If y x, is y 64 ?

Question

If y > x, is y > 64 ?

(1) x has 7 factors (all even but one) and is divisible by only one prime number.

(2) |y - 64| > |x - 64|

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Answer Choices

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

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Saquib
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Official Answer

D

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rohit8865 · Answer

(1) x has minimum value = 2^6 =64
thus y>x=64
y>64
suff

(2) sq. both side we get 
y^2-128y > x^2-128x
or y^2 - x^2 - 128y + 128x >0
y^2 - x^2 - 128(y -x ) >0
taking y-x common out

(y-x)(y+x-128)>0
as y-x > 0 given
then 
y+x>128------(a)
and y-x >0------(b)

adding (a) and (b)
2y > 128
or y> 64

suff..

Ans D

goalMBA1990 · Answer

Hi, I didn't get how you derive first statement sufficient? Can you please explain in more detail?

Thanks in advance.

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rohit8865 · Answer

no. of factors of x^y is y+1 
let 2^ 2 =4 its factors are 1,2,4 = 3nos. =  2 +1...

hope it helps

Armaan209 · Answer

Statement 1. Remenber the rule only perfect squares have odd number of factors.

Y>x is Y>64?
We can also say is x<= 64

1. X is a perfect square and only 64 has 7 factors also it has only one prome factor that is 2.
so x= 64 and Y>64.

Navyashrivastava · Answer

Hi, 
I took out the same conclusion x= 64 but it also says that one factor is odd and rest are even. How will that be justified?

Armaan209 · Answer

Hi Navya

The odd factor is 1. we miss 1 and the number itself often.

If y > x, is y > 64 ?

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