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q + r equals the square of p

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q + r equals the square of p

by sanju09 » Fri Oct 07, 2011 5:06 am
If p, q, and r are three consecutive positive integers such that p < q < r and if q + r equals the square of p, what is the value of p + q + r?
(A) 3
(B) 6
(C) 9
(D) 12
(E) 15
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by shankar.ashwin » Fri Oct 07, 2011 5:15 am
3,4 and 5 is the only possibility I can think of. Hence 12
Last edited by shankar.ashwin on Fri Oct 07, 2011 5:19 am, edited 1 time in total.
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by Anurag@Gurome » Fri Oct 07, 2011 5:19 am
sanju09 wrote:If p, q, and r are three consecutive positive integers such that p < q < r and if q + r equals the square of p, what is the value of p + q + r?
(A) 3
(B) 6
(C) 9
(D) 12
(E) 15
q + r = p²
A is not possible as the integers are positive.
B. 1, 2, 3 but q + r = p² is not true.
C. 2, 3, 4 but q + r = p² is not true.
D. 3, 4, 5. Here 4 + 5 = 9 = 3²; TRUE

The correct answer is D.
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by svd.kumar » Sun Oct 09, 2011 9:27 am
Hi,

Best way of doing this would be take numbers as n, n+1, n+2

so we have n+1+n+2 = n^2
n^2-2n-3 = 0
n^2-3n+n-3=0
n(n-3)+1(n-3)=0
(n+1)(n-3) = 0
n = -1 or 3

-1, 0 , 1
3, 4, 5

So answer is either 0 or 12
we have only 12 given in options

Cheers,
SVD
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by gmatclubmember » Sun Oct 09, 2011 10:28 am
svd.kumar wrote:Hi,

Best way of doing this would be take numbers as n, n+1, n+2

so we have n+1+n+2 = n^2
n^2-2n-3 = 0
n^2-3n+n-3=0
n(n-3)+1(n-3)=0
(n+1)(n-3) = 0
n = -1 or 3

-1, 0 , 1
3, 4, 5

So answer is either 0 or 12
we have only 12 given in options

Cheers,
SVD
Even if 0 would have been in the answer choices it would have been incorrect. since the nos. are positive consecutive integers so there sum has to be non zero positive. and hence 12 :)
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by factor26 » Sun Oct 09, 2011 12:53 pm
Hi,

i had a quick question and was hoping someone can help me out ... when the question stem references "consecutive integers" can we assume the numbers are right next to eachother (4,5,6) or can it be consecutive in the pattern arrangement (2,4,6)?

if its not by a pattern arrangement ... can someone please provide me with an example of how the GMAC would ask for this type of question. sorry for the horrible grammar i'm typing off my blackberry and am in a rush. thanks!!
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by sanju09 » Mon Oct 10, 2011 2:45 am
factor26 wrote:Hi,

i had a quick question and was hoping someone can help me out ... when the question stem references "consecutive integers" can we assume the numbers are right next to eachother (4,5,6) or can it be consecutive in the pattern arrangement (2,4,6)?

if its not by a pattern arrangement ... can someone please provide me with an example of how the GMAC would ask for this type of question. sorry for the horrible grammar i'm typing off my blackberry and am in a rush. thanks!!
Hi factor26, on GMAC when the question stem reads "consecutive integers", they unequivocally mean the patterns like 4, 5, 6; -2, -1, 0; or 12, 11, 10 etc. For the patterns like 2, 4, 6 and 5, 7, 9, the question stem would read "consecutive positive even integers" and "consecutive positive odd integers" respectively. You won't ever sense perplexed in wordings of a GMAC question so don't worry mate.
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by saketk » Mon Oct 10, 2011 4:06 am
sanju09 wrote:If p, q, and r are three consecutive positive integers such that p < q < r and if q + r equals the square of p, what is the value of p + q + r?
(A) 3
(B) 6
(C) 9
(D) 12
(E) 15
p= 3
Q= 4
r= 5

Satisfies the given condition

q + r = p^2
4+5 = 9

the correct answer is option D
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