On a science exam, the scores received by a group of students

Question

On a science exam, the scores received by a group of students represented a set of consecutive even integers. If the average of the scores was 35, what was the highest score received by a student?

(1) The difference between the highest and lowest scores received by the students was 22 points.

(2) The lowest score received by a student was 24.

Bunuel · Accepted Answer

Official Solution:

On a science exam, the scores received by a group of students represented a set of consecutive even integers. If the average of the scores was 35, what was the highest score received by a student?

First of all, in evenly spaced sets, such as a set of consecutive even integers, the average always equals the median. Next, the fact that the median of a set of consecutive even integers is 35, an odd integer, indicates that the number of scores (students) is even, with the median being the average of two middle scores. Thus, there would be an equal number of scores below and above the median. So we can have the following cases for the score distribution:

• {34, 36} - if there were two students;

• {32, 34, 36, 38} - if there were four students;

• {30, 32, 34, 36, 38, 40} - if there were six students;

and so on.

(1) The difference between the highest and lowest scores received by the students was 22 points.

There would be only one possible distribution with this difference between the highest and lowest scores, so we can determine the highest score received by a student (just for reference, it would be 46). Sufficient.

(2) The lowest score received by a student was 24.

Similarly, there would be only one possible distribution with this lowest score, so we can determine the highest score received by a student (again, it would be 46). Sufficient.

Answer: D

Bunuel · Answer

Similar question to practice: https://gmatclub.com/forum/on-a-shipmen ... 44409.html

Dereno · Answer

Given that the scores are sets of consecutive even integer.

Average = 35.

Highest score = ?

Average = (first term + Last term)/2

Let the first term be an and the last term be b.

a+b = 35*2 = 70

a+b =70

Statement 1:

(1) The difference between the highest and lowest scores received by the students was 22 points.

b-a = 22

we know that a+b = 70

2b = 92

b= 46.  The highest score is 46.

Sufficient

Statement 2:

(2) The lowest score received by a student was 24.

average is 35, which is between 34 and 36.

if lowest score is 24, the sequence is consecutive.

There are six terms between 24 and 34 {24,26,28,30,32,34}

So, similarly six terms should be after the average. They are { 36,38,40,42,44,46}.

So, the last term 46.

OR a+b = 70

24+b = 70

b = 46 ( the highest number ) .

Sufficient .

Option D

gmatophobia · Answer

Given that the scores received by each student is an even integer. The fact that the average is 35, tells us two things

1. The number of terms in the set is even
2. 34 and 36 are members of the set.

Statement 1

(1) The difference between the highest and lowest scores received by the students was 22 points.

As we know that 34 and 36 are members of the set, let's see what happens when we add two numbers 32, and 38 to the set

32  34 36  38

The difference between the lowest and the highest term is 6

Adding two more terms

30   32  34 36 38  40

The difference between the lowest and the highest term is 10 i.e. we see an increase of 4

Hence, for a given difference, we can find the number of terms and the highest value in that set. This statement is sufficient. We can eliminate B, C, and E.

Statement 2

(2) The lowest score received by a student was 24.

We know from the pre-analysis that the number of terms in the set is even and that 34 and 36 are the members of the set.

The number of terms to the left of 34, should be equal to the number of terms to the right of 36.

24 ..... 34 36 .....

As we know that lowest term is 24, and the common difference between two adjacent terms is 2, we can find the number of terms to the left of 34. Once, this is know the same number of terms must exist to the right of 36, thereby giving us the largest value in the set.

This statement alone is also sufficient.

Option D

On a science exam, the scores received by a group of students

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

On a science exam, the scores received by a group of students

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards