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Is x^2 > 5^2 ?

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Bunuel
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Is x^2 > 5^2 ? [#permalink] New post   02 Jun 2016, 11:56
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49% (02:22) correct 51% (02:17) wrong based on 153 sessions
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Is x^2 > 5^2 ?

(1) |x+5| = 3|x - 5|

(2) |x| > 3
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C
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Re: Is x^2 > 5^2 ? [#permalink] New post   02 Jun 2016, 13:35
x^2 > 5^2 => x^2 > 25 => Is x > 5 or x < -5.
Statement 1 : |x+5| = 3|x - 5|, solving this will give us x = 2.5 or 10. For 2.5, the answer is No, for 10 the answer is yes. So insufficient.
Statement 2 : |x| > 3. For x = -4 the answer is No, for x = 6, the answer is Yes. So insufficient.

Combining, the only solution is x= 10, for which the answer is Yes. Hence C.
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Re: Is x^2 > 5^2 ? [#permalink] New post   05 Jun 2016, 02:54
Bunuel wrote:
Is x^2 > 5^2 ?

(1) |x+5| = 3|x - 5|

(2) |x| > 3



Here the expression didn't tell that the number is integer.Based on available information in the question x could be in fraction,integer or decimal expression

Statement 1: According to the given statement x= 2.5 or 10 then for x=2.5, \(\sqrt{2.5}\)<\(\sqrt{5}\) and for x =10,\(\sqrt{10}\)>\(\sqrt{5}\).. [b]Not Sufficient[b]


Statement 2: According to the given information x could be 3.5,4,5,6,7,8 etc,So x<5,x=5 or x>5,for x<5 then \(\sqrt{x}\) <\(\sqrt{5}\) and for x=5 then \(\sqrt{x}\)=\(\sqrt{5}\) and for x>5 then \(\sqrt{x}\)>\(\sqrt{5}\)..[b]Not Sufficient

Combining two statements together we found that x=10,which is greater than 5.

Correct Answer C
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Re: Is x^2 > 5^2 ? [#permalink] New post   20 May 2018, 03:00
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Considering statement (1) alone:
If x > 5, then
x + 5 = 3(x - 5) => x + 5 = 3x - 15 => 2x = 20 => x = 10 (Yes)

If -5 < x < 5, then
x + 5 = 3(5 - x) => x + 5 = 15 - 3x => 4x = 10 => x = 2.5(No)

Insufficient

Considering statement (2) alone:
If |x| > 3, then either x > 3 or x < -3
So, if x = 6, then xˆ2 > 5ˆ2 (Yes)
but if x = -4, then xˆ2 < 5ˆ2 (No)

Insufficient

Considering statement (1) and (2) together:
From statement (1), we have x = 2.5 or x = 10
From statement (2), we have x > 3 or x < -3

The only value that works for both the statements is x =10

The answer is (C).
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Re: Is x^2 > 5^2 ? [#permalink] New post   21 Feb 2020, 06:29
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Re: Is x^2 > 5^2 ? [#permalink]
21 Feb 2020, 06:29
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