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What is the value of x?
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05 Oct 2022, 03:55
05 Oct 2022, 03:55
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What is the value of x ?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022) - Gain 20 Kudos & Get FREE Access to GRE Prep Club TESTS
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GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
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GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
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Joined: 20 Feb 2017
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Re: What is the value of x?
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17 Oct 2022, 00:55
17 Oct 2022, 00:55
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Expert Reply
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.
gmatclubot
Re: What is the value of x? [#permalink]
17 Oct 2022, 00:55
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