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On the number line above, p, q, r, s, and t are five consec [#permalink]

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07 Dec 2012, 08:30

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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.

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

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07 Dec 2012, 08:37

Expert's post

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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?

{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]

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11 Dec 2012, 04:54

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]

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16 Dec 2012, 23:41

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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]

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11 Jan 2014, 10:17

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. _________________

learn the rules of the game, then play better than anyone else.

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

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24 Feb 2015, 12:22

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

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24 Feb 2015, 22:38

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Hi All,

This DS question is full of Number Properties and the math involved is fairly straight-forward. However, if you don't see the "elegant" approach to answer this question, then you can still use "brute force" and some basic Arithmetic to get the correct answer.

We're given a number line with 5 variables on it. We're told that the variables represent 5 CONSECUTIVE EVEN INTEGERS. That's a very specific set of "restrictions", so you can use them to your advantage if you have to "play around" with this question. We're asked for the AVERAGE of the 5 integers. Since we know that they're consecutive evens, if we can figure out ANY of them, then we can figure out the others AND answer the question.

Fact 1: Q + S = 24

Looking at the drawing, we know that Q, R and S are 3 CONSECUTIVE EVEN INTEGERS, so even if we don't know how to do the Algebra here, we can still run some TESTs....

IF Q, R and S are.... 2, 4 and 6, then Q+S = 8. That's too small though (it's supposed to be 24)

IF Q, R and S are a bit bigger, say.... 8, 10 and 12, then Q + S = 20. This is still too small, but it's getting closer to 24...

IF Q, R and S are.... 10, 12 and 14, then Q + S = 24. This is a MATCH for what we're looking for. We can also figure out the missing values (they're 8 and 16).

By making these variables larger or smaller, the sum of Q+S won't = 24, so we know that the 10/12/14 example is the ONLY possibility that fits. Fact 1 is SUFFICIENT.

Fact 2: The average of Q and R is 11

Since Q and R are 2 CONSECUTIVE EVEN INTEGERS, we're going to need 2 numbers that are close to 11....

IF Q and R are.... 8 and 10, then the average is 9 (which is not a match; it's supposed to be 11)

IF Q and R are... 10 and 12, then the average is 11. This is a MATCH.

Making Q and R any bigger will raise the average (and it won't match), so we know that 10 and 12 are the ONLY possible values that fit. The other numbers would be 8, 14 and 16. Fact 2 is SUFFICIENT.

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