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On the number line above, p, q, r, s, and t are five

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by BTGmoderatorDC » Tue Apr 02, 2019 10:35 pm

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On the number line above, p, q, r, s, and t are five consecutive even integers in increasing order. What is the average (arithmetic mean) of these five integers?

(1) q + s =24
(2) The average (arithmetic mean) of q and r is 11.

OA D

Source: Official Guide
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Source: — Data Sufficiency |

by Jay@ManhattanReview » Thu Apr 04, 2019 12:12 am
BTGmoderatorDC wrote:Image

On the number line above, p, q, r, s, and t are five consecutive even integers in increasing order. What is the average (arithmetic mean) of these five integers?

(1) q + s =24
(2) The average (arithmetic mean) of q and r is 11.

OA D

Source: Official Guide
Since p, q, r, s, and t are five consecutive even integers, the average (arithmetic mean) of these five integers would be r.

we have

q = p + 2;
r = p + 4;
s = p + 6;
t = p + 8

So, we have to get the value of p +4.

Let's take each statement one by one.

(1) q + s =24

p + 2 + p + 6 = 24 => 2p + 8 = 24 => p = 8 => r = p + 4 = 8 + 4 = 12. Sufficient.

(2) The average (arithmetic mean) of q and r is 11.

=> [(p + 2) + (p + 4)]/2 = 11 => 2p + 6 = 22 => p = 8 => r = p + 4 = 8 + 4 = 12. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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by swerve » Thu Apr 04, 2019 10:26 am
Statement 1.
The number of terms is \(5\) so the center term i.e \(r\) will be the average as the series is an arithmetic progression, so it can be found by \(\frac{q +s}{2} = 12\).

Statement 2.
Given \(\frac{q + r}{2} = 11\).

Also \(q = r-2\) (as all are even consecutive integers in a series). So again the average can be found out.

Therefore, the correct answer is __D__
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