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calculation

by clock60 » Mon Oct 18, 2010 2:03 pm
hi guys,
can somebody advise best way to below problem
4,896/((1/0,07)+(1/0,16))=?
a)0,238
b)0,262
c)0,625
d)0,649
e)6,25
oa A
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by limestone » Mon Oct 18, 2010 6:12 pm
Hi,
My approach is to convert all into fraction:

1/0.07 = 100/7
1/0.16 = 100/16 = 50/8
100/7 + 50/8 = (100*8 + 50*7)/ 7*8 = 1150/56

Now I note that 56*2 = 112, which is near to 115, then
1150/56 = (115*10)/(56*2*1/2) =115/112 * 10/(1/2)

Since 115/112 is slightly greater than 1, 115/112 * 10/(1/2) should be slighly greater than 1*10*2 (or 20) too.

Thus 4.896/((1/0.07)+(1/0.16)) is slightly less than 4.896/20
or the result must be slightly less than 0.2448.

Hence Pick A
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by Geva@EconomistGMAT » Mon Oct 18, 2010 10:22 pm
limestone wrote:Hi,
My approach is to convert all into fraction:

1/0.07 = 100/7
1/0.16 = 100/16 = 50/8
100/7 + 50/8 = (100*8 + 50*7)/ 7*8 = 1150/56

Now I note that 56*2 = 112, which is near to 115, then
1150/56 = (115*10)/(56*2*1/2) =115/112 * 10/(1/2)

Since 115/112 is slightly greater than 1, 115/112 * 10/(1/2) should be slighly greater than 1*10*2 (or 20) too.

Thus 4.896/((1/0.07)+(1/0.16)) is slightly less than 4.896/20
or the result must be slightly less than 0.2448.

Hence Pick A
Pretty close to what limestone said, only with the aid of a bit of ballparking:
100/7 = ~14
100/16 = ~6
Thus, the bottom of the fraction is ~20, and the entire fraction is slightly less than 5/20 = 0.25 - A is the only answer that works.

I don't know if it's relevant here, but this is not a calculations I would even attempt on the GMAT. Any problem that seems to force me to work this hard and leave such a degree of uncertainty whether the answer is A or B probably has an alternative solution method - GMAT quant questions are usually constructed in this way, so that test takers still have a chance to work the problem in a reasonable amount of time by thinking GMAT.
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by pzazz12 » Tue Oct 19, 2010 2:30 am
limestone wrote:Hi,
My approach is to convert all into fraction:

1/0.07 = 100/7
1/0.16 = 100/16 = 50/8
100/7 + 50/8 = (100*8 + 50*7)/ 7*8 = 1150/56

Now I note that 56*2 = 112, which is near to 115, then
1150/56 = (115*10)/(56*2*1/2) =115/112 * 10/(1/2)

Since 115/112 is slightly greater than 1, 115/112 * 10/(1/2) should be slightly greater than 1*10*2 (or 20) too.

Thus 4.896/((1/0.07)+(1/0.16)) is slightly less than 4.896/20
or the result must be slightly less than 0.2448.

Hence Pick A
Thank u.... Is there any simple method to solve these type of problems.........
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