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## Professor Vasquez

tagged by: Brent@GMATPrepNow

This topic has 4 expert replies and 0 member replies
rsarashi Master | Next Rank: 500 Posts
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#### Professor Vasquez

Sat Sep 02, 2017 10:29 pm
Professor Vasquez gave a quiz to two classes. Was the range of scores fro the first class equal to the range of scores for the second class?
(1) In each class, the number of students taking the quiz was 26, and the lowest score in each class was 70.
(2) IN each class, the average (arithmetic mean) score on the quiz was 85

OAE

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Scott@TargetTestPrep GMAT Instructor
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Mon Sep 11, 2017 10:26 am
rsarashi wrote:
Professor Vasquez gave a quiz to two classes. Was the range of scores fro the first class equal to the range of scores for the second class?
(1) In each class, the number of students taking the quiz was 26, and the lowest score in each class was 70.
(2) IN each class, the average (arithmetic mean) score on the quiz was 85

OAE
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.

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Brent@GMATPrepNow GMAT Instructor
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Sun Sep 03, 2017 6:22 am
rsarashi wrote:
Professor Vasquez gave a quiz to two classes. Was the range of scores fro the first class equal to the range of scores for the second class?

(1) In each class, the number of students taking the quiz was 26, and the lowest score in each class was 70.
(2) In each class, the average (arithmetic mean) score on the quiz was 85
Target question: Was the range of scores for the first class equal to the range of scores for the second class?

Neither statement alone seems sufficient, so let's jump straight to....

Statements 1 and 2 combined
There are several scenarios that satisfy BOTH statements. Here are two:
Case a:
First class scores: {70, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 100}
Second class scores: {70, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 100}
In this case, the range for the first class EQUALS the range for the second class

Case b:
First class scores: {70, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 100}
Second class scores: {70, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 86, 99}
In this case, the range for the first class is GREATER THAN the range for the second class

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Aside: notice that for case b, I took the last two values (85 and 100) in the first class and replaced them with 86 and 99 for the second class. Since both pairs of numbers have the same sum, this ensured that the class average remained 85.

Cheers,
Brent

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GMATGuruNY GMAT Instructor
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Sun Sep 03, 2017 3:57 am
rsarashi wrote:
Professor Vasquez gave a quiz to two classes. Was the range of scores fro the first class equal to the range of scores for the second class?
(1) In each class, the number of students taking the quiz was 26, and the lowest score in each class was 70.
(2) IN each class, the average (arithmetic mean) score on the quiz was 85
Statements combined:
In each class, the sum of the 26 scores = (count)(average) = 26*85.
Lowest score in each class = 70.
It's possible that the highest score in each class is the SAME, in which case the range for the first class will be equal to the range for the second class.
It's possible that the highest score in the first class is GREATER than the highest score in the second class, in which case the range for the first class will NOT be equal to the range for the second class.
Thus, the two statements combined are INSUFFICIENT.

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Jay@ManhattanReview GMAT Instructor
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Sun Sep 03, 2017 4:00 am
rsarashi wrote:
Professor Vasquez gave a quiz to two classes. Was the range of scores for the first class equal to the range of scores for the second class?

(1) In each class, the number of students taking the quiz was 26, and the lowest score in each class was 70.
(2) In each class, the average (arithmetic mean) score on the quiz was 85.

OAE
We have to determine whether the range of scores for the first class equal to the range of scores for the second class.

We know that Range = Highest score - Lowest score

Statement 1: In each class, the number of students taking the quiz was 26, and the lowest score in each class was 70.

This certainly does not help. We do not know that highest score for the classes, thus, we cannot calculate the range for any class. The information that the number of students in each class is 26 is of no help.

Statement 2: In each class, the average (arithmetic mean) score on the quiz was 85.

This certainly does not help. We cannot calculate the range for any class.

Statement 1 & 2:

Even after combining the two the statements will not help.

For the first class...
Lowest score = 70;
Average score = 85;
Total score = 85*26 = Some figure
However, we cannot get the unique value of Highest score.

Similarly,

For the second class...
Lowest score = 70;
Average score = 85;
Total score = 85*26 = Some figure
However, we cannot get the unique value of Highest score.

The highest scores for each class may be the same or different, so we cannot get the unique answer. Insufficient.

Hope this helps!

-Jay
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