It is currently 22 Jan 2018, 04:39

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43363
Is (6a + x^2)^(1/2) = a + x ? [#permalink]

### Show Tags

01 Oct 2017, 23:03
Expert's post
2
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

47% (01:23) correct 53% (01:48) wrong based on 55 sessions

### HideShow timer Statistics

Is $$\sqrt{6a + x^2} = a + x$$ ?

(1) x is not a positive integer.
(2) a is a negative integer.
[Reveal] Spoiler: OA

_________________
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 827
Location: India
GPA: 3.82
Is (6a + x^2)^(1/2) = a + x ? [#permalink]

### Show Tags

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

Option C
Intern
Joined: 30 Mar 2017
Posts: 5
Re: Is (6a + x^2)^(1/2) = a + x ? [#permalink]

### Show Tags

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.
Math Expert
Joined: 02 Aug 2009
Posts: 5537
Re: Is (6a + x^2)^(1/2) = a + x ? [#permalink]

### Show Tags

09 Jan 2018, 19:33
1
KUDOS
Expert's post
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
_________________

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

BANGALORE/-

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