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 Post subject: GMAT Statistics
PostPosted: Mon Dec 06, 2010 2:00 pm 
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Joined: Sun May 30, 2010 3:15 am
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Three students were given three tests, the results of the first two tests are shown above. Student 1 and Student 3 received equal scores on Test 3. As a result, Student 1’s average (arithmetic mean) score over the three tests was 50 percent higher than Student 3’s average. What was the score Students 1 and 3 received on Test 3?

A. 33
B. 34
C. 35
D. 36
E. 39

(B) Let x be the score that both Student 1 and Student 3 received on Test 3.
Since Student 1's average is 50% higher than Student 3's average, Student 1's average is 1.5 times that of Student 3.
The average for Student 1 is (30 + 50 + x)/3, and the average for Student 3 is (14 + 28 + x)/3.

So we can solve for x as follows:
(30 + 50 + x)/3 = ((14 + 28 + x)/3) × 1.5
(80 + x)/3 = ((42 + x)/3) × 1.5
(80 + x)/3 = (63 + 1.5x)/3
80 + x = 63 + 1.5x
17 = 0.5x
x = 34.

The correct answer is choice (B).
----------

Can you tell me how you got 1.5 for 50%? I would think 50 percent is .5.

Thank you.


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 Post subject: Re: math (test 2, question 19): algebra
PostPosted: Mon Dec 06, 2010 2:13 pm 
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Joined: Sun May 30, 2010 2:23 am
Posts: 498
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.. Student 1’s average (arithmetic mean) score over the three tests was 50 percent higher than Student 3’s average.

Student 3’s average is considered to be 100%. If we denote it by y, then it is 100% of y, which is the same as 1 × y.

Student 1’s average is 50% higher. Therefore it is (100% + 50%) of y, which is the same as (1 + 0.5) × y = 1.5y.

If we were told that Student 1’s average score was 50% of the student 3’s average score, then it would be 50% of y, which would be the same as 0.5y.


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