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21 Sep 2018, 01:17
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
73% (02:11) correct
27%
(02:29)
wrong
based on 244
sessions
History
Date
Time
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Not Attempted Yet
In the right triangle above, what is the length of AC?
(A) 9
(B) 10
(C) 12
(D) 13
(E) 15
Attachment:
Capture (1).JPG [ 22.98 KiB | Viewed 7944 times ]
21 Sep 2018, 01:23
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Bunuel
Most frequent right triangles used in GMAT are as shown in attachment
Now we have to think of right triangle with sides (x-1), (x+2) and (x+5) i.e. sides with length separated by 3 units
As we see there is a right triangle 9-12-15 which fits
hence, x-1 = 9
i.e. x = 10
i.e. AC = x+2 = 12
Answer: Option C
Attachments
Geometry 5 Special right triangle1.jpg [ 123.92 KiB | Viewed 7982 times ]
21 Sep 2018, 06:13
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Bunuel
Since we have a right triangle, we can apply the Pythagorean Theorem
When we do so we get: (x - 1)² + (x + 2)² = (x + 5)²
Expand each square to get: (x² - 2x + 1) + (x² + 4x + 4) = x² + 10x + 25
Simplify left side to get: 2x² + 2x + 5 = x² + 10x + 25
Subtract x² from both sides to get: x² + 2x + 5 = 10x + 25
Subtract 10x from both sides to get: x² - 8x + 5 = 25
Subtract 25 from both sides to get: x² - 8x - 20 = 0
Factor: (x - 10)(x + 2) = 0
So, EITHER x = 10 OR x = -2
We can rule out the solution x = -2, since that would make some of the lengths NEGATIVE
So, it MUST be the case that x = 10
AC has length x + 2
So, AC = 10 + 2 = 12
Answer: C
Cheers,
Brent
