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is there a quick way to solve this

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is there a quick way to solve this [#permalink] New post 11 Dec 2010, 15:35
What is X?

(480/x) = (480/x+16) + 5

To get rid of the x as denomintor, I was thinking of multyiplying the numerator with (x)(x+16) but it seems convulted and long for a gmat problem...any shortcuts..

Thanks!
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Re: is there a quick way to solve this [#permalink] New post 11 Dec 2010, 17:20
sudimba wrote:
What is X?

(480/x) = (480/x+16) + 5

To get rid of the x as denomintor, I was thinking of multyiplying the numerator with (x)(x+16) but it seems convulted and long for a gmat problem...any shortcuts..

Thanks!


Hi!

Do you have answer choices? Almost certainly the quickest way to get the right answer is to backsolve.

You could also work it out intiutively - we know that 480/x is 5 more than 480/(x+16). So, what factor pairs of 480 have one number that's 5 apart and another that's 16 apart?

1 480
2 240
3 160
4 120
5 96
6 80
8 60
10 48
12 40
15 32
16 30
20 24

the only pairs that match are 10*48 and 15*32 (x=32, x+16=48; 480/32 = 15 which is 5 more than 480/48 = 10).

So, x=32.
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Re: is there a quick way to solve this [#permalink] New post 11 Dec 2010, 18:47
sudimba wrote:
What is X?

(480/x) = (480/x+16) + 5

To get rid of the x as denomintor, I was thinking of multyiplying the numerator with (x)(x+16) but it seems convulted and long for a gmat problem...any shortcuts..

Thanks!


480/x = 480/(x+16) + 5
=> 96/x = 96/(x+16) +1 (div. entire eqn by 5)
=> 96x+96*16 = 96x +x2 +16x
=> x2 + 16x - 96*16 = 0 (Also, 96*16 = 48*2*16 = 48*32, And 48-32=16)
=> x2 + 48x - 32x - 48*32 =0
=> x= (-48, 32)

note: x2 = "x squared"

i think it can be done in 2 mins since we don't have to complete the multiplication of any big numbers.
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Re: is there a quick way to solve this [#permalink] New post 12 Dec 2010, 18:36
Expert's post
sudimba wrote:
What is X?

(480/x) = (480/x+16) + 5

To get rid of the x as denomintor, I was thinking of multyiplying the numerator with (x)(x+16) but it seems convulted and long for a gmat problem...any shortcuts..

Thanks!


\frac{480}{x} = \frac{480}{{x+16}} + 5
\frac{96}{x} = \frac{96}{{x+16}} + 1

If there are no options to help out at this stage, consider that numbers in GMAT problems almost always fall beautifully in place.
I will first try x = 16 because I know 16*6 = 96
I get \frac{96}{16} = \frac{96}{{16+16}} + 1
6=4 (x is not 16)
Since I need to reduce the left hand side, I will try a bigger value of x, 24 because 96/24 = 4 but 24+16 = 40 which doesn't divide 96 completely.
Next number I will try will be 32 since 96/32 = 3. Also 96/(32 + 16) = 2. This satisfies the equation.
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Re: is there a quick way to solve this   [#permalink] 12 Dec 2010, 18:36
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