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.

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:

Re: x and y are positive integers. When 16x is divided by y,
[#permalink]

Show Tags

27 Feb 2017, 15:21

1

Top Contributor

3

GMATPrepNow wrote:

x and y are positive integers. When 16x is divided by y, the quotient is x, and the remainder is 4. What is the sum of all possible y-values?

A) 7 B) 12 C) 19 D) 26 E) 41

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

------NOW ONTO THE QUESTION------------------------------

When 16x is divided by y, the quotient is x, and the remainder is 4. Applying the above rule, we can write: 16x = (y)(x) + 4 Subtract xy from both sides: 16x - xy = 4 Factor: x(16 - y) = 4

Since x and (16 - y) are both positive integers, there are 3 possible solutions: #1: x = 1 and (16 - y) = 4, in which case y = 12 #2: x = 2 and (16 - y) = 2, in which case y = 14 #3: x = 4 and (16 - y) = 1, in which case y = 15

What is the sum of all possible y-values? SUM = 12 + 14 + 15 = 41

Re: x and y are positive integers. When 16x is divided by y,
[#permalink]

Show Tags

27 Feb 2017, 16:19

2

Great question! I solved it a very similar way to you all. (16x)/y = x + 4 --> 16x = xy + 4 --> y = (16x - 4)/x ---> y = 16 - 4/x.

We know from the prompt that Y is an integer, therefore, the only values of X that will make Y and integer is 0, 1, 2, 4. However, the prompt says that X & Y are positive integers. Therefore we can't use 0. So plugging in the values of 1, 2, and 4 into the equation, you're left with 15 + 14 + 12 = 41.

Re: x and y are positive integers. When 16x is divided by y,
[#permalink]

Show Tags

25 Aug 2018, 23:24

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________