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On the number line above, p, q, r, s, and t are five consec [#permalink]
07 Dec 2012, 07:30

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Difficulty:

25% (medium)

Question Stats:

71% (01:54) correct
29% (01:12) wrong based on 202 sessions

Attachment:

Number line.png [ 2.33 KiB | Viewed 3313 times ]

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.

Re: On the number line above, p, q, r, s, and t are five consec [#permalink]
07 Dec 2012, 07:37

Expert's post

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?

{p, q, r, s, t} is an evenly spaced set thus its mean = median = middle term = r.

(1) q + s =24. Since q, r and s are consecutive even integers, then q=r-2 and s=r+2 --> (r-2)+(r+2)=24 --> r=12. Sufficient.

(2) The average (arithmetic mean) of q and r is 11. (r-2)+r=2*11 --> r=12. Sufficient.

Re: On the number line above, p, q, r, s, and t are five consec [#permalink]
11 Dec 2012, 03:54

Walkabout wrote:

Attachment:

Number line.png

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.

Ans. : Let p=x, q=x+2, r=x+4 , s=x+6, t=x+8 to find the mean we need to find x. From statement 1 , we get 2x+8=24 From statement 2 we get x+3=11 Therefore the answer is (D). _________________

Re: On the number line above, p, q, r, s, and t are five consec [#permalink]
16 Dec 2012, 22:41

Expert's post

kelleygrad05 wrote:

My understanding of consecutive integers, is that they are separated by only 1, i.e. 3, 4, 5, 6, 7, 8

I was able to find the first statement sufficient, but not the second, mainly because the answer uses the formula p + (p+2) +....

Why is 2 being added to P?

We are not told that p, q, r, s, and t are consecutive integers. We are given that p, q, r, s, and t are five consecutive EVEN integers. For example 2, 4, 6, 8, 10. _________________

Re: On the number line above, p, q, r, s, and t are five consec [#permalink]
11 Jan 2014, 09:17

They are basically giving us some equation in disguise.

1. q+s=24 but for a fact set we know that the leap between q and s is 4 and this translates into an equation that subtracted gives us the value of q from which we can calculate the average. 2. q+r=22 same old story, the leap between q and r this time is 2 units. r-q=2 subtract it from the given equation and you are done you got one value, the remaining values follow logically.

D. _________________

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Re: On the number line above, p, q, r, s, and t are five consec
[#permalink]
11 Jan 2014, 09:17