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sudimba
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is there a quick way to solve this 11 Dec 2010, 16:35
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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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skovinsky
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is there a quick way to solve this 11 Dec 2010, 18:20
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sudimba
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!
Show more

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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dreambeliever
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is there a quick way to solve this 11 Dec 2010, 19:47
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sudimba
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!
Show more

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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is there a quick way to solve this 12 Dec 2010, 19:36
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sudimba
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!
Show more

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

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.



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!