I15-10

Question

Five students from a class have been shortlisted for a scholarship based on their scores in four subjects: Math, Physics, English, and Biology. The minimum qualifying score may differ by subject, and each subject is equally weighted in the evaluation. The table below lists the scores received by each student, with a maximum possible score of 80 per subject.
      Students   Math   Physics   English   Biology       Ana   80   75   72   68       Boris   75   75   71   67       Caroline   79   74   72   78       Donald   76   75   72   65       Eva   73   77   70   65

For each of the following statements, select  True  if the statement can be verified to be true based on the information provided. Otherwise, select  False .

Bunuel · Answer

Official Solution:

Statement 1: 
 
Sorting by scores in each subject shows that Ana consistently had the highest or second-highest scores across all subjects. Therefore, if only two students were to be selected for the scholarship, Ana would have to be one of them. Therefore, this statement is True.
 
 Statement 2: 
 
In Biology, Donald had a lower score than both Boris and Caroline—65 compared to 67 and 78, respectively. If the minimum required score in Biology was 66 or 67, Donald would not qualify for the scholarship. Therefore, this statement is False.
 
 Statement 3: 
 
A minimum required score of 80% corresponds to a score of 64 in each subject. However, none of the students have a score below 64 in any subject. Therefore, if the minimum were set at 64, all students would qualify for the scholarship. Therefore, this statement is False.

Correct answer:

If only two students were to be selected for the scholarship, then Ana would have been one of them.  "True"

If Boris and Caroline were to be selected for the scholarship, then Donald would have also been selected.  "False"

If the minimum required score were set at 80% in each subject, then only three students would have qualified for the scholarship.  "False"

Bunuel · Answer

I have revised the question, solution, and formatting by adding more details to enhance clarity.

Rashmi96 · Answer

I did not quite understand the solution. in 2nd question , how do we know that minimum marks is set for choosing, rather than total overall marks

Bunuel · Answer

The question explicitly states that "the minimum qualifying score may differ by subject, and each subject is equally weighted in the evaluation." This makes it clear that the selection criteria are based on subject-specific minimum scores rather than total overall marks.

FormulaFlame · Answer

When processing a lot of data and under time pressure, I find it difficult to remember every single minute condition, which is why I frequently answer questions like Q2 incorrectly. Even after responding to the question, I could not understand why it was incorrect.

Bunuel · Answer

The statement is false because Donald’s Biology score is lower than both Boris and Caroline’s. If the Biology cutoff is 66 or 67, Boris and Caroline would qualify, but Donald wouldn’t. So, his selection isn’t guaranteed even if they are selected.

himabindureddy · Answer

but why a Biology cut off?? why not a cut off for English or Math, in which case Donald would have been selected??

Bunuel · Answer

Donald scored higher than either Boris or Caroline in Math, Physics, and English, for example, higher than Boris in Math, higher than Caroline in Physics, and higher than Boris in English, so in those subjects he could not have been disqualified. But in Biology he had the lowest score of the three (65, compared with 67 and 78). If the Biology cutoff were 66 or 67, Boris and Caroline would qualify but Donald would not. So the statement is not necessarily true and must be marked False.

himabindureddy · Answer

But here, Boris too scored the lowest among the three in both Math and English.

Bunuel · Answer

You are not following the logic. Boris having the lowest in Math and English doesn’t matter here, the statement we’re testing is about Donald. Donald had higher scores than at least one of Boris or Caroline in Math, Physics, and English, so he could not have been excluded there. In Biology he had the lowest score, so with a cutoff of 66 or 67 Boris and Caroline would qualify while Donald would not. That is why the statement is False.

himabindureddy · Answer

Got it Bunuel!! Thank you

GulfTube · Answer

Statement 1:

"If only two students were to be selected...". To select exactly two students, the minimum qualifying scores  must b e set at a level that allows  exactly two people  to pass.

Because Ana is consistently in the top two for every single subject, any such cutoff makes Anna eligible. Hence  True

I15-10

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My Rewards

Students	Math	Physics	English	Biology
Ana	80	75	72	68
Boris	75	75	71	67
Caroline	79	74	72	78
Donald	76	75	72	65
Eva	73	77	70	65

True	False
		If only two students were to be selected for the scholarship, then Ana would have been one of them.
		If Boris and Caroline were to be selected for the scholarship, then Donald would have also been selected.
		If the minimum required score were set at 80% in each subject, then only three students would have qualified for the scholarship.