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What is the value of y^3 - t^3?

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metallicafan
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What is the value of y^3 - t^3? [#permalink] New post   23 Nov 2011, 09:57
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What is the value of y^3 - t^3?

(1) y - t = 3
(2) y^2 - t^2 = 21

Source: gmathacks.com
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C
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BDSunDevil
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Re: What is the value of y^3 - t^3? [#permalink] New post   23 Nov 2011, 11:31
1. + 2.
(y+t)(y-t)=21
3*(y+t)=21
Y+t=7 and y-t=3 so we can solve for both t and y.
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Re: What is the value of y^3 - t^3? [#permalink] New post   13 Sep 2012, 12:55
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metallicafan wrote:
A fast way to solve this question? I solved it, but it took me more than 2 min :s.

What is the value of \(y^3 - t^3\)?
(1) \(y - t = 3\)
(2) \(y^2 - t^2 = 21\)

I spent a lot of time in solving the equations with the possible values of y and t.

Source: gmathacks.com



(1) - (y-t) = 3 ----> Y & t can be anything -Insufficient
(2) (y+t)(y-t) = 3 x 7 ----> (y+t) can be 3 or 7 -----> i.e. y will be 5 for sure but t can be 2 or -2 ----> Insufficient
(1+2) (y+t)= 7 because (y-t) = 3----> y = 5 & t=2--->Sufficient

Hope it helps.
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Re: What is the value of y^3 - t^3? [#permalink] New post   13 Sep 2012, 13:39
y^3 - t^3 or x^3 - y^3 is the same if you are more comfortable

(x-y) * (x^2 - y^2) -----> (x - y) * (x - y) * (x + y)

1) x - y = 3 -----> 3 * 3 * (x + y) ----> we do no have the value od (x + Y)

2) we have 21 BUT not (x - y)

1) + 2) we have 3 * 21 ----> Sufficient

;)
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Re: What is the value of y^3 - t^3? [#permalink] New post   13 Sep 2012, 14:14
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carcass wrote:
y^3 - t^3 or x^3 - y^3 is the same if you are more comfortable

(x-y) * (x^2 - y^2) -----> (x - y) * (x - y) * (x + y)

1) x - y = 3 -----> 3 * 3 * (x + y) ----> we do no have the value od (x + Y)

2) we have 21 BUT not (x - y)

1) + 2) we have 3 * 21 ----> Sufficient

;)


Hi Carcass,

You are right that it does not make any difference between y,t & x,y.

But you made a mistake in the formula \(x^3-y^3\) is not equal to \((x-y)\) * \((x^2 - y^2)\)
Instead \((x-y)^3\) is equal to \(x^3-y^3\) + \(3xy(x-y)\)

I Hope it helps.
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Re: What is the value of y^3 - t^3? [#permalink] New post   13 Sep 2012, 16:08
fameatop wrote:
carcass wrote:
y^3 - t^3 or x^3 - y^3 is the same if you are more comfortable

(x-y) * (x^2 - y^2) -----> (x - y) * (x - y) * (x + y)

1) x - y = 3 -----> 3 * 3 * (x + y) ----> we do no have the value od (x + Y)

2) we have 21 BUT not (x - y)

1) + 2) we have 3 * 21 ----> Sufficient

;)


Hi Carcass,

You are right that it does not make any difference between y,t & x,y.

But you made a mistake in the formula \(x^3-y^3\) is not equal to \((x-y)\) * \((x^2 - y^2)\)
Instead \((x-y)^3\) is equal to \(x^3-y^3\) + \(3xy(x-y)\)

I Hope it helps.
:shocked :wall ...........oh lord, after a long day of work the gmat is even worse.

Some Mod could say how to attack this question properly AND in the faster manner
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Re: What is the value of y^3 - t^3? [#permalink] New post   14 Sep 2012, 04:41
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What is the value of y^3 - t^3?

(1) y - t = 3. If \(y=3\) and \(t=0\), we have one value for \(y^3 - t^3\) and for \(y=4\) and \(t=1\) another. Not sufficient.

(2) y^2 - t^2 = 21. The same here. Not sufficient.

(1)+(2) From (2) we have \((y-t)(y+t)=21\). Since from (1) \(y - t = 3\), then \(3(y+t)=21\) --> \(y+t=7\). So we have two distinct linear equation with two unknowns: \(y+t=7\) and \(y - t = 3\), which means that we can solve for them and get the value of \(y^3 - t^3\). Sufficient.

Answer: C.

Hope it's clear.
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Re: What is the value of y^3 - t^3? [#permalink] New post   10 May 2021, 15:16
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Re: What is the value of y^3 - t^3? [#permalink]
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