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

Question

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

Bunuel · Answer

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.

amanvermagmat · Answer

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

matt882 · Answer

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

Matt

KaiWan · Answer

Why it cannot be negative?

Posted from my mobile device

Bunuel · Answer

If you examine the solutions above closely, you'll notice that p ends up being 5, which is positive. Thus, your question doesn't make sense: p can't be negative since we determined it's 5, which is not a negative number.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards