Exam / Average / Median

pkw209 wrote:What is the best way to solve this one?

The scores on a certain exam were 60, 75, 100 70 and x. If the median score was 5 points lower than the average score on the exam, which of the following could be x?

60 70 75 100 x
First, the average is (305 +x)/5 = 61 + x/5

Thus the median m= 56 + x/5

Since 70 <= m <= 75

70 <= 56 +x/5 <= 75
70 <= x <= 95

Note that if 70 < m < 75, m= x
and thus 4/5 x = 56, which implies that x = 70

Thus x could be either 70 or 95

It was very wise of you to look at the answer choices, as they get you to the answer faster!

Thanks, Kevin. How did you know this?

Since 70 <= m <= 75

Because Median is the middle number after arranging the numbers in Sequence. As there are 5 numbers provided, middle number is either 75 or a number between 70 & 75.

Hope that clarifies

pkw209 wrote:What is the best way to solve this one?

The scores on a certain exam were 60, 75, 100 70 and x. If the median score was 5 points lower than the average score on the exam, which of the following could be x?

a) 75

b) 80

c) 85

d) 90

e) 95

answer is e

Based on the answer choices, I was able to identify that the median had to be 75. With that info I was able to create an equation. However, if the answer choices DID NOT allow you to determine what the median was, how would you solve this problem?

average score = 61 +x/5


Case 1: If x<70
Median is 70

=> 61 + x/5 = 70 +5
x=70

Case 2: If 70<x<75
Median is x

61 +x/5 = x+5

x= 5/4*56 = 70

Case 3:
If x>75

Median is 75
61 + x/5 = 75+5

x = 19*5 = 95

So for the given conditions to prevail x has to be either 70 or 95; 95 features the options

Ascending order
60 70 75 100 position of x undecided.
total of 60+70+75+100 = 305
avg. of 5 nos = (305+x)/5 = 61+ x/5
the diff from the median is 5
x cannot have 0 in its unit digit
so a, c or e
if the median is 60 70 75 or 100
then x/5 should have 9 in its unit digit.
a) 75/5 = 15 c)85/5 = 17
e) 95/5 = 19
if x is the median ?

pkw209 wrote:What is the best way to solve this one?

The scores on a certain exam were 60, 75, 100 70 and x. If the median score was 5 points lower than the average score on the exam, which of the following could be x?

a) 75

b) 80

c) 85

d) 90

e) 95

The average is:

(60 + 75 + 100 + 70 + x)/5 = (305 + x)/5

Let’s plug in answer choices to see which could be x, given that the median is 5 less than the average:

A) average = 380/5 = 76, and scores are 60, 70, 75, 75, 100; mean is 76 and median is 75 doesn’t work.

B) average = 385/5 = 77, and scores are 60, 70, 75, 77, 100; mean is 77 and median is 75 doesn’t work.

C) average = 390/5 = 78, and scores are 60, 70, 75, 85, 100; mean is 78 and median is 75 doesn’t work.

D) average = 395/5 = 79, and scores are 60, 70, 75, 90, 100; mean is 79 and median is 75 doesn’t work.

E) average = 400/5 = 80, and scores are 60, 70, 75, 95, 100; mean is 80 and median is 75, which is exactly 5 points less; this is possible.

Answer: E