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Is (6a + x^2)^(1/2) = a + x ?

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Is (6a + x^2)^(1/2) = a + x ? [#permalink]

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New post 01 Oct 2017, 23:03
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47% (01:23) correct 53% (01:48) wrong based on 55 sessions

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Is (6a + x^2)^(1/2) = a + x ? [#permalink]

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New post 02 Oct 2017, 03:23
Bunuel wrote:
Is \(\sqrt{6a + x^2} = a + x\) ?

(1) x is not a positive integer.
(2) a is a negative integer.


Statement 1: Nothing mentioned about \(a\), hence the value cannot be calculated. \(x\) is either \(0\) or a negative no. Insufficient

Statement 2: nothing mentioned about x, hence value cannot be calculated. Insufficient

Combining 1 & 2, we know that x=0 or x<0 and a<0 so a+x<0. So RHS is always negative.
But LHS of the question stem is a square root which is always positive. Hence LHS is not equal to RHS. Sufficient

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Re: Is (6a + x^2)^(1/2) = a + x ? [#permalink]

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New post 09 Jan 2018, 19:24
\(\sqrt{6a + x^{2}} = a + x\)
Simplifies to...
\(6a + x^2 = a^2 + x^2 + 2ax\)
\(6a = a^2 + 2ax\)
\(6 = a + 2x\)

Statement 1 tells us that \(x\leq{0}\). It doesn't say anything about \(a\). So we can have \(x = -1\) and \(a = 8\), in which case \(a + 2x = 6\). Or we can have \(x = -1\) and \(a = -1\), in which case \(a + 2x = -3\). Insufficient.

Statement 2 tells us that \(a<0\). It doesn't say anything about \(x\). Like for Statement 1, for any negative value of \(a\) we can use a value of \(x\) which may or may not fit the equation \(6 = a + 2x\). Insufficient.

Combining both statements, since \(a\) is negative and \(x\) is at most 0, \(a + 2x\) is negative and thus can never equal 6. Sufficient.
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Re: Is (6a + x^2)^(1/2) = a + x ? [#permalink]

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New post 09 Jan 2018, 19:33
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Bunuel wrote:
Is \(\sqrt{6a + x^2} = a + x\) ?

(1) x is not a positive integer.
(2) a is a negative integer.



TIP- whenever you see a SQUARE ROOT or a MODULUS on one side, and the choices/statements give you no specific values but type of integers they are, such as zero, negative etc, CHECK if the other side is NEGATIVE

So here whatever be in the equation, the LHS is a square root and a square root can never be NEGATIVE, so check RHS ..
RHS is a+x...
Combined we know x is non Positive, so max value will be 0 and a is NEGATIVE so a+x will be NEGATIVE..
Thus RHS is NOT equal to LHS..
Sufficient

C
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


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Re: Is (6a + x^2)^(1/2) = a + x ?   [#permalink] 09 Jan 2018, 19:33
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