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.

Join timely conversations and get much-needed information about your educational future in our free event series. The sessions will focus on a variety of topics, from going to college in a pandemic to racial inequality in education.

When positive integer N is divided by 18, the remainder is x [#permalink]
05 Jun 2018, 07:54

1

This post received KUDOS

Expert's post

00:00

Question Stats:

57% (02:02) correct
42% (02:04) wrong based on 57 sessions

When positive integer N is divided by 18, the remainder is x. When N is divided by 6, the remainder is y. Which of the following are possible values of x and y?

i) x = 9 and y = 3 ii) x = 16 and y = 2 iii) x = 13 and y = 7

A) i only B) i and ii only C) i and iii only D) ii and iii only E) i,ii and iii

Brent Hanneson – Creator of greenlighttestprep.com If you enjoy my solutions, you'll like my GRE prep course. Sign up for GRE Question of the Dayemails

Re: When positive integer N is divided by 18, the remainder is x [#permalink]
07 Jun 2018, 06:47

1

This post received KUDOS

Expert's post

GreenlightTestPrep wrote:

When positive integer N is divided by 18, the remainder is x. When N is divided by 6, the remainder is y. Which of the following are possible values of x and y?

i) x = 9 and y = 3 ii) x = 16 and y = 2 iii) x = 13 and y = 7

A) i only B) i and ii only C) i and iii only D) ii and iii only E) i,ii and iii

Let's examine each statement separately...

i) x = 9 and y = 3 Let's come up with a value of N that satisfies this condition. How about N = 9? 9 divided by 18 = 0 with remainder 9 (i.e., x = 9) ...and 9 divided by 6 = 1 with remainder 3 (i.e., y = 3) Perfect, statement i is TRUE Check the answer choices.....ELIMINATE D

ii) x = 16 and y = 2 Can you come up with a value of N that satisfies this condition? How about N = 16? 16 divided by 18 = 0 with remainder 16 (i.e., x = 16, which WORKS) However, 16 divided by 6 = 2 with remainder 4 (i.e., y = 4. NO GOOD)

How about N = 34? 34 divided by 18 = 1 with remainder 16 (i.e., x = 16, which WORKS) However, 34 divided by 6 = 5 with remainder 4 (i.e., y = 4. NO GOOD)

We can keep testing N-values until we convince ourselves that there are no values of N that makes those values (x = 16 and y = 2) possible. So, statement ii is FALSE Check the answer choices.....ELIMINATE B and E

HOWEVER, if you need more convincing that statement ii is FALSE, we can make the following observations: When positive integer N is divided by 18, the remainder is x: so, we can say that N = 18k + x for some integer k When positive integer N is divided by 6, the remainder is y: so, we can say that N = 6j + y for some integer j We can combine the two equations to get: 18k + x = 6j + y Isolate x to get: x = y + 6j - 18k Factor right side to get: x = y + 6(j - 3k) Rewrite as: x = y + some multiple of 6 This means we'll never have the case where x = 16 and y = 2, because 16 CANNOT be written as 2 + some multiple of 6 So, statement ii is FALSE

iii) x = 13 and y = 7 We must be careful with this one. While it is true that 13 CAN be written as 7 + some multiple of 6, we must also consider the following property of remainders: When positive integer N is divided by positive integer D, the remainder R is such that 0 ≤ R < D For example, if we divide some positive integer by 7, the remainder will be 6, 5, 4, 3, 2, 1, or 0

Based on the above property, when we divide N by 6, the remainder can be 5, 4, 3, 2, 1, or 0 So, the remainder CANNOT be 7 In other words, y CANNOT equal 7 So, statement iii is FALSE ELIMINATE C

Answer: A

RELATED VIDEO

_________________

Brent Hanneson – Creator of greenlighttestprep.com If you enjoy my solutions, you'll like my GRE prep course. Sign up for GRE Question of the Dayemails

Re: When positive integer N is divided by 18, the remainder is x [#permalink]
15 Sep 2019, 12:51

1

This post received KUDOS

I don't feel this approach is right, but I got the right answer. Brent, please let me know if this approach has any validity.

So, I said:

18Q + x = N = 6Q + y

18Q + x = 6Q + y

Then I plugged in numbers for x and y, for example:

18Q + 9 = 6Q + 3

Then I imagined Q was 1, so we get

27 = 9

It's plain that the two sides aren't equal, but they are multiples of one another.

I used the same thing to look at the other solutions, and saw they weren't multiples of one another.

I read your solution again, and I think I may have made a mistake in writing Q for both sides instead of Q sub 1 and Q sub 2. We are told N is the same, but we're not told Q is the same.

So, I guess I could say

18Q_1 + 9 = 6Q_2 + 3

Given Q_1 and Q_2 could be different values.

The other solutions won't be multiples of each other, and therefore can't be equal whatever Q_1 and Q_2 are. For example, if x = 13 and y = 17, we get

18Q_1 + 13 = 6Q_2 + 7

if both Qs are 1, we get

31 = 13, which are clearly not multiples of each other, and therefore no matter what the Q's are for both sides, the two sides will never be equal.

I found the same to be true for the other answer choices. None of them resulted in multiples.

Was on the right path? Or was getting the right answer just a coincidence?

PS Sorry, if my line of reasoning was confusing. It felt confusing to me writing it.

Re: When positive integer N is divided by 18, the remainder is x [#permalink]
16 Sep 2019, 06:54

1

This post received KUDOS

Expert's post

arc601 wrote:

I don't feel this approach is right, but I got the right answer. Brent, please let me know if this approach has any validity.

So, I said:

18Q + x = N = 6Q + y

18Q + x = 6Q + y

Then I plugged in numbers for x and y, for example:

18Q + 9 = 6Q + 3

Then I imagined Q was 1, so we get

27 = 9

It's plain that the two sides aren't equal, but they are multiples of one another.

I used the same thing to look at the other solutions, and saw they weren't multiples of one another.

I read your solution again, and I think I may have made a mistake in writing Q for both sides instead of Q sub 1 and Q sub 2. We are told N is the same, but we're not told Q is the same.

So, I guess I could say

18Q_1 + 9 = 6Q_2 + 3

Given Q_1 and Q_2 could be different values.

The other solutions won't be multiples of each other, and therefore can't be equal whatever Q_1 and Q_2 are. For example, if x = 13 and y = 17, we get

18Q_1 + 13 = 6Q_2 + 7

if both Qs are 1, we get

31 = 13, which are clearly not multiples of each other, and therefore no matter what the Q's are for both sides, the two sides will never be equal.

I found the same to be true for the other answer choices. None of them resulted in multiples.

Was on the right path? Or was getting the right answer just a coincidence?

PS Sorry, if my line of reasoning was confusing. It felt confusing to me writing it.

It's fine to write 18Q_1 + x = 6Q_2 + y But it might be less confusing to write: 18k + x = 6j + y (where j and k are integers)

Now check the answer choices.. i) x = 9 and y = 3 We get: 18k + 9 = 6j + 3 (it this possible given that k and j are positive integers?) Rearrange to get: 6j - 18k = 9 - 3 Simplify to get: 6(j - 3k) = 6 Divide both sides by 6 to get: j - 3k = 1 We can see that there are many ways this can be possible. For example, j = 4 and k = 1 is one solution.

Keep going with other statements....
_________________

Brent Hanneson – Creator of greenlighttestprep.com If you enjoy my solutions, you'll like my GRE prep course. Sign up for GRE Question of the Dayemails

Re: When positive integer N is divided by 18, the remainder is x [#permalink]
24 Mar 2020, 04:09

1

This post received KUDOS

Please tell me if this is right N = 18k+ x N = 6j + y y-x = 18k - 6j y-x = 6(3k-j) This means y-x is a multiple of 6 So A) x=9 y=3 y-x=-6 which is divisible by 6 B) x=16 y=2 y-x=-14 which is not divisible by 6 so eliminate it C) x=13 y=7 since y<6 eliminate it Only A is left.

greprepclubot

Re: When positive integer N is divided by 18, the remainder is x
[#permalink]
24 Mar 2020, 04:09