GRE Prep Club Daily Prep
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Apr 25Crafting an Impactful Resume: Balancing Detail with Brevity
10:00 AM EDT
-10:30 AM EDT
Showcase your achievements through impactful storytelling! Get ready for an LIVE session on April 25, Learn how to craft compelling narratives on your resume that resonate with admission committees.
Apr 26Get a Top GRE Score with Target Test Prep
12:00 PM EDT
-01:00 PM EDT
The Target Test Prep course represents a quantum leap forward in GRE preparation, a radical reinterpretation of the way that students should study. In fact, more and more Target Test Prep students are scoring 329 and above on the GRE.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
When positive integer N is divided by 18, the remainder is x
[#permalink]
05 Jun 2018, 07:54
05 Jun 2018, 07:54
1
3
Bookmarks
00:00
Question Stats:
59% (02:02) correct
40% (02:03) wrong based on 82 sessions
Hide Show timer Statistics
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
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
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: When positive integer N is divided by 18, the remainder is x
[#permalink]
07 Jun 2018, 06:47
07 Jun 2018, 06:47
1
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
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
Re: When positive integer N is divided by 18, the remainder is x
[#permalink]
15 Sep 2019, 12:51
15 Sep 2019, 12:51
1
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.
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.
