I17-04

Question

A university conducts a written examination and an interview to admit students to a research program. A student is selected only if the student scores more than  x\%  in both the written examination and the interview, and has at least  z  years of work experience, where  x  and  z  are integers. The written examination is scored out of 100 marks, and the interview is scored out of 50 marks, with each score being an integer.The table below shows the scores, work experience, and selection outcomes for five students who applied to the program.
      Name   Written Score   Interview Score   Work Experience (years)   Outcome       Amit   70   40   3   Selected        Bunty   80   20   7   Rejected       Priya   75   35   2   Rejected       Reetu   69   38   10   Rejected       Shukla   72   35   4   Selected

Bunuel · Answer

Official Solution:

Amit (written 70, interview 40, experience 3 years) was selected with a written score of 70%. Shukla (written 72, interview 35, experience 4 years) was selected with an interview score of 35, which is exactly 70% of the 50-mark interview. So, scoring  70% is sufficient  in both the written examination and the interview.
 
On the other hand, Reetu (written 69, interview 38, experience 10 years) — who had more than 70% in the interview and more experience than Amit — was obviously rejected because of her written score of 69%. This makes it clear that  69% is not sufficient . Thus,  x = 69\% , meaning a candidate must score more than 69% in both components.
 
So, a candidate must get 70% or higher in the interview to be selected.

Correct answer:

Based on the information provided, what is the minimum interview percentage a student must get to be selected?  "70"

Bunuel · Answer

This MSR question and its solutions have been completely revised and improved.

AlapPatel · Answer

For the written test, we have an example where a person was selected at 70% and another was rejected at 69%. This means that we can be sure that 70% is the threshold. However, for the interview, the lowest selection score is at 70% while the highest rejection is at 40%. Doesn't this mean that the selection threshold for the interview could be anywhere between > 40 and <= 70?

Bunuel · Answer

Shukla was selected with an interview score of  35 , which is exactly  70%  of 50. That proves 70% in the interview is sufficient.

Reetu was rejected despite scoring  38  in the interview (76%) and having  10 years  of experience. So her rejection must be due to her written score of  69% , which confirms that 69% is not sufficient.

Since no one with an interview score above 35 was rejected due to interview performance, and 35 (70%) led to selection, the  minimum interview percentage required is 70% .

Luca46 · Answer

I like the solution - it’s helpful.

odionam · Answer

Hi Bunnel

see the question word A student is selected only if the student scores   more than x%   x% in both the written examination and the interview, 
it says more than X % to be select so if 70 would no then 70% of 50 =35 which is equal to 70% not more than 70 so answer would be 69 since 35 has been selected which is more than 69% of X kindly see the wordings in Tab please clarify and reply. if it would be 70% shukla was rejected because he scored 35 and still selected

Bunuel · Answer

The key is that  70% is not the value of x .

Shukla scored 35/50 = 70% and was selected, so we know that x must be  less than 70 .

Reetu’s data shows that 69% is not sufficient, so x must be at least 69. Since x is an integer,  x = 69 .

Therefore, the requirement is to score  more than 69% . Since the interview score must be an integer out of 50, the smallest possible score above 69% is 35/50 =  70% .

So 69% is the cutoff value x, while  70% is the minimum interview percentage a student can actually score and satisfy the requirement .

I17-04

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My Rewards

Name	Written Score	Interview Score	Work Experience (years)	Outcome
Amit	70	40	3	Selected
Bunty	80	20	7	Rejected
Priya	75	35	2	Rejected
Reetu	69	38	10	Rejected
Shukla	72	35	4	Selected

	35
	69
	70
	71
	Cannot be determined

	35
	69
	70
	71
	Cannot be determined