Equations (Consec Integers): If q, r, and s are consecutive

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II: Master | Next Rank: 500 Posts; Posts: 400; Joined: Mon Dec 10, 2007 1:35 pm; Location: London, UK; Thanked: 19 times; GMAT Score:680

by II » Tue May 20, 2008 3:18 pm

If q, r, and s are consecutive even integers and q < r < s, which of the following CANNOT be the value of s^2 – r^2 – q^2 ?

(A) -20 (B) 0 (C) 8 (D) 12 (E) 16

Would be interested in seeing the various approaches to solving this question.

Thanks in advance.
II

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Source: Beat The GMAT — Problem Solving | Tue May 20, 2008 3:18 pm

VP_Jim: GMAT Instructor; Posts: 1223; Joined: Thu May 01, 2008 3:29 pmFollowed by: 15 members; Location: Los Angeles, CA; Thanked: 185 times

by VP_Jim » Tue May 20, 2008 5:39 pm

The first thing that comes to mind for me is to plug in numbers, since all of our answer choices are pretty close together and nice, low numbers to work with, it shouldn't be that bad.

I'd start with q=-2, r=0, and s=2. Plugging that in to the given equation gives us 0, so that's not the answer.

Then I'd change the numbers: q=0, r=2, s=4, which gives us 12, so that's out.

q=2, r=4, s=6 gives us 16. Now since we've hit the highest answer choices, I'd start lowering the numbers.

q=-4, r=-2, s=0 gives us -20, so that's out.

One more thought: if I were crunched for time, I might've stopped once I showed it could be 0 and 12, since we skipped 8, I would've guessed that's the answer.

The only one we haven't used is 8, so that's the answer. A little time consuming but at least we're sure we're correct - the numbers don't lie!

Jim S. | GMAT Instructor | Veritas Prep

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luvaduva: Senior | Next Rank: 100 Posts; Posts: 84; Joined: Tue Feb 05, 2008 8:52 pm; Thanked: 8 times

by luvaduva » Tue May 20, 2008 6:25 pm

Jim's approach is probably the quickest, but if you are just dying for a quadratic then...

q, q+2, q+4

(q+4)^2 - (q+2)^2 - q^2 => q^2 + 8q + 16 - q^2 - 4q - 4 - q^2 => -q^2 + 4q + 12

Set this equal to each answer and see if it produces an acceptable answer. Multiply it through by a negative and remember to do the same with each answer..q^2 -4q -12 = -( ):

a) q^2 -4q -32 = 0 => (q-8)(q+4)=0, q = 8 or -4 OKAY
b) q^2 -4q -12 = 0 => (q+2)(q-6)=0, q =-2 or 6 OKAY
c) q^2 -4q -4 = 0 => NOT OKAY. This is your answer.

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AleksandrM: Legendary Member; Posts: 566; Joined: Fri Jan 04, 2008 11:01 am; Location: Philadelphia; Thanked: 31 times; GMAT Score:640

by AleksandrM » Wed May 21, 2008 9:15 am

I think more than anything this number is testing whether you know that 0 is an even integer.

https://second-lap.blocked/

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