Problem Solving

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%

The OA is the option A.

I don't have any idea of how to solve this PS question. Could anyone show me some light here? Please.

I'd be thankful. <i class="em em-neutral_face"></i>

For mid term grade to be minimum, her final grade should be maximum, as her semester grades are fixed. So, max value value of her final grade will be 100

Now, let her mid term grade be x

0.75*100 + 0.25* x= 88
On solving, x= 52%

________________________________________

Shahrukh Moin Khan
QA Mentor at Breakspace
https://www.mbabreakspace.com
PGDM: IIM Calcutta
B.Tech IIT Roorkee

Hello Vjesus12.

Let's take a look at your question.

Let's call:

m - the grade obtained in the midterm exam
f - the grade obtained in the final exam

m gives 25% of the semester grade and f gives 75%.

We know that Lindsey's semester grade was 88%.

So, we have that $$m\cdot25\%+f\cdot75\%=88\%$$ $$m\cdot0.25+f\cdot0.75=0.88$$ Since we want to know what is the lowest possible score that Lindsey could have received on her midterm exam, then we have to maximize the grade obtained in the final exam.

So, let's suppose that she got 1 in the final exam, hence $$m\cdot0.25+1\cdot0.75=0.88$$ $$m\cdot0.25=0.88-0.75$$ $$m\cdot0.25=0.13$$ $$m=\frac{0.13}{0.25}$$ $$m=0.52.$$ That is to say, the lowest possible score that Lindsey could have in the midterm exam is 52%.

This implies that the correct answer is the option A.

I hope it helps you. <i class="em em-smiley"></i>