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A set has exactly five consecutive positive

by Vincen » Sun Oct 08, 2017 11:37 am
A set has exactly five consecutive positive integers starting with 1.What is the percentage decrease in the average when the greatest number is removed from the set?

A)5
B)8.5
C)12.5
D)15.2
E)16.6

The OA is E

How should I do this PS question? Should I calculate both averages and then compare them?
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by Jay@ManhattanReview » Sun Oct 08, 2017 8:41 pm
Vincen wrote:A set has exactly five consecutive positive integers starting with 1.What is the percentage decrease in the average when the greatest number is removed from the set?

A)5
B)8.5
C)12.5
D)15.2
E)16.6

The OA is E

How should I do this PS question? Should I calculate both averages and then compare them?
The given set is {1, 2, 3, 4, 5}. Since this is an equally spaced set, its average would be the middle-most number = 3.

After removing the greatest number 5, we get the set {1, 2, 3, 4}. This is also an equally spaces set, but the number of elements is even, thus, the average would be the average of the two middle-most numbers, 2 and 3. Thus, the new average = (2 + 3)/2 = 2.5.

The percentage decrease in the average when the greatest number is removed from the set = [(3 - 2.5) / 3]*100% = [0.5 / 3]*100% = 16.67%.

The correct answer: E

Hope this helps!

-Jay

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by Matt@VeritasPrep » Wed Oct 11, 2017 5:52 pm
Initial set: 1, 2, 3, 4, 5
Initial average: 3

New set: 1, 2, 3, 4
New average: 2.5

Decrease = (2.5 - 3)/3 = -.5/3 = -1/6 ≈ 16.67%
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by Scott@TargetTestPrep » Sun Nov 24, 2019 5:40 pm
Vincen wrote:A set has exactly five consecutive positive integers starting with 1.What is the percentage decrease in the average when the greatest number is removed from the set?

A)5
B)8.5
C)12.5
D)15.2
E)16.6

The OA is E

How should I do this PS question? Should I calculate both averages and then compare them?
The original average = (1 + 2 + 3 + 4 + 5)/5 = 3.

The new average = (1 + 2 + 3 + 4)/4 = 2.5

(2.5 - 3)/3 x 100 = -0.5/3 x 100 = -1/6 x 100 ≈ -16.7

We see that the average is decreased by approximately 16.7%.

Answer: E

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by [email protected] » Mon Nov 25, 2019 10:16 am
Hi All,

We're told that a set has exactly five CONSECUTIVE positive integers starting with 1. We're asked for the percentage decrease in the average when the greatest number is removed from the set. This question requires the use of the Percent Change Formula:

Percent Change = (New - Old)/(Old) = (Difference)/(Original

The original set of numbers is 1, 2, 3, 4, 5, so the average of that set is (1+2+3+4+5)/5 = 15/5 = 3

Once we remove the greatest number, we're left with 1, 2, 3, 4, so the average of that new set is (1+2+3+4)/4 = 10/4 = 2.5

The Percent Change would be (2.5 - 3)/3 = .5/3 = 1/6 = 16 2/3%

Final Answer: E

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