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20 Mar 2015, 07:11
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
81% (02:08) correct
19%
(02:38)
wrong
based on 274
sessions
History
Date
Time
Result
Not Attempted Yet
What is the value of x?
A. 2
B. 3
C. 4
D. 5
E. 6
Attachment:
righttrianglealgebra_figure.PNG [ 3.11 KiB | Viewed 6114 times ]
This is a very simple exercise of the Pythagorean Theorem. The tricky part is the FOIL.
\(a^2 + b^2 = c^2\)
\((3x+3)^2 + (x+2)^2 = (2x+7)^2\)
\((9x^2 + 18x + 9) + (x^2 + 4x + 4) = (4x^2 + 28x + 49)\)
\(10x^2 + 22x + 13 = 4x^2 + 28x + 49.\)
\(6x^2 -6x - 36 = 0\)
\(6(x^2 - x - 6) = 0\)
\(6(x-3)(x+2) = 0\)
\(x = 3\) or \(x = -2.\)
Since x can't be negative, we know that x=3.
Answer: B
OR, the ADVANCED GMATer would notice that all of the answers are integers that are easily manageable. A quicker approach would be to plug these values in and find a known pythagorean triple.
x = 2 results in (4,9,11). Not a pythagorean triple.
x = 3 results in (5,12,13). This is a known pythagorean triple and we can stop here. We have found our answer:
Answer B.
\(a^2 + b^2 = c^2\)
\((3x+3)^2 + (x+2)^2 = (2x+7)^2\)
\((9x^2 + 18x + 9) + (x^2 + 4x + 4) = (4x^2 + 28x + 49)\)
\(10x^2 + 22x + 13 = 4x^2 + 28x + 49.\)
\(6x^2 -6x - 36 = 0\)
\(6(x^2 - x - 6) = 0\)
\(6(x-3)(x+2) = 0\)
\(x = 3\) or \(x = -2.\)
Since x can't be negative, we know that x=3.
Answer: B
OR, the ADVANCED GMATer would notice that all of the answers are integers that are easily manageable. A quicker approach would be to plug these values in and find a known pythagorean triple.
x = 2 results in (4,9,11). Not a pythagorean triple.
x = 3 results in (5,12,13). This is a known pythagorean triple and we can stop here. We have found our answer:
Answer B.
General Discussion
nachobioteck
GMAT 2: 700 Q47 V40
Posts: 147
20 Mar 2015, 10:15
Kudos
Bookmarks
Bunuel
The easiest way to do it, is to plug in the answer choices, and then check if they fit the pythagorean theorem. That way you avoid having to do FOIL and the algebra. I started by plugging B and got the right answer right away.
