If x and y are nonzero integers, is x/y an integer?

Question

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

Bunuel · Accepted Answer

If x and y are nonzero integers, is x/y an integer?

(1) x is the product of 2 and some other integer --> x=2*integer --> x is an even number. Not sufficient, since no info about y.

(2) There is only one pair of positive integers whose product equals y --> y is a prime number or 1. Not sufficient, since no info about x.

(1)+(2) If  x=2  and  y=2=prime  then  \frac{x}{y}=1=integer  but if  x=2  and  y=3=prime  then  \frac{x}{y}=\frac{1}{3}
eq{integer} . Not sufficient.

Answer: E.

AbeinOhio · Answer

Question is asking whether X is divisible by Y

1. OK so this tells us that x is even - Not sufficient

2. this tells us that y is prime or 1 - insufficient

1 + 2 if x is even and y is prime or 1 do we always get an integer? Answer is no.. sometimes we do when Y is 2 or 1 we would get an integer.. hence insufficent

Answer is E

pacifist85 · Answer

Hi,

I did do it like you, but I have one question.

So, statement one tells us that x=2*n, n is an integer.

Does this also tell us that x>=2, or we would also count 0, so x could be zero?

Bunuel · Answer

The stem says that x and y are  nonzero  integers, so neither x nor y can be 0.

LordStark · Answer

The questions is asking whether X is divisible by y or x is a multiple of y.

Statement 1: x = 2 * q . here q can be any integer other than 0. therefore not sufficient
statement 2: Only a prime number is a product of two positive integers. therefore y could be any prime number. Not sufficient

combined: no link between q and y, therefore not sufficient.

Eduardo86 · Answer

Hi

1) said x is a multiple of two, so we have an even integer, but we do not know which one is. So the statement is not sufficient.

2)Say y is a prime number because only a specific pair will have as result y. 
axb=y if y=3 a and b are 1 and 3. And there is only one pair of integers to give 3. If y=9 we have 9x1 and 3x3, two different possibility. So y is a prime number. Statement 2 is not sufficient.

1+2) we know that x is a multiple of 2 and we know that y is a prime number.

If x is 2,4,8, and y is 2 so x/y is an integer if y is = 3 we do not have an integer. Because we do not know y value is not sufficient.

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If x and y are nonzero integers, is x/y an integer?

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If x and y are nonzero integers, is x/y an integer?

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