Professor Vasquez gave a quiz to two classes. Was the range of scores

It's clear E.

Range=Highest term - Lowest term

For (1)+(2): \(\frac{70+a_2+a_3+...+a_{26}}{26}=85\) --> \(70+a_2+a_3+...+a_{26}=26*85\) --> as there are numerous combinations for 26 numbers to total 26*85 (even when the lower limit of these numbers is fixed), then there are numerous values for \(range=a_{26}-70\). So the ranges may or may not be equal.
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IMO E.
As per statement 1, we cannot confirm the range to be same for both.
As per statement 2 as well we cannot confirm the range to be same for both.
Combining both also, we cannot infer that range to be same.

I believe its E .

A - no info about the highest value.
B - mean cant help much

A+B -> we have smallest value 70, mean 85..but we cant predict if their ranges are equal.


correct me if i have missed something

The answer is E

1) from this,we just know lower score and no. of students only. but we need highest score
2) From this , we just know the average which is no useful

A+B still we cant find highest score inorder to find range value.

Range = Max - Min so we need to know the Max & Min score in each class...

State 1 Gives No. of students and Min scores in both classes. Clearly not sufficient

State 2: From this we can conclude that the sum of the scores in both classes are same. Can't deduce anything further from this as well. So not Sufficient

So Answer is E

BUT I have a question > if it was given that the standard deviation of the scores in both classes are same, then the answer would be C right?

Please confirm. Thanks

Not necessarily. Consider the following cases:
[2, 2, 3, 4, 4] and [2, 2, 3, 3, 5].

Both have the same minimum values, and the same mean. However, the SDs are different. Agree?

We need to determine whether the range of scores from the first class was equal to the range of scores from the second class.

Statement One Alone:

In each class, the number of students taking the quiz was 26, and the lowest score in each class was 70.

We see that each class had a lowest score of 70; however, without any information regarding the highest scores, statement one alone is not sufficient to answer the question.

Statement Two Alone:

In each class, the average (arithmetic mean) score on the quiz was 85.

Knowing the average score does not tell us anything about the range. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using both statements, we see that we only know the low end of the range. Without knowing the high end of the range, we cannot determine an answer. For instance, if all the students in both classes scored 85 on the exam, then the range in both classes is zero, and thus the ranges are equal. However, if in one of the classes one student scored 70, one student scored 100, and the rest scored 85, then the range in this class is 100 - 70 = 30, and thus the ranges may not be equal.

Answer: E
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Can someone add the tag Gmatprep to this one. Its a Gmatprep problem.

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Done. Thank you.
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#1
total students = 26 , lowest score 70 ; but we dont know highest score or avg
in sufficient
#2
avg = 85 ; highest & lowest score not know in sufficeint

from 1 & 2
we cannot deduce highest score only total score sum can be obtained
IMO E

Bunuel
I Guess there is small typo error in the highlighted part. Please check.

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Edited the typo. Thank you.
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Upd: Never mind, looked at it with a fresh head, and everything made sense again.

Hello! I am having trouble wrapping my head around this.

We know that: 26 persons took the test in each class and the lowest score in both classes was 70 with the average being 85. Surely this tells us that the highest score was 100 in both classes? I dont understand how you can have the same lowest score and the same average but not the same highest score.

Hello all, I am struggling with weighted average / data sufficiency topics like those tested in this problem. Specifically, I am trying to create a scenario in which sufficiency would be created by ensuring that there must be a max 100% scorer to balance out the minimum 70% scorer.

What I have come up with is the following amendment to statement (2): In each class, the average (arithmetic mean) score on the quiz was 85, the average score of the women in both classes was less than 70%, and there were more women than men in both classes."

Does this amendment require there to be at least one man who scored 100% or higher? Of course, if the man scored higher than 100%, that would also create more than one potential max and the minimum could be a range of values, but I just want to make sure I am thinking about this in the right terms?

Any links to similar problems would be great too

Thanks!!

ScottTargetTestPrep
Thank you for your response. To clarify your explanation, "For instance, if all the students in both classes scored 85 on the exam, then the range in both classes is zero, and thus the ranges are equal" don't we know one scored 70, so the range would never be 0? I think you just forgot to apply statement 1 when disproving them together for this example.

The fact that we do not have any information regarding the highest scores is why statement one is not sufficient. Sure, we can prove that using actual numbers, but we do not have to.
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