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A student averages 72 on 5 tests. If the lowest score is dropped, the

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A student averages 72 on 5 tests. If the lowest score is dropped, the  [#permalink]

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New post 26 Dec 2018, 10:38
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A student averages 72 on 5 tests. If the lowest score is dropped, the average rises to 84. What is the lowest score?

A. 18
B. 24
C. 32
D. 43
E. 48

Source: Kaplan GMAT Math Workbook - Sixth Edition
Page# 305

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Re: A student averages 72 on 5 tests. If the lowest score is dropped, the  [#permalink]

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New post 26 Dec 2018, 11:51
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SajjadAhmad wrote:
A student averages 72 on 5 tests. If the lowest score is dropped, the average rises to 84. What is the lowest score?

A. 18
B. 24
C. 32
D. 43
E. 48

Source: Kaplan GMAT Math Workbook - Sixth Edition
Page# 305



Sum of 5 tests = 5*72 = 360

Sum of 4 tests = 4*84 = 336

Lower score that was discarded = 360 - 336 = 24

B is the correct answer.
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Re: A student averages 72 on 5 tests. If the lowest score is dropped, the  [#permalink]

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New post 26 Dec 2018, 17:23
SajjadAhmad wrote:
A student averages 72 on 5 tests. If the lowest score is dropped, the average rises to 84. What is the lowest score?

A. 18
B. 24
C. 32
D. 43
E. 48

Source: Kaplan GMAT Math Workbook - Sixth Edition
Page# 305


I like the solution given above. However, you can also treat this as a weighted averages problem, if you don't notice the clever approach with the sums of the scores!

Consider the 72 average as an average of the 4 higher tests, and the 1 lower test.

lowest test ------------------- 72 ------ 4 higher tests

We know that the average of the 4 higher tests is 84, so we can fill that in:

lowest test ------------------- 72 ------ 4 tests averaging 84

The 4 tests that average 84, are 12 points above the overall average. Since there are four of those tests, and only one 'lowest test', the lowest test must be four times further from the average. That means it has to be 4*12 = 48 points below the average.

To find the actual score, figure out what number is 48 points lower than 72. 72-48 = 24. The answer is B.
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Re: A student averages 72 on 5 tests. If the lowest score is dropped, the  [#permalink]

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New post 26 Dec 2018, 17:33
SajjadAhmad wrote:
A student averages 72 on 5 tests. If the lowest score is dropped, the average rises to 84. What is the lowest score?

A. 18
B. 24
C. 32
D. 43
E. 48

Source: Kaplan GMAT Math Workbook - Sixth Edition
Page# 305


Let the lowest score be x. On dropping the lowest score, the increase in average is=84-72=12. This increase can be attributed to decrease lowest score was impacting on the previous average, which means the lowest score was 12*4=48 less than the previous average=72-48=24. Hence, the lowest score was 24.

IMO, Option B.
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Re: A student averages 72 on 5 tests. If the lowest score is dropped, the &nbs [#permalink] 26 Dec 2018, 17:33
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