went back on their promise

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Thu May 06, 2010 5:48 am

Two-fifths of the voters promise to vote for P and the rest promise to vote for Q. Of these, on the last day, 15% of the voters went back on their promise to vote for P and 25% of voters went back of their promise to vote for Q, and P lost by 2 votes. What was the total number of voters?
(A) 84
(B) 90
(C) 95
(D) 100
(E) 110

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Source: Beat The GMAT — Problem Solving | Thu May 06, 2010 5:48 am

ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Thu May 06, 2010 5:55 am

sanju09 wrote:Two-fifths of the voters promise to vote for P and the rest promise to vote for Q. Of these, on the last day, 15% of the voters went back on their promise to vote for P and 25% of voters went back of their promise to vote for Q, and P lost by 2 votes. What was the total number of voters?
(A) 84
(B) 90
(C) 95
(D) 100
(E) 110

Say there were x voters in the city

0.4x promised to vote for P out of which 0.06x voted for Q
0.6x promised to vote for Q out of which 0.15x voted for P

Total votes P got = 0.49x
Total votes Q got = 0.51x

0.02x =2
x=100

Always borrow money from a pessimist, he doesn't expect to be paid back.

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liferocks: Legendary Member; Posts: 576; Joined: Sat Mar 13, 2010 8:31 pmFollowed by: 1 member; Thanked: 97 times

by liferocks » Thu May 06, 2010 5:58 am

if 500x is total number of voter
200x promises for P
300x promises for Q

total number of vote P get=200x-200x*15/100+300x*25/100=200x-30x+75x=245x

Q get 500x-245x=255x

so q get 10x more which is equal to 2

total number of voters=2*500/10=100
Ans option D

"If you don't know where you are going, any road will get you there."
Lewis Carroll

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