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If the points p, q r and s are equally spaced in a number line, where

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If the points p, q r and s are equally spaced in a number line, where  [#permalink]

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New post 23 May 2017, 00:03
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If the points p, q r and s are equally spaced in a number line, where p < q < r < s then, what is the value of q?

(1) p + r = 10
(2) p + q + r = 15
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If the points p, q r and s are equally spaced in a number line, where  [#permalink]

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New post 23 May 2017, 00:31
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If the points p, q r and s are equally spaced in a number line, where p < q < r < s then, what is the value of q?

(1) p + r = 10. Since the points p, q r and s are equally spaced, then q is the average of p and r, so q = (p + r)/2 = 10/2 = 5. Sufficient.

(2) p + q + r = 15. The same here: q = (p + r)/2 --> 2q = p + r --> 2q + q = 15 --> q = 5. Sufficient.

Answer: D.
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Re: If the points p, q r and s are equally spaced in a number line, where  [#permalink]

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New post 23 May 2017, 00:37
If p, q, r, s are evenly spaced on a number line such that p < q < r < s, then
we can also say that the values of p, q, r, s will be in an Arithmetic Progression (AP)
q lies in the middle of p & r, r lies in the middle of q & s

In an AP, middle term is always the arithmetic mean of its two adjacent terms (previous term and next term)
That is the basic meaning of an 'evenly spaced' set or AP.
So q will be the arithmetic mean of p & r

Statement 1. p + r = 10
Thus q = 10/2 = 5. Sufficient

Statement 2. p + q + r = 15
Since q is average of p&r, p+r= 2q
Or p+q+r = 2q+q = 3q = 15
or q = 5. Sufficient

Hence answer is D
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Re: If the points p, q r and s are equally spaced in a number line, where  [#permalink]

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New post 29 May 2017, 08:34
niteshwaghray wrote:
If the points p, q r and s are equally spaced in a number line, where p < q < r < s then, what is the value of q?

(1) p + r = 10
(2) p + q + r = 15



Another possible approach:

Let's write p, the least number of the series, equal "a", a generic number, and k represents the distance between two numbers.
Therefore the numbers of the series are q= a+k, r= a+2k, s= a+3k.

1- p+r= 2a+2k = 10 --> a+k=5 = q --------> SUFF
2- p+r+s = 3a+3k=15 --> a+k = 5 = q ------> SUFF

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Re: If the points p, q r and s are equally spaced in a number line, where  [#permalink]

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New post 23 Jul 2018, 04:16
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