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

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by BTGmoderatorDC » Sun Jul 14, 2019 7:36 pm

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C

D

E

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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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by Jay@ManhattanReview » Mon Jul 15, 2019 8:47 pm
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 in increasing order, we can write them as q = p + 2; r = p + 4; s = p + 6; t = p + 8.

Average of p, q, r, s, and t = middle-most among them; since these integers are evenly spaced, median and mean would be the same.

Average of p, q, r, s, and t = r = p + 4

If we get the value of any integers, we get the answer.

Let's take each statement one by one.

(1) q + s = 24

(p + 2) + (p + 6) = 24 => p = 8. Sufficient.

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

=> (q + r)/2 = 11

q + r = 22 => (p + 2) + (p + 4) = 22 => p = 8. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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