?

(1) Paul is 163 centimeters tall --> P=163. Not sufficient.

(2) Thom is 173 centimeters tall --> directly gives the value of T. Sufficient.

Hi Bunuel,

I have a doubt in this question. Kindly correct me if i am wrong.

Let the height of John Paul Tom
5x 3x 4x
John - Paul = 2(John - Tom)
5x-3x = 2 (5x-4x)
LHS = RHS
Average height of 3 = 12x/3 = 4x

(1) 3x = 163----> we can find the value of 4x as there is no restriction on the value x can take.---> Sufficient
(2) 4x = 173 ----> Sufficient

Can you tell me WHY i am wrong wrt OA

Waiting for response.

You cannot arbitrary assume that the heights are 5x, 3x and 4x. Why not 10x, 6x, and 8x?

It doesn't make any difference whether we are taking 5x,3x& 4x or 10x, 6x, and 8x
Because average in first case is 4x & in second case is 8x
If we are given in first case 3x = 163 & in second case 6x = 163
We want the value of 4x in first case & 8x in second case
In Both cases answer will be same which is 163*4/3

Kindly enlighten
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Re: The difference between John's and Paul's heights is twice [#permalink]

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14 Sep 2012, 08:46
fameatop wrote:

Hi Bunuel,

I have a doubt in this question. Kindly correct me if i am wrong.

Let the height of John Paul Tom
5x 3x 4x
John - Paul = 2(John - Tom)
5x-3x = 2 (5x-4x)
LHS = RHS
Average height of 3 = 12x/3 = 4x

(1) 3x = 163----> we can find the value of 4x as there is no restriction on the value x can take.---> Sufficient
(2) 4x = 173 ----> Sufficient

Can you tell me WHY i am wrong wrt OA

Waiting for response.[/quote]

You cannot arbitrary assume that the heights are 5x, 3x and 4x. Why not 10x, 6x, and 8x?[/quote]

It doesn't make any difference whether we are taking 5x,3x& 4x or 10x, 6x, and 8x
Because average in first case is 4x & in second case is 8x
If we are given in first case 3x = 163 & in second case 6x = 163
We want the value of 4x in first case & 8x in second case
In Both cases answer will be same which is 163*4/3

Kindly enlighten[/quote]

All you can assume is that the three heights are T - x, T, and T + x for some positive x, where T is Thom's height.
See my previous post:
the-difference-between-john-s-and-paul-s-heights-is-twice-130320.html#p1121568

Take the three heights 163, 173, and 183. 183 - 163 = 20 = 2(183 - 173)
Is 163/3 = 173/4 = 183/5? No!
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Re: The difference between John's and Paul's heights is twice [#permalink]

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14 Sep 2012, 09:19
EvaJager wrote:
fameatop wrote:

You cannot arbitrary assume that the heights are 5x, 3x and 4x. Why not 10x, 6x, and 8x?

It doesn't make any difference whether we are taking 5x,3x& 4x or 10x, 6x, and 8x
Because average in first case is 4x & in second case is 8x
If we are given in first case 3x = 163 & in second case 6x = 163
We want the value of 4x in first case & 8x in second case
In Both cases answer will be same which is 163*4/3

Kindly enlighten[/quote]

All you can assume is that the three heights are T - x, T, and T + x for some positive x, where T is Thom's height.
See my previous post:
the-difference-between-john-s-and-paul-s-heights-is-twice-130320.html#p1121568
Take the three heights 163, 173, and 183. 183 - 163 = 20 = 2(183 - 173)
Is 163/3 = 173/4 = 183/5? No![/quote]

If you go by my method using option (1), the three heights will be 271.66, 163, 217.3 & the differences in height is 108.66, 54.33 which satisfies the original statement.

I could be wrong Had the question stated that the heights are integer values, but nothing of such sort is mentioned.
Why i am wrong?

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Re: The difference between John's and Paul's heights is twice [#permalink]

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14 Sep 2012, 09:35
fameatop wrote:
EvaJager wrote:
fameatop wrote:

You cannot arbitrary assume that the heights are 5x, 3x and 4x. Why not 10x, 6x, and 8x?

It doesn't make any difference whether we are taking 5x,3x& 4x or 10x, 6x, and 8x
Because average in first case is 4x & in second case is 8x
If we are given in first case 3x = 163 & in second case 6x = 163
We want the value of 4x in first case & 8x in second case
In Both cases answer will be same which is 163*4/3

Kindly enlighten

All you can assume is that the three heights are T - x, T, and T + x for some positive x, where T is Thom's height.
See my previous post:
the-difference-between-john-s-and-paul-s-heights-is-twice-130320.html#p1121568
Take the three heights 163, 173, and 183. 183 - 163 = 20 = 2(183 - 173)
Is 163/3 = 173/4 = 183/5? No![/quote]

If you go by my method using option (1), the three heights will be 271.66, 163, 217.3 & the differences in height is 108.66, 54.33 which satisfies the original statement.

I could be wrong Had the question stated that the heights are integer values, but nothing of such sort is mentioned.
Why i am wrong?

It is a DS question. Also the triplet 163, 173, 183 satisfies the requirements. So, how can (1) be sufficient?
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Re: The difference between John's and Paul's heights is twice [#permalink]

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22 Mar 2013, 06:38
fameatop wrote:
Bunuel wrote:
The difference between John's and Paul's heights is twice the difference between John's and Thom's heights. If John is the tallest, what is the average (arithmetic mean) height of the three?

J-P=2(J-T) --> J-P=2J-2T --> 2T=J+P. Question: (J+P+T)/3=? --> (2T+T)/3=T=?

(1) Paul is 163 centimeters tall --> P=163. Not sufficient.

(2) Thom is 173 centimeters tall --> directly gives the value of T. Sufficient.

Hi Bunuel,

I have a doubt in this question. Kindly correct me if i am wrong.

Let the height of John Paul Tom
5x 3x 4x
John - Paul = 2(John - Tom)
5x-3x = 2 (5x-4x)
LHS = RHS
Average height of 3 = 12x/3 = 4x

(1) 3x = 163----> we can find the value of 4x as there is no restriction on the value x can take.---> Sufficient
(2) 4x = 173 ----> Sufficient

Can you tell me WHY i am wrong wrt OA

Waiting for response.

3x 4x 5x is fine for their heights just as 3x 5x 7x is. Note that 3x(Paul's height) is constant, while average shifts from 4x to 5x.
Re: The difference between John's and Paul's heights is twice   [#permalink] 22 Mar 2013, 06:38
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