Problem Solving

I got this problem correct using brute force algebra, but the process took to long. What is the most efficient method to solve problems like this one?


Mr. Kramer, the losing candidate in a two-candidate election, received 942,568 votes, which was exactly 40 percent of all votes cast. Approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast?

a. 10%
b. 12%
c. 15%
d. 17%
e. 20%

OA = D

What I feel is the # of votes here is just a GMAT trick(because everything can be expressed as a % of total votes casted). That's an ugly # :)
Let the total # of votes casted is T and % of Remaining votes he would need to reach 50% of total votes be "x"

So Given

Mr. Kramer's current votes + x% of 0.6 T = T/2
=> 0.4 T (given) + (x/100 ) * 0.6 T = T/2

Cancelling T on both Sides

0.4 + (x/100 ) * 0.6 =0.5
=> (x/100 ) * 0.6 =0.1
=> x = 100/6 ~ 17 (D)

Hope this helps.

tonebeeze wrote:I got this problem correct using brute force algebra, but the process took to long. What is the most efficient method to solve problems like this one?


Mr. Kramer, the losing candidate in a two-candidate election, received 942,568 votes, which was exactly 40 percent of all votes cast. Approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast?

a. 10%
b. 12%
c. 15%
d. 17%
e. 20%

OA = D

Here is another solution:

Total no of votes: X

Votes received : .4X
Remaining Votes : .6X
Remaining votes he would need to reach 50% of total votes : .1X

Required % = (.1X/.6X ) * 100 = 16.666~ 17