If k is a positive integer and 0

Question

If k is a positive integer and 0 < x < 1,000, is  \frac{128}{x^2}  an integer?

(1) x = k^6
(2) k = 2y, where y is a positive integer

HKD1710 · Answer

128 = 2^7

stmt:1 ->> x = k^6
if k = 2, then yes 2^7/2^6 is an Integer. YES
if k = 3, then yes 2^7/3^6 is an NOT Integer. NO

Insuff

stmt:2 ->>
k = 2y, where y is a positive integer 
we know nothing about X. so insuff.

combine stmt-1 and stmt-2:
x = k^6
k = 2y
x = (2y)^6 
x = 2^6 * y^6 
x^2 = 2^12 * (y)^12

2^7/(2^12 * (y)^12) is DEFINITLY NOT an integer. so answer is NO. SUFFICIENT

Option C is correct.

chetan2u · Answer

k is a positive integer and 0 < x < 1,000, is  \frac{128}{x^2}  an integer...
 if x is an integer,  \frac{128}{x^2}  will be an integer ONLY if x=2,4, or 8

lets see the statements.. 
 (1) x = k^6 
since k is an integer, x is also an integer..
and here k can take ONLY values of 1, 2, and 3 since x<1000..
 when k is 1 or 2 .. ans is YES
if k is 3, ans is NO 
Insuff

(2) k = 2y, where y is a positive integer 
 no relation between x and k or y.. 
Insuff..

combined..
 we know k is EVEN and ONLY 2 fits in..
so x= 2^6 = 64
ans is YES 
Suff

C

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If k is a positive integer and 0 < x < 1,000, is

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