If integers x and y are distinct factors of 24, then which o

Question

If integers x and y are distinct factors of 24, then which of the following CANNOT be a factor of 24?

I. (x + y)^2
II. x^2 - y^2
III. xy + y^2

A. I only
B. I and II
C. II and III
D. II only
E. III only

For I. Can we say 24 = 2^3 * 3 -> Hence, it can not be square of value (x + y)?
and II & III - we don't know from a given info?

Bunuel · Accepted Answer

The question should read:
 If integers x and y are distinct   factors   of 24, then which of the following CANNOT be a factor of 24?

I. (x + y)^2
II. x^2 - y^2
III. xy + y^2

A. I only
B. I and II
C. II and III
D. II only
E. III only

The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, and 24.

I. (x + y)^2. This is a perfect square. 24 has only two factors which are perfect square 1 and 4. (x + y)^2 can be neither of them: it obviously cannot be 1 and it cannot be 4 because we are told that x and y are distinct.
 
II. x^2 - y^2. If x = 2 and y = 1, then x^2 - y^2 = 3, which IS a factor of 24.

III. xy + y^2. If x = 2 and y = 1, then xy + y^2 = 3, which IS a factor of 24.

Answer: A.

Hope it's clear.

desaichinmay22 · Answer

It is given that x and y are distinct of 24. They are not necessarily two different integers. If we assume x and y to be 1, then (x+y)^2 will be a factor of 24.
Experts please explain.

Bunuel · Answer

Edited the original post. A word " factor " was missing there.

robanm90 · Answer

Bunuel how do you decide the factors for the equation? If you use X=3 and Y=2 (both factors of 24) the equation (5) is not factor of 24
Thanks

Bunuel · Answer

The question asks: which of the following CANNOT be a factor of 24.

So, the correct option is the one which won't give a factor of 24 for ANY possible values of x and y.

x^2 - y^2 gives a factor of 24 for some values of x and y (x = 2 and y = 1), so it is not a part of a correct answer.

AA2014 · Answer

for factors of 24: 1, 4 are the only perfect squares and 1 and 2 cannot be (x+y)... so I cant be true...
Rest of them can be true taking x=2 and y=1.

I wonder why the first post says distinct factors and yet says they need not be distinct integers????????????????????

mvictor · Answer

I got relatively easy to the answer choice:

I. (x + y)^2
if x=1
y=2 then 3^2 = 9, and this cannot be a factor of 24.

now, we can eliminate C, D, and E, and we are left with A and B only.

II. x^2 - y^2
x=2 y=1
4-1 = 3-> factor of 24.

B eliminated -> answer A.

Naia · Answer

What if x=-3 and y=1?

Then (x+y)^2 = (-3+1)^2 = (-2)^2=4. In this case first statement can be used to make a factor for 24.

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If integers x and y are distinct factors of 24, then which o

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If integers x and y are distinct factors of 24, then which o

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