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by sreak1089 » Fri Jul 10, 2009 8:52 am
IMO Ans D

Solution below:


Let us say a & b are the two numbers:
a+b = s --> (1)
and a = (p/q)b

substituting for a in (1):

b(p/q) + b = s
b(p+q)/q = s
=> b = qs/(p+q)

substitute for b in (2):

a + qs/(p+q) = s
a = s - qs(p+q)
= (s(p+q) - qs)/(p+q)
= ps/(p+q)[spoiler][/spoiler][/spoiler]
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by Ian Stewart » Fri Jul 10, 2009 9:11 am
Let's call the two numbers a and b. Three options here:

-choose numbers for a and b. Work out s, p and q, and plug these into each answer. If only one answer gives you your numbers a and b, it must be right. If two answers both give you the right numbers a and b, try again.

-we know the two numbers add to s. Well, try adding the numbers in each answer choice - the right answer has to give you s. Only D does.

-do the algebra:

a + b = s
a/b = p/q

So a = s - b, and a = pb/q, so s-b and pb/q must be equal:

pb/q = s - b
pb/q + b = s
b(p/q + 1) = s
b = s/[p/q + 1]
b = sq/(p + q)

from which D must be correct (no need to find a).
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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