Exam / Average / Median

[pkw209]

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?

[kevincanspain]

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!

[pkw209]

Thanks, Kevin. How did you know this?

Since 70 <= m <= 75

[vvijay146]

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

[ajith]

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

[kstv]

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 ?

[Jeff@TargetTestPrep]

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