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Interesting GMATFix Problem-34

by arora007 » Wed Sep 22, 2010 2:52 pm
In a group of men and women, each person is German or Spanish, but not both. Is the ratio of German men to German women smaller than the ratio of German men and Spanish women to German women and Spanish men?

1) The ratio of Spanish women to Spanish men is smaller than the ratio of German men and Spanish women to German women and Spanish men.
2)The ratio of Spanish women to Spanish men is greater than the ratio of women to men
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by this_time_i_will » Wed Sep 22, 2010 6:33 pm
sud be A.
the question basically asks
is GM/GW < GM/GW * SM/SW?

I says: SW/SM < GM/GW * SM/SW
so clearly, SM/SW > GM/GW * SM/SW
This means, SM/SW > GM/GW

So obviously, GM/GW >GM/GW * SM/SW.
And a definite answer to the question is NO.
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by limestone » Wed Sep 22, 2010 7:38 pm
I think the question asks: compare GM/GW to (GM + SW)/ (GW + SM)
In order to compare a/b to c/d, we can indirectly compare a*d and b*c (a,b,c,d must be positive). For example
if ad>bc then a/b>c/d. Then I'll try to compare GM * (GW+ SM) to GW * (GM +SW).
GM * (GW+ SM) = GM*GW + GM*SM
GW * (GM +SW) = GW*GM + GW*SW
both have GM*GW, so eliminate it. I'll compare only GM*SM to GW*SW

1. SW/SM < (GM+SW)/(GW+SM) or
SW*(GW+SM) < (GM+SW)*SM or SW*GW + SW*SM < GM*SM + SW*SM, eliminate the bold item in both sides :
SW*GW < GM*SM, hey look, this is what we need to know to solve the above-mention ratio. => Suff

2. SW/SM > W/M or SW/SM > (SW+GW)/(SM+GM), then using the same method:
SW*(SM+GM) > (SW+GW)*SM or SW*SM + SW*GM> SW*SM + GW*SM, eliminate SW*SM in both sides :
SW*GM>SM*GW, this is not the relationship we're looking for. We need SW to be with GW and SM to be with GM.
Hence Insuff.

IMO: A, only I suff.
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by arora007 » Wed Sep 22, 2010 8:47 pm
OA is A
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