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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!
(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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11 Dec 2010, 18:20
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sudimba
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.
11 Dec 2010, 19:47
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sudimba
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.
