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Updated on: 11 Feb 2020, 19:04
Originally posted by BrentGMATPrepNow on 06 Nov 2019, 07:50.
Last edited by BrentGMATPrepNow on 11 Feb 2020, 19:04, edited 1 time in total.
Last edited by BrentGMATPrepNow on 11 Feb 2020, 19:04, edited 1 time in total.
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
65% (02:46) correct
35%
(02:56)
wrong
based on 259
sessions
History
Date
Time
Result
Not Attempted Yet
\(15^2 - 63^2 + 27^2 - 22^2 + (54)(15) + (44)(63)=\)
A) 53
B) 83
C) 91
D) 93
E) 105
A) 53
B) 83
C) 91
D) 93
E) 105
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Updated on: 07 Nov 2019, 07:07
Originally posted by BrentGMATPrepNow on 06 Nov 2019, 16:00.
Last edited by BrentGMATPrepNow on 07 Nov 2019, 07:07, edited 1 time in total.
Last edited by BrentGMATPrepNow on 07 Nov 2019, 07:07, edited 1 time in total.
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GMATPrepNow
Key Properties:
#1: \((x + y)^2 = x^2 + 2xy + y^2\)
#2: \((x - y)^2 = x^2 - 2xy + y^2\)
#3: \(x^2-y^2 = (x+y)(x-y)\)
Given: \(15^2 - 63^2 + 27^2 - 22^2 + (54)(15) + (44)(63)\)
Notice that 15 appears in two terms, and 63 appears in two terms.
Also, if we recognize that 54 = (2)(27), we see that 27 appears twice.
And, if we recognize that 44 = (2)(22), we see that 22 appears twice.
Here's what I mean: \(15^2 - 63^2 + 27^2 - 22^2 + (2)(27)(15) + (2)(63)(22)\)
Let's group the similar terms to get: \(27^2 + (2)(27)(15) +15^2 - 63^2 + (2)(63)(22)-22^2\)
Rewrite to get: \([27^2 + (2)(27)(15) +15^2] - [63^2 - (2)(63)(22)+22^2]\)
Notice that \(27^2 + (2)(27)(15) +15^2\) looks a lot like the expansion in key property #1, and \(63^2 - (2)(63)(22)+22^2\) looks a lot like the expansion in key property #2
So, we can factor them as follows: \((27+15)^2 - (63-22)^2\)
Simplify: \(42^2 – 41^2\) [aha! A difference of squares!!]
Use property #3 to factor the expression: \((42+41)(42-41)\)
Simplify: \((83)(1)\)
Evaluate: \(83\)
Answer: B
Cheers,
Brent
General Discussion
06 Nov 2019, 10:20
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Hmmm, I figured I'd see a solution by now.
Here are two hints:
1) There is a nice solution that's much faster than simply calculating each part
2) In many cases, the GMAT tests your algebra skills by giving you questions like the above. I wrote an article about it called Common mistake - Not recognizing “hidden” algebra questions : https://www.gmatprepnow.com/articles/co ... -questions
Cheers,
Brent
Here are two hints:
1) There is a nice solution that's much faster than simply calculating each part
2) In many cases, the GMAT tests your algebra skills by giving you questions like the above. I wrote an article about it called Common mistake - Not recognizing “hidden” algebra questions : https://www.gmatprepnow.com/articles/co ... -questions
Cheers,
Brent
