Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Hi Brent, Great Q... But statement 2 is sufficient as we are looking for value of x and that is 5..

Arggh!

I wrote that question a couple of weeks ago, and had the correct answer is D. This morning, before posting it, I answered the question TWICE and got A both times. Of course, I was incorrectly reading the target question as "What is the value of y"

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

Show Tags

27 Mar 2017, 12:08

nice question. is there any other simple way to solve this problem? Thank you...
_________________

“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.” ― Henry Wadsworth Longfellow

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

1) When 9x is divided by 2y, the quotient is x, and the remainder is 5 2) When 5y is divided by x, the quotient is y, and the remainder is 0

Target question:What is the value of x?

Statement 1: When 9x is divided by 2y, the quotient is x, and the remainder is 5 There's a nice rule that say, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2 Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3

So, from the above rule, we can write: 9x = 2yx + 5 Rewrite this as: 9x - 2yx = 5 Factor out the x to get: x(9 - 2y) = 5 Since x and 9 - 2y MUST BE INTEGERS, and since their PRODUCT is 5, we know that EITHER x = 1 and 9 - 2y = 5 OR x = 5 and 9 - 2y = 1

If x = 1 and 9 - 2y = 5, then x = 1 and y = 2 If x = 5 and 9 - 2y = 1, then x = 5 and y = 4

At this point it LOOKS LIKE there are two possible values for x. However, when we test these values, we have a problem.

If we plug x = 1 and y = 2 into statement 1, we get: When 9(1) is divided by 2(2), the quotient is 1, and the remainder is 5. We can see this this is NOT TRUE. So, x = 1 and y = 2 is NOT A SOLUTION

If we plug x = 5 and y = 4 into statement 1, we get: When 9(5) is divided by 2(4), the quotient is 5, and the remainder is 5. In other words, When 45 is divided by 8, the quotient is 5, and the remainder is 5. This WORKS. So, x = 5 and y = 4 IS A SOLUTION

So, we can conclude that x = 5 Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: When 5y is divided by x, the quotient is y, and the remainder is 0 So, from the above rule, we can write: 5y = xy + 0 Rewrite this as: 5y - xy = 0 Factor: y(5 - x) = 0 So, either y = 0, or x = 5 Since we're told y is POSITIVE, we know that y does not equal 0, which means x must equal 5 Since we can answer the target question with certainty, statement 2 is SUFFICIENT

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

Show Tags

28 Mar 2017, 09:58

Yes, Thanks for video.
_________________

“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.” ― Henry Wadsworth Longfellow

gmatclubot

Re: If x and y are positive integers, what is the value of x?
[#permalink]
28 Mar 2017, 09:58