q + r equals the square of p

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

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

The mind is everything. What you think you become. -Lord Buddha

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The Princeton Review - Manya Abroad
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Source: Beat The GMAT — Problem Solving | Fri Oct 07, 2011 5:06 am

shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

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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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

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 = pÂ²
A is not possible as the integers are positive.
B. 1, 2, 3 but q + r = pÂ² is not true.
C. 2, 3, 4 but q + r = pÂ² is not true.
D. 3, 4, 5. Here 4 + 5 = 9 = 3Â²; TRUE

The correct answer is D.

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svd.kumar: Junior | Next Rank: 30 Posts; Posts: 27; Joined: Tue Sep 21, 2010 7:38 am; Thanked: 4 times

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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gmatclubmember: Master | Next Rank: 500 Posts; Posts: 158; Joined: Sat Sep 03, 2011 10:31 amFollowed by: 2 members; Thanked: 29 times

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

a lil' Thank note goes a long way

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factor26: Senior | Next Rank: 100 Posts; Posts: 99; Joined: Sun Mar 13, 2011 12:42 pm

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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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

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.

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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saketk: Legendary Member; Posts: 608; Joined: Sun Jun 19, 2011 11:16 amFollowed by: 8 members; Thanked: 37 times

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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