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Integer problem

by Vishnu88 » Sat May 07, 2011 2:34 am
If x and y are nonzero integers, is x/y an integer?

1. x is a product of 2 and some other integer
2. There is only one pair of positive integers whose product equals y

Appreciate if you could elaborate on statement 2 and explain how it is used in deriving the right answer.

Cheers!
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by pemdas » Sat May 07, 2011 3:32 am
confused term 'product' initially

x is not 0 means NOT all numbers can be factors of x
y is not 0 means any number is theoretically divisible by y (with the remainder or not)

this DS can be rephrased -> is y a factor of x?
st(1) x=2*i, where i is integer. (2*i)/y Not Sufficient, as we don't know y
st(2) y=f*g, where f and g are integers. Among all integers only 1 and 1 can form the unique pair (1 and 0 can't, as 0 is not +ve), hence y=1 (we are not told that one pair of different +ve integers). So x/y=x/1 Sufficient, as we know if x is any number it's divisible by 1.
IOM b
Vishnu88 wrote:If x and y are nonzero integers, is x/y an integer?

1. x is a product of 2 and some other integer
2. There is only one pair of positive integers whose product equals y

Appreciate if you could elaborate on statement 2 and explain how it is used in deriving the right answer.

Cheers!
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by clock60 » Sat May 07, 2011 5:27 am
hi guys, my try
(1) says nothing except x is even integer
(2) i hope that it says that y is prime
any prime integer can be performed with product of 1 and itself
if y=1*2=2 it can be product of only one pair=1*2
if y is not prime say y=6,then it can be performed as
y=2*3-one pair, or 6*1-another pair.but it is not allowed according st2
so from 2 we know that y is prime but no info about x so insuff
both
x=2, y=2 here x is multiple of y, but
x=2, y=5 here x is not multiple
to me the answer is E
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by champmag » Sat May 07, 2011 6:10 am
IMO :E

1.) First Statement gives info only about X and that X is an even Number. So this statement is not sufficient to find whether X/Y is an integer.

2.) This statement says that Y is a prime Number----not sufficient.

Taking 1 and 2 together-

If X=2*3 Y=3, then X/Y is an integer.
If X=2*3, Y=7, the X/Y is not an integer.

So both the statements taken together are also not sufficient.

so E.
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