When the integer n is divided by 2, the quotient is u and the remainder ... ...

When the integer n is divided by 2, the quotient is u and the remainder is 1. When the integer n is divided by 5, the quotient is v and the remainder is 3. Which one of the following must be true?
(A) 2u + 5v = 4
(B) ...
(C) ...
(D) ...
(E) ...

*This question is included in Introduction to Nova GRE Math

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Posted: 04/07/2012 15:38
I am just very confused by the wording of this problem the math makes sense after the problem is translated. I don't know how to translate on my own though.
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Posted: 04/07/2012 23:35
Rebekah, let's help you here. "When the integer n is divided by 2" = n/2;
"the quotient is u, and the remainder is 1" = u + 1/2. Why is "the remainder is 1" translated as 1/2? Because we were dividing the integer by 2, so any remainder must also div by 2, hence 1/2.

Now, translate the next sentence: "when integer n is divided by 5" = n/5; the quotient is v and the remainder is 3" = v + 3/5

So we have two equations:
n/2 = u + 1/2, which can be rewritten after multiplying by 2 as n = 2u + 1
n/5 = v + 3/5, which can be rewritten after multiplying by 5 as n = 5v + 3

I hope this helps. If you liked the explanation, please rate us in the App Store.
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Posted: 07/03/2012 10:47
Pls help me here: translating the first sentence, isn't it n/2=u+1?. Similarly, translating the second sentence is n/5=v+3?
Or did I misunderstand the language here? Thanks for helping.
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Posted: 07/03/2012 20:00
Anh, no it isn't n/2 = u + 1. The remainder needs to be represented as a fraction; since n is divided by 2, the remainder 1 must also be divided by 2.

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Posted: 05/29/2012 15:43
I agree, the wording is confusing. I just look at it like this:

n=[what we don't know, the quotient]*[what it's divided by]+[remainder].

Then set the 2 equations equal to each other and solve. Great luck!

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Posted: 06/19/2012 21:28
I don't understand how it jumps from a positive addition problem to a subtraction problem. I still don't see why the answer 2u+5v=4 is wrong. Is it some simple rule I'm forgetting?

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Posted: 06/20/2012 10:43
K Rob,

We know:
n = 2u+1 and n = 5v + 3 from the question, then
2u = n -1 and 5v = n -3, so
2u + 5v = n -1 + n -3 = 2n -4
You cannot get 2u +5v = 4 if n is not 4

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Posted: 09/02/2012 11:36
How do i get from
' 2u+5v = 2n -4 ' to the answer?
Really confused

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Posted: 09/02/2012 18:04
Julie, express n using v or u. Then simplify the equation. You will get the right answer.."
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Posted: 04/04/2013 00:02
I'm not exactly sure what your reply to Julie's question means. I have the same question as her.
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Posted: 04/04/2013 00:53
Here is a repost of an earlier explanation:
"When the integer n is divided by 2" = n/2;
"the quotient is u, and the remainder is 1" = u + 1/2. Why is "the remainder is 1" translated as 1/2? Because we were dividing the integer by 2, so any remainder must also div by 2, hence 1/2.

Now, translate the next sentence: "when integer n is divided by 5" = n/5; the quotient is v and the remainder is 3" = v + 3/5

So we have two equations:
n/2 = u + 1/2, which can be rewritten after multiplying by 2 as n = 2u + 1
n/5 = v + 3/5, which can be rewritten after multiplying by 5 as n = 5v + 3

Then set n = n, 2u + 1 = 5v + 3.

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Posted: 10/01/2012 23:48
What am I doing wrong here:
After translating into math
n/2+u=1
n/2+u=1/2
(x2)= n+2u=1,,,,,,how did u get "n=2u+1"

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Posted: 10/02/2012 01:38

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Posted: 10/03/2012 17:37
the answer is right. i just need more details as to how it was transformed into 2u-5v=2. If someone forgets the basics of math, this can be quite confusing.
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Posted: 10/03/2012 19:20
LJ, thanks for posting. The point of this app is exactly that, to help you remember the basics, so that you don't get tripped up in the actual test. Good luck.

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Posted: 11/03/2012 16:04
I'm not sure how 2u + 1 = 5v + 3
Rearranges to 2u - 5v = 2
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Posted: 11/03/2012 19:59
Sara, that is from basic algebra. You can add or subtract or multiply or divide both sides of an equation, if you use the same number. 2u+1=5v+3; subtract 1 from both sides, then subtract 5v from both sides.

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Posted: 01/27/2013 02:58
This question looked like that n is the one divided but not the rest, hence it seems to me that, for the jest equation as an example,
n/2=v+1
Because to get the "n" you have to multiply both by 2 so
n=2v+2
It seems weird to get
n/2=v+1/2 because if this is the case v also needs to be divided by 2
n/2=v/2+1/2
I can still tell that this one is obviously wrong understanding from the question. My question is why v is not divided if the reminder is divided by 2.

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Posted: 01/27/2013 03:11
"the quotient is u, and the remainder is 1" = u + 1/2. Why is "the remainder is 1" translated as 1/2? Because we were dividing the integer by 2, so any remainder must also div by 2, hence 1/2.

But why not dividing u also?
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