M7MBA wrote:Is √(56x) an integer?
(1) x is a multiple of 14.
(2) 28 is not a factor of x.
The OA is the option E.
Why is E the correct choice? Could anyone explain this DS question to me? Please. Thanks in advance.
For √(56x) to be an integer, 56x must be a perfect square.
Let's factorize √(56x) an integer.
√(56x) = √(2^3*7*x) = 2.√(2*7*x) = 2√(14x)
=> If 14x is a perfect square, the answer is yes, else no.
Let's see each statement one by one.
(1) x is a multiple of 14.
If x = 14, we see that 14x = 14*14 = 14^2, a perfect squre: the answer is yes; however, x = 14*3, we see that 14x = 14*14*3, not a perfect squre: the answer is No. Insufficient.
(2) 28 is not a factor of x.
If x = 14 (not a factor of 28), we see that 14x = 14*14 = 14^2, a perfect squre: the answer is yes; however, x = 14*3 (not a factor of 28), we see that 14x = 14*14*3, not a perfect squre: the answer is No. Insufficient.
(1) and (2) together
Both the examples discussed above are applicable here too. Insufficient.
The correct answer:
E
Hope this helps!
-Jay
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