The ratio of p to q to r is 2:7:11, and r is 6 greater than the sum of

Question

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 ?

(A) 27
(B) 33
(C) 39
(D) 54
(E) 60

BrentGMATPrepNow · Accepted Answer

Nice question!

Let's rewrite all three values ( p ,  q  and  r ) in terms of ONE variable.

To begin, we can see that  \frac{p}{q} = \frac{2}{7} 
Cross multiply to get:  2q = 7p 
Divide both sides by  2  to get:  q = \frac{7p}{2}

Similarly, we can see that  \frac{p}{r} = \frac{2}{11} 
Cross multiply to get:  2r = 11p 
Divide both sides by  2  to get:  r = \frac{11p}{2}

r is 6 greater than the sum of p and q.  
In other words:  r - (p + q) = 6 
Substitute values to get:  \frac{11p}{2} - (p + \frac{7p}{2}) = 6 
To eliminate the fractions, multiply both sides by 2 to get:  11p - (2p + 7p) = 12 
Simplify:  2p = 12 , which means  p = 6

What is the value of  p + r  ?  
Now that we know  p = 6 , we can calculate the value of  r  as follows:  r = \frac{11p}{2}= \frac{11(6)}{2}=33 
 p + r = 6 + 33 = 39

Answer: C

Abhishek009 · Answer

p : q : r = 2x : 7x : 11x

p + q = 9x  &  r = 11x

So,  11x - 9x = 6

Thus,  x = 3

Hence,  p + r = 3(2 + 11) =39 , Answer msut be (C)

pleasefix · Answer

Nice question. I spent way too much time on this at first.

We are given all items in relation to each other, which can be translated as; p/2=q/7=r/11.
Furthermore, we are given r=p+q+6.

And finally, we need to find r+p =?.

Step 1)  Calculate what r is in terms of p
r=11p/2

Step 2)  insert in question
r+p = 11p/2+p = 13p/2

So we want to know the value of p now.

Step 3)  Calculate the value of p by substituting everything into the other equation based on the ratios:
r=p+q+6 =>
11p/2 = p + (7p/2) +6
11p/2 = 9p/2 + 6
2p/2 = 6
p = 6

Step 4)  is filling in p in the question (as calculated in step 1)

13p/2 = (13*6)/2 = 13*3 = 39

p = 39 is answer C

100mitra · Answer

r = (p + q) + 6
11x = (2x + 7x) + 6
11x - 9x = 6
 X = 3

P = 2x = 2*3 = 6
R = 11x = 11*3 = 33
P+ R = 33+6 = 39
 Option C = 39

Posted from my mobile device

MathRevolution · Answer

If p = 2 , q = 7 and r = 11 then r(11) is 2 greater than (p + q = 2 + 7 = 9)

For 'r' to be '6' greater, multiply the values by '3'.

p = 6, q = 21 and r = 33 => 33 is '6' greater than (p + q = 6 + 21 = 27)

Hence, p + r = 6 + 33 = 39

Answer C

xoxokunal · Answer

I made equation as 11x + 6 = (2x + 7x) i.e. r + 6 = p + q where am i getting it wrong?

Will it be right in case if question would have said r is 6 more than (p+q)?

Little bit confused in greater than and more than words. Can someone exlain?

Bunuel · Answer

The phrase "r is 6 greater than the sum of p and q" means r = (p + q) + 6. See there, r is equal to 6 more than (p + q). Therefore, your equation should be 11x = (2x + 7x) + 6.

I hope this clears up the confusion!

xoxokunal · Answer

Yeah! Thank you so much.

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The ratio of p to q to r is 2:7:11, and r is 6 greater than the sum of

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