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# In a particular course, only two grades are given all semester: the

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Math Expert
Joined: 02 Sep 2009
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In a particular course, only two grades are given all semester: the  [#permalink]

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18 Aug 2015, 01:45
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82% (01:50) correct 18% (02:23) wrong based on 183 sessions

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In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible score that Lindsey could have received on her midterm exam?

A. 52%
B. 64%
C. 72%
D. 76%
E. 80%

Kudos for a correct solution.

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Re: In a particular course, only two grades are given all semester: the  [#permalink]

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18 Aug 2015, 04:49
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Bunuel wrote:
In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible score that Lindsey could have received on her midterm exam?

A. 52%
B. 64%
C. 72%
D. 76%
E. 80%

Kudos for a correct solution.

Let m be the score in the mid term and f be the score in finals.

Per the question,

$$\frac{0.25m+0.75f}{1}$$ $$= 0.88$$

For minimising m, we need to maximise f and thus put f = 1, we get

$$m = \frac{0.13}{0.25} = 0.52$$.

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Re: In a particular course, only two grades are given all semester: the  [#permalink]

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18 Aug 2015, 21:38
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Bunuel wrote:
In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible score that Lindsey could have received on her midterm exam?

A. 52%
B. 64%
C. 72%
D. 76%
E. 80%

Kudos for a correct solution.

IMO : A

Let us consider out of 100 marks Lindsey's semester grade marks was 88.

Given Final exam marks account for 75% of semester grade and mid term marks account for 25% of semester grade.

88 marks = (0.25)mid term marks + (0.75)final exam marks

We need minimum mid term marks. Hence Final exam he must score the maximum marks i.e. 100
88 marks = (0.25)mid term marks + (0.75)*100
13 = (0.25) * mid term marks

Thus Mid term marks = 52 out of 100 i.e. 52%
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Re: In a particular course, only two grades are given all semester: the  [#permalink]

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19 Aug 2015, 03:26
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Assume the total = 100 ......> Lindsay' mark=88

To obtain the min possible in the midterm exam, it must had full mark in final exam 75........> 88-75=13

13/25= ??? above 50 as 12.5 is 50%. Answer is 52%

Math Expert
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Posts: 58427
Re: In a particular course, only two grades are given all semester: the  [#permalink]

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23 Aug 2015, 11:56
Bunuel wrote:
In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible score that Lindsey could have received on her midterm exam?

A. 52%
B. 64%
C. 72%
D. 76%
E. 80%

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

If the midterm counts for 25% of the total grade, then the final exam must count for the remaining 75%, meaning that in this weighted average problem the final is weighted 3 times as much as the midterm. Using the weighted average mapping strategy, then, and maximizing her final exam score so that you minimize her midterm score, you have:

100-------------88----------------------------x

And you know that the ratio is 3:1. Since the final exam score of 100 is weighted heavier, then the difference of 12 between 100 and 88 is the "1" part of the ratio, meaning that 3(12) is the 3 portion. That equals 36, so the midterm score (x) is 36 less than the weighted average of 88. 88 - 36 = 52, so the correct answer is 52%.
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Re: In a particular course, only two grades are given all semester: the  [#permalink]

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21 Apr 2017, 11:31
Bunuel wrote:
In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible score that Lindsey could have received on her midterm exam?

A. 52%
B. 64%
C. 72%
D. 76%
E. 80%

Kudos for a correct solution.

How I did it I took smart numbers
Since
mid term count 25% so 25 marks from mid term
final exam count 75% mean 75
if we have to answer what is min score she score to have 88% on final
suppose she score 75 now 75 is 13 short of 88 so
75+13=88
so Lindsey scored 13/25 on mid term which is approx 52%
Choice A
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In a particular course, only two grades are given all semester: the  [#permalink]

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21 Apr 2017, 11:58
The mid-term grade is 1/4 of the final grade, and the prompt asks for the lowest value that she can score on the test and maintain an 88%.

88=x+100+100+100/4

352=x+300

52=x

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Re: In a particular course, only two grades are given all semester: the  [#permalink]

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26 Jan 2018, 10:47
Bunuel wrote:
In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible score that Lindsey could have received on her midterm exam?

A. 52%
B. 64%
C. 72%
D. 76%
E. 80%

To find Lindsey’s lowest possible score on the midterm, we can assume that Lindsey received a 100 on her final exam. Let’s let x = her midterm score; thus, we have

0.25x + 0.75(100) = 88

0.25x + 75 = 88

0.25x = 13

x = 13/0.25 = 52

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Re: In a particular course, only two grades are given all semester: the   [#permalink] 26 Jan 2018, 10:47
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