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67² + (2)(67)(133) + 133² =

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by Brent@GMATPrepNow » Thu Nov 04, 2021 8:22 am

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67² + (2)(67)(133) + 133² =

A) 36,000
B) 40,000
C) 48,000
D) 54,000
E) 62,500

Answer: B
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Re: 67² + (2)(67)(133) + 133² =

by Brent@GMATPrepNow » Fri Nov 05, 2021 6:55 am
Brent@GMATPrepNow wrote: ↑
Thu Nov 04, 2021 8:22 am
 67² + (2)(67)(133) + 133² =

A) 36,000
B) 40,000
C) 48,000
D) 54,000
E) 62,500

Answer: B
Source: www.gmatprepnow.com
This question is part of our collection of Fool Me Once questions (https://www.gmatprepnow.com/articles/fo ... -questions), because many students will fail to see that this more of an Algebra question than a computational question.
In fact, if you recognize that 67² + (2)(67)(133) + 133² closely resembles the special product x² + 2xy + y², then you can calculate the value in a matter of seconds.

Notice that x² + 2xy + y² can be factored to get x² + 2xy + y² = (x + y)²
The expression 67² + (2)(67)(133) + 133² can be factored the same way.

We get: 67² + (2)(67)(133) + 33² = (67 + 133)² = (200)² = 40,000

Answer: B
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