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# The ratio of p to q to r is 2:7:11, and r is greater than the sum of p

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Intern
Joined: 13 Aug 2017
Posts: 8
The ratio of p to q to r is 2:7:11, and r is greater than the sum of p  [#permalink]

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13 Aug 2018, 15:55
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Hi, need help with a proportions problem. Any help would be greatly appreciated!

The ratio of p to q to r is 2:7:11, and r is 6 greater than the sum of p and q. What is the value of p+r?

I would assume I can get r = 6 + p + q, but don't know what to do after.
Senior SC Moderator
Joined: 22 May 2016
Posts: 2208
The ratio of p to q to r is 2:7:11, and r is greater than the sum of p  [#permalink]

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13 Aug 2018, 16:31
neiln413b wrote:
Hi, need help with a proportions problem. Any help would be greatly appreciated!

The ratio of p to q to r is 2:7:11, and r is 6 greater than the sum of p and q. What is the value of p+r?

I would assume I can get r = 6 + p + q, but don't know what to do after.

neiln413b , welcome to GMAT Club!

Do you have answer options? If so, please post them (or reply here and I will).
PS questions should have options and specified sources.

Please see Rules for Posting, here.

For your question, use a multiplier, $$x$$, see footnote.*
Ratio of
p | q | r
2x|7x|11x

$$r=(p+q)+6$$

$$11x=(2x+7x)+6$$
$$2x=6$$
$$x=3$$

That $$x$$ is the multiplier.

$$p=2x=(2*3)=6$$
$$r=11x=(11*3)=33$$

$$(p+r)= (6+33)=39$$

Hope that helps.

*All ratios have parts.
If we have things in the ratio
$$3 : 4 : 5$$
in most cases we really mean that the things are in the ratio
$$3x : 4x: 5x$$

Say the ratio parts were lengths of sides in a special right triangle:
$$3x-4x-5x$$

Let $$x=2$$
$$3x = 6$$ and so on
Hence ACTUAL lengths are
$$6:8:10$$
We just used the ratio parts times a multiplier to get ACTUAL lengths, and those lengths are in the same ratio as the original.
The ratio of p to q to r is 2:7:11, and r is greater than the sum of p &nbs [#permalink] 13 Aug 2018, 16:31
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# The ratio of p to q to r is 2:7:11, and r is greater than the sum of p

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