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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]  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]  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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Prepare with Kaplan and save $150 on a course! Kaplan Reviews Manager Joined: 24 Nov 2010 Posts: 209 Location: United States (CA) Concentration: Technology, Entrepreneurship Schools: Ross '15, Duke '15 Followers: 2 Kudos [?]: 50 [0], given: 7 Re: is there a quick way to solve this [#permalink] 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. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 5863 Location: Pune, India Followers: 1481 Kudos [?]: 7972 [0], given: 190 Re: is there a quick way to solve this [#permalink] 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. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: is there a quick way to solve this   [#permalink] 12 Dec 2010, 18:36
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