Is x 6 ? (1) x^(1/2) 2.5 (2) x 37^(1/2)

Question

Is x > 6 ?

(1)  \sqrt{x} > 2.5

(2)  x > \sqrt{37}

ENGRTOMBA2018 · Accepted Answer

The mistake you are making is that  x^2 = 36  has 2 roots  \pm 6  (as it is a second degree equation in x) but  x=\sqrt{36}  only has 1 solution = +6 as it is a linear equation in x

Thus, from statement 2,  x > \sqrt{37}  means that  x > 6.aaa  and NOT  x > - 6.aaa

Remember this rule for GMAT.

Thus both statements are sufficient.

D is the correct answer.

Hope this helps.

akxshay · Answer

I understand that 1) is SUFFICIENT because x > 6.25 hence x > 6, but not sure why 2) is SUFFICIENT ?

37^1/2 can have two values -6.08 and +6.08. If I consider +6.08 then it is sufficient, but what about the negative value ?

If I take the negative value then x > -6.08 which means x is not > 6. Hence the answer should be A), but the OA is D)

I am sure I am making some mistake, kindly help me to understand if my interpretation of taking a -ve is wrong and why ?

akxshay · Answer

Got it, Thanks a lot ! It does make sense. Cheers !

Bunuel · Answer

The square root function cannot give negative result :  \sqrt{nonnegative \ value}\geq{0} . For example,  \sqrt{4}=2  (not +2 and -2).  In contrast, the equation  x^2=25  has TWO solutions, +5 and -5,  because both 5^2 and (-5)^2 equal to 25.

Kinshook · Answer

Is x > 6 ?

1)  \sqrt{x} > 2.5 
x>6.25>6
x>6
SUFFICIENT

2)  x > \sqrt{37} 
 x>\sqrt{37}>\sqrt{36}=6 
x>6
SUFFICIENT

IMO D

Kinshook · Answer

Asked: Is x > 6 ?

1)  \sqrt{x} > 2.5 
x > 6.25 > 6
SUFFICIENT

2)  x > \sqrt{37} 
x > \sqrt{37} > \sqrt{36} = 6
x> 6
SUFFICIENT

IMO D

sampad · Answer

i am really speechless after seeing this solution. sqrt of 37 is only 6.abc not -6.abc. But for x^2=25 x will have 2 values +5 and -5. So can anyone please explain how we are getting the values of x. is it not the sqrt of 25?

Basim2016 · Answer

Dear Sampad,

X^2 has 2 solutions, becuase it has the power of 2. Kindly read earlier /above posts.
Surely, you will be clear after reading above posts

Regards,
Basim

bumpbot · Answer

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Is x > 6 ? (1) x^(1/2) > 2.5 (2) x > 37^(1/2)

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