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.
n is a positive integer. The remainder when 5n is divided by
[#permalink]
27 Oct 2016, 12:40
27 Oct 2016, 12:40
1
Expert Reply
9
Bookmarks
00:00
Question Stats:
70% (01:22) correct
29% (01:21) wrong based on 207 sessions
Hide Show timer Statistics
n is a positive integer.
The remainder when 5n is divided by 4 is 3.
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
The remainder when 5n is divided by 4 is 3.
Quantity A |
Quantity B |
The remainder when 10n is divided by 4 |
2 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Drill 2
Question: 12
Page: 288
Question: 12
Page: 288
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: n is a positive integer. The remainder when 5n is divided by
[#permalink]
12 Nov 2016, 14:10
12 Nov 2016, 14:10
8
2
Bookmarks
sandy wrote:
n is a positive integer.
The remainder when 5n is divided by 4 is 3.
The remainder when 5n is divided by 4 is 3.
Quantity A |
Quantity B |
The remainder when 10n is divided by 4 |
2 |
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
The remainder when 5n is divided by 4 is 3
Applying the above rule, we get: 5n = 4k + 3 (for some integer k)
Divide both sides by 5 to get: n = (4k + 3)/5
Quantity A: The remainder when 10n is divided by 4
Replace n with (4k + 3)/5 to get: 10n = 10((4k + 3)/5) = 8k + 6
If 10n = 8k + 6, what is the remainder when 8k + 6 is divided by 4?
Notice that 8k + 6 = 8k + 4 + 2
= 4(2k + 1) + 2
As we can see, 4(2k + 1) is a MULTIPLE OF 4
This means that 4(2k + 1) + 2 is 2 greater than a MULTIPLE OF 4
So, if we divide 4(2k + 1) + 2 by 4, the remainder will be 2
We get....
Quantity A: 2
Quantity B: 2
Answer:
Show: ::
C
RELATED VIDEO
General Discussion
Re: n is a positive integer. The remainder when 5n is divided by
[#permalink]
27 Oct 2016, 12:42
27 Oct 2016, 12:42
Expert Reply
Explanation
If the remainder is 3, then 5n must be 3 more than a multiple of 4, such as 4, 8, 12, or 16. Try adding 3 to these multiples to find a possible value for 5n. 12 + 3 yields 15 as a value for 5n; n = 3. Quantity A is the remainder when 30 is divided by 4, or 2. Eliminate choices A and B.
Try a different number. If n is 7, then 5n is 35, which also has a remainder of 3 when divided by 4. In Quantity A, 70 divided by 4 has a remainder of 2. For any other numbers you try, choice C will be the answer.
If the remainder is 3, then 5n must be 3 more than a multiple of 4, such as 4, 8, 12, or 16. Try adding 3 to these multiples to find a possible value for 5n. 12 + 3 yields 15 as a value for 5n; n = 3. Quantity A is the remainder when 30 is divided by 4, or 2. Eliminate choices A and B.
Try a different number. If n is 7, then 5n is 35, which also has a remainder of 3 when divided by 4. In Quantity A, 70 divided by 4 has a remainder of 2. For any other numbers you try, choice C will be the answer.
