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

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What is the value of y^3 - t^3? [#permalink] New post 23 Nov 2011, 08:57
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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
[Reveal] Spoiler: OA

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Re: What is the value of y^3 - t^3? [#permalink] New post 23 Nov 2011, 10:31
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, 11:55
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, 12:39
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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, 13:14
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, 15:08
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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, 03:41
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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 Nov 2013, 19:29
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Re: What is the value of y^3 - t^3?   [#permalink] 10 Nov 2013, 19:29
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