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## the value of p + q + r?

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sanju09 GMAT Instructor
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the value of p + q + r? Thu Feb 16, 2012 3:53 am
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If p:q = (3/7):2 and q:r = 7:(11/2), what is the value of p + q + r?
I. The value of q is equal to the sum of p and r.
II. p + 3 q - 2 r = 23.

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mankey GMAT Destroyer!
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Thu Feb 16, 2012 10:24 am
IMO: D.

p:q:r::3/14:1:11:14

Using a ratio and a linear equation you will be able to solve the equation, assume all variables in any one variable.

What is the OA?

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Thu Feb 16, 2012 10:24 am
If p:q = (3/7):2 and q:r = 7:(11/2), what is the value of p + q + r?
The question can be rephrased to if p:q:r = 3:14:11 then what is the value of p + q + r?
Quote:
I.The value of q is equal to the sum of p and r.
Since p:q:r = 3:14:11, we can represent p,q,r in terms of x(x = a positive integer)
p = 3x
q = 14x
r = 11x
q = p+q => 14x = 14x. Since, we still are not aware of the value of x, Statement 1 is insufficient to answer the question
Quote:
II.p + 3 q - 2 r = 23.
p + 3 q - 2 r = 3x + (3*14x) - (2*11x) = 23x = 23. Implies x = 1 and p+q+r=3+14+11=28. Statement 1 is sufficient to answer the question

IMO B

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amit.trivedi@ymail.com GMAT Destroyer!
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Fri Feb 17, 2012 1:44 am
Well very intelligent question but not difficult...

From simultaneous equations perspective, the answer comes down to be C, as you need 2 equations...

But B alone can give the answer...

Statement 1 alone is absolutely insufficient to provide with an answer...

Statement 2:

(p:q:r) = (3:14:11)

let x be the common element between then,

p = 3x ; q = 14x ; r = 11x

now putting the values in the second equation, we get

23x = 23 hence x = 1

when x =1, the total of (p+q+r) = 28 which is the right answer...

THa OA is B.

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amit.trivedi@ymail.com GMAT Destroyer!
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Fri Feb 17, 2012 1:47 am
Actually statement 1 creates situation like 14x = 14x which is not a valid equation by itself...

Hence statement 1 is insufficient...

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Sat Feb 18, 2012 6:56 am
sanju09 wrote:
If p:q = (3/7):2 and q:r = 7:(11/2), what is the value of p + q + r?
I. The value of q is equal to the sum of p and r.
II. p + 3 q - 2 r = 23.

To combine ratios with a common element, the common element must be represented by the same value in each ratio.

p:q = (3/7) : 2 = 3:14.
q:r = 7 : (11/2) = 14:11.
Combining the ratios:
p:q:r = 3:14:11.

Statement 1: q = p+r.
No new information here.
In p:q:r = 3:14:11, p+r = 3+11 = 14, which is the value of q.

Thus, given ANY combination that satisfies p:q:r = 3:14:11, q=p+r.
If the values in the ratio are doubled so that p=6, q=28, and r=22, q=p+r.
If the values in the ratio are tripled so that p=9, q=42 and r=33, q=p+r.

Since an infinite number of combinations are possible, no way to determine p+q+r.
INSUFFICIENT.

Statement 2: p + 3q - 2r = 23.
This equation is satisfied by the values in the ratio.
If p=3, q=14, and r=11, then p + 3q - 2r3 + 3(14) - 2(11) = 23.
Thus, this is the ONLY combination that will work here.
Any MULTIPLE of 3:11:14 will yield a MULTIPLE of 23.
Thus, p+q+r = 3+14+11 = 28.
SUFFICIENT.

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