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.

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:

42% (01:53) correct
57% (01:54) wrong based on 14 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

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

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 Sign up for my free GRE Question of the Dayemails

greprepclubot

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