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# If x and y are positive integers, what is the value of xy?

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Re: If x and y are positive integers, what is the value of xy? [#permalink]
Bunuel wrote:
If x and y are positive integers, what is the value of xy?

(1) $$x! = 6y!$$

(2) $$\frac{\frac{x!}{y}}{(x-2)!} = \frac{30}{y}$$

This question is a part of Are You Up For the Challenge: 700 Level Questions collection.
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Re: If x and y are positive integers, what is the value of xy? [#permalink]
Is this type of algebra part of GMAT focus?
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Re: If x and y are positive integers, what is the value of xy? [#permalink]
dhwanit2412 wrote:
Is this type of algebra part of GMAT focus?

­
Yes, the algebra in the question falls within the scope of the GMAT Focus. However, pure algebraic questions are no longer a part of the DS syllabus of the GMAT.

DS questions in GMAT Focus encompass various types of word problems, such as:

• Word Problems
• Work Problems
• Distance Problems
• Mixture Problems
• Percent and Interest Problems
• Overlapping Sets Problems
• Statistics Problems
• Combination and Probability Problems

While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."

Check GMAT Syllabus for Focus Edition

You can also visit the Data Sufficiency forum and filter questions by OG 2024-2025, GMAT Prep (Focus), and Data Insights Review 2024-2025 sources to see the types of questions currently tested on the GMAT.

So, you can ignore this question.

Hope it helps.­
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Re: If x and y are positive integers, what is the value of xy? [#permalink]
If x and y are positive integers, what is the value of xy?

(1) $$x! = 6y!$$
Factorial makes the question a little difficult. Assuming that RHS is y! and not (6y)!.
6! = 6*(5!) gives xy = 30
&
3! = 6*(1!) gives xy = 3

INSUFFICIENT.

(2) $$\frac{\frac{x!}{y}}{(x-2)!} = \frac{30}{y}$$­
$$\frac{x!}{(x-2)!} = 30$$­
x(x-1) = 30
x = 6 as x can't be negative (x = -5)

But y can take any value. So, xy can be anything.

INSUFFICIENT.

Together 1 and 2
x = 6 and y = 5
xy = 30

SUFFICIENT.