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# Is the product of two positive integers x and y divisible by the sum o

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Is the product of two positive integers x and y divisible by the sum o [#permalink]

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24 Jun 2017, 03:29
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Is the product of two positive integers x and y divisible by the sum of x and of y ?

(1) x=y

(2) x=2
[Reveal] Spoiler: OA

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Md. Abdur Rakib

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Is the product of two positive integers x and y divisible by the sum o [#permalink]

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24 Jun 2017, 07:01
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Is the product of two positive integers x and y divisible by the sum of x and of y ?

The question asks whether $$\frac{xy}{x+y}=integer$$

(1) x=y. The question becomes: is $$\frac{x^2}{2x}=\frac{x}{2}=integer$$? If x is even, the answer will be YES but if x is odd the answer will be NO. Not sufficient.

(2) x=2. Clearly insufficient.

(1)+(2) Since from (2) we know that x is even, then from (1) we'll have an YES answer. Sufficient.

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Re: Is the product of two positive integers x and y divisible by the sum o [#permalink]

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26 Jun 2017, 14:36
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Is the product of two positive integers x and y divisible by the sum of x and of y ?

In other words:

$$\frac{x * y}{x + y}$$ = Integer?

$$(1) x=y$$

x = y

$$\frac{x^2}{2x}$$

$$\frac{x}{2}$$

In order for x to be divided completely, x has to be an even number, if it is an odd we it will not divisible.

Hence, (1) is =====> NOT SUFFICIENT

$$(2) x=2$$

This does not give us any information on value of y

Hence, (2) is =====> NOT SUFFICIENT

Now, lets combine (1) & (2)

$$\frac{x}{2} = \frac{2}{2} = 1$$ = Integer

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Re: Is the product of two positive integers x and y divisible by the sum o [#permalink]

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17 Nov 2017, 12:35
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Expert's post
AbdurRakib wrote:
Is the product of two positive integers x and y divisible by the sum of x and of y ?

(1) x=y

(2) x=2

We can write the question:

Is xy/(x + y) = integer?

Statement One Alone:

x = y

Since x = y, we have:

Is xy/(x + y) = integer?

Is (x)(x)/(x + x) = integer?

Is x^2/2x = integer?

Is x/2 = integer?

Since we don’t have a value of x, we cannot determine whether x/2 is an integer. For example, if x = 2, then x/2 is an integer; however, if x = 3, then x/2 is not an integer. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

x = 2

Only knowing that x = 2 is not enough to determine whether xy/(x + y) = integer. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using the statements together, we see that since x is 2, we can say that 2/2 = 1, which is an integer.

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Re: Is the product of two positive integers x and y divisible by the sum o   [#permalink] 17 Nov 2017, 12:35
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