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OG 12, Q 166 (%)

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OG 12, Q 166 (%)

by rahul.s » Thu Feb 04, 2010 5:45 am
During a certain season, a team won 80 percent of its first 100 games and 50 percent of its remaining games. If the team won 70 percent of its games for the entire season, what was the total number of games that the team played?

(A) 180
(B) 170
(C) 156
(D) 150
(E) 105

OA: D

i got the right answer but i wanted to know whether my approach was right since i'm quite weak with framing equations.

let x = remaining games (total - 100)
so, 80 + 50x/100 = (70/100) * (x + 100)
(8000 + 50x)/100 = (70x + 7000)/100
8000 - 7000 = 70x - 50x
1000 = 20x
x = 50
so total no. of games = 100 + 50 = 150

thoughts?
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by ajith » Thu Feb 04, 2010 5:48 am
rahul.s wrote:During a certain season, a team won 80 percent of its first 100 games and 50 percent of its remaining games. If the team won 70 percent of its games for the entire season, what was the total number of games that the team played?

(A) 180
(B) 170
(C) 156
(D) 150
(E) 105

OA: D

i got the right answer but i wanted to know whether my approach was right since i'm quite weak with framing equations.

let x = remaining games (total - 100)
so, 80 + 50x/100 = (70/100) * (x + 100)
(8000 + 50x)/100 = (70x + 7000)/100
8000 - 7000 = 70x - 50x
1000 = 20x
x = 50
so total no. of games = 100 + 50 = 150

thoughts?
I would have done the same. Well done
Always borrow money from a pessimist, he doesn't expect to be paid back.
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by rahul.s » Thu Feb 04, 2010 6:03 am
ajith wrote:I would have done the same. Well done
appreciate it, especially since it's coming from a math wiz :)
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by varundaga05 » Wed Jun 16, 2010 7:48 pm
I think it is a very length approach.

Instead if we go by putting values it is less time consuming.

Example
========

105 * .70 will give fractions so we skip this choice
150*.70 = 105

Now 100 gives 80 and remaining 150 - 100 = 50 gives 25

i.e. 80 + 25 = 105 which is matching our result of 150 *.75.

Its much easier
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by Testluv » Wed Jun 16, 2010 10:27 pm
varundaga05 wrote:I think it is a very length approach.

Instead if we go by putting values it is less time consuming.

Example
========

105 * .70 will give fractions so we skip this choice
150*.70 = 105

Now 100 gives 80 and remaining 150 - 100 = 50 gives 25

i.e. 80 + 25 = 105 which is matching our result of 150 *.75.

Its much easier
Fantastic approach. At Kaplan, we call this backsolving. Just a note for when you are applying this approach: it is best to start with choice B or D. Since the answer choices are arranged in order, this minimizes the number of answer choices you have to check.

(More minor point: When you saw that 105*.7 yielded a fraction, not only could you skip E, you could actually eliminate it--the number of games won must be an integer.)
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