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Official GMAT Quest - %

by preciousrain7 » Tue Jan 15, 2008 4:35 pm
Mr. Kramer, the losing candidate in a two-candidate election, received 942,568 votes, which was exactly 40 percent of all the 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%

Official ans is: D

What's an easy way of doing this? Thanks a BUNCH!
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by desihokie » Tue Jan 15, 2008 5:57 pm
is the answer D?
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by preciousrain7 » Tue Jan 15, 2008 6:23 pm
desihokie wrote:is the answer D?

yes! how?
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by desihokie » Tue Jan 15, 2008 6:55 pm
This is what i did:
let the crazy number 942...=z

the total votes = z/0.4 or say, remaining votes = 0.6z/0.4 = 3z/2

now say, y% of this needs to be added to z in order to get 50% of total (total =z/0.4)

=> (3z/2) y% + z = (z/0.4)50% = z/0.8 = 5z/4
=> (3z/2) y% = (5z/4) - (z) = z/4
=> y% = {z/4 * 2/3z}
=> y% = 1/6
=> y = 100/6 = 16.666% ~= 17%

Tell me if this makes sense.
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by simplyjat » Tue Jan 15, 2008 9:01 pm
When you see these big numbers, and the answer asked it approximate you can slightly change the number according to your own needs :)

so 40% = 942,568 ~ 1,000,000
100% = 1,000,000 * 5/2 = 2,500,000 (for ease of calculation lets say just 25)

so Kramer got 10 out of 25 votes. To get 50% votes he should get 12.5
number of more votes required = 12.5 - 10 = 2.5
number of remaining votes = 25 - 10 = 15

percentage of more votes required = 100 * 2.5 / 15 = 16.67 ~17% (closest answer choice)
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by desihokie » Tue Jan 15, 2008 9:07 pm
Wow! thats even easier!!, Thanks, simplyjat!
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by Stuart@KaplanGMAT » Tue Jan 15, 2008 9:10 pm
He needs 10% of the total votes to get at least 50% of them.

He already has 40% of the votes, which means that there's 60% of the votes remaining.

Therefore he needs 10%/60% = 1/6 of the remaining votes.

1/6 = 16.67% = approx 17%.
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by simplyjat » Tue Jan 15, 2008 10:13 pm
The explanation given by Stuart is straight and correct. I was tempted to provide the approximation strategy :)
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by preciousrain7 » Wed Jan 16, 2008 12:33 pm
Stuart Kovinsky wrote:He needs 10% of the total votes to get at least 50% of them.

He already has 40% of the votes, which means that there's 60% of the votes remaining.

Therefore he needs 10%/60% = 1/6 of the remaining votes.

1/6 = 16.67% = approx 17%.
Thank you!
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by preciousrain7 » Wed Jan 16, 2008 12:34 pm
simplyjat wrote:When you see these big numbers, and the answer asked it approximate you can slightly change the number according to your own needs :)

so 40% = 942,568 ~ 1,000,000
100% = 1,000,000 * 5/2 = 2,500,000 (for ease of calculation lets say just 25)

so Kramer got 10 out of 25 votes. To get 50% votes he should get 12.5
number of more votes required = 12.5 - 10 = 2.5
number of remaining votes = 25 - 10 = 15

percentage of more votes required = 100 * 2.5 / 15 = 16.67 ~17% (closest answer choice)
where do you get the 5/2 from in the equation 100% = 1,000,000 * 5/2 = 2,500,000
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by simplyjat » Wed Jan 16, 2008 10:10 pm
where do you get the 5/2 from in the equation 100% = 1,000,000 * 5/2 = 2,500,000
40 % is 2/5 of 100%, i.e. 40/100 = 2/5
not invert the ratio, 100/40 = 5/2, i.e. 100 is 5/2 of 40%
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