Average Problem

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talaangoshtari: Master | Next Rank: 500 Posts; Posts: 154; Joined: Wed May 21, 2014 4:29 amFollowed by: 1 member; Thanked: 8 times

by talaangoshtari » Mon May 04, 2015 10:20 pm

There are at least three times as many boys as girls in a class. On a test, the boy's average score is 78, and the girl's average score is 94. Which of the following could be the average test score for the entire class?

Indicate all such valies.
A.88
B.86
C.84
D.82
E.80

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Source: Beat The GMAT — Problem Solving | Mon May 04, 2015 10:20 pm

regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

by regor60 » Tue May 05, 2015 5:15 am

talaangoshtari wrote:There are at least three times as many boys as girls in a class. On a test, the boy's average score is 78, and the girl's average score is 94. Which of the following could be the average test score for the entire class?

Indicate all such valies.
A.88
B.86
C.84
D.82
E.80

Number of Boys = 3x(Number of Girls) + "X" >"X" represents "at least"

Total students = 3G + G +"X"

Total points = (3Gx78) +94G

Class average = G x[(3x78)+94]/(4G + X)

= 328G/(4G + X)

If X=0, then Class Average could equal 82. Class Average can only go down if there are additional students, so that eliminates 88, 86 and 84.

What X is needed for an 80 average: 80 x (4G + X)= 328G

X=G/10 > so use 10 girls and 1 extra > 328 x 10/[(4 x 10) + 1] =3280/41 =80 > so 80 is also possible

I was a little sloppy before which can make all the difference

Last edited by regor60 on Tue May 05, 2015 7:36 am, edited 2 times in total.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue May 05, 2015 5:55 am

talaangoshtari wrote:There are at least three times as many boys as girls in a class. On a test, the boy's average score is 78, and the girl's average score is 94. Which of the following could be the average test score for the entire class?

Indicate all such valies.
A.88
B.86
C.84
D.82
E.80

The prompt implies that more than one of the five answer choices might be correct.
On the GMAT, only ONE of the five answer choices will be correct.
What is the source of this problem?

Let B = the number of boys, G = the number of girls, and A = the average for the entire class.

There are at least three times as many boys as girls in a class.
Test the THRESHOLD:
The smallest possible ratio for boys to girls.
Here, the SMALLEST POSSIBLE RATIO for boys to girls is 3 to 1.

Let B=3 and G=1.
Since the average for the boys is 78 and the average for the girls is 94, we get:
A = (3*78 + 94)/4 = 82.

Since the boys' average is lower than the girls' average, increasing the ratio of boys to girls will LOWER the average for the entire class.
Since the smallest possible ratio of boys to girls yields an average of 82 for the entire class, and increasing the ratio of boys to girls will lower the average for the entire class, the value of A must be 82 or less.
Thus, options D and E are possible.

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talaangoshtari: Master | Next Rank: 500 Posts; Posts: 154; Joined: Wed May 21, 2014 4:29 amFollowed by: 1 member; Thanked: 8 times

by talaangoshtari » Tue May 05, 2015 7:39 am

Hi, thank you for your response. I'm preparing for the GRE...The source of this problem is: Barron's 6 GRE Practice Tests.

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