Discussion
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?
*This question is included in Introduction to Nova GRE Math, question #3
(A)  2u + 5v = 4 
(B)  ... 
(C)  ... 
(D)  ... 
(E)  ... 
(F)  ... 
The solution is
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.
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.
"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.
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.
Or did I misunderstand the language here? Thanks for helping.
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.

Edit
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!
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!
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?
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
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
Posted: 09/02/2012 11:36
How do i get from
' 2u+5v = 2n 4 ' to the answer?
Really confused
' 2u+5v = 2n 4 ' to the answer?
Really confused
Posted: 09/02/2012 18:04
Julie, express n using v or u. Then simplify the equation. You will get the right answer.."
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.
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.
"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.
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"
After translating into math
n/2+u=1
n/2+u=1/2
(x2)= n+2u=1,,,,,,how did u get "n=2u+1"
Posted: 10/02/2012 01:38
Hussam, your question has been answered in the thread. Please follow the previous posts by Joel Brainer our contributor.
Posted: 10/03/2012 17:37
the answer is right. i just need more details as to how it was transformed into 2u5v=2. If someone forgets the basics of math, this can be quite confusing.
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.
Posted: 11/03/2012 16:04
I'm not sure how 2u + 1 = 5v + 3
Rearranges to 2u  5v = 2
Rearranges to 2u  5v = 2
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.
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.
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.
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?
But why not dividing u also?
Posted: 01/29/2013 12:41
Kiyomi, good follow up question. Why not divide u also? Because of the language used in the problem.
Quotient means the result of a division, just like product is the result of a multiplication. Thus, explicit in the language is that u is already including the dividing by 2 operation. Whereas, remainder is just the integer that is left when the division operation is done, so a remainder is not a fraction until it is divided by the divisor.
I am not a native speaker of English, so I had to learn these terms myself in order to do math problems in English.
Quotient means the result of a division, just like product is the result of a multiplication. Thus, explicit in the language is that u is already including the dividing by 2 operation. Whereas, remainder is just the integer that is left when the division operation is done, so a remainder is not a fraction until it is divided by the divisor.
I am not a native speaker of English, so I had to learn these terms myself in order to do math problems in English.
Posted: 09/20/2013 14:34
I would like to learn it as dividend= divisor( quotient) + remainder...
M I following correctly?
M I following correctly?
Posted: 10/07/2013 17:15
Sw Vy, that is correct.
Posted: 11/21/2013 20:09
Please explain this one
Posted: 11/21/2013 20:32
Hi Barbara, this problem has been explained at length several times in this discussion thread. Please look up the thread. Thanks.
Posted: 11/27/2014 23:07
Yes me too
Posted: 09/25/2015 23:20
It feels like this question can ask for a lot of math if you happen to try the four wrong answers first. Do you have a suggestion for narrowing down the correct answer to fewer choices so we don't waste a lot of time?
Posted: 09/25/2015 23:23
Never mind. I see were I misunderstood what this was asking.