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Positive integer n leaves a remainder of 4 after division by

by RBBmba@2014 » Fri Mar 27, 2015 3:58 am

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Positive integer n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5. If n is greater than 30, what is the remainder that n leaves after division by 30?

(A) 3

(B) 12

(C) 18

(D) 22

(E) 28

OA: E

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by GMATGuruNY » Fri Mar 27, 2015 4:16 am
RBBmba@2014 wrote:Positive integer n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5. If n is greater than 30, what is the remainder that n leaves after division by 30?

(A) 3

(B) 12

(C) 18

(D) 22

(E) 28
We can PLUG IN THE ANSWERS, which represent the REMAINDER when n is divided by 30.
Implication:
n = (multiple of 30) + (correct remainder).

Thus, if we add 30 to the answer choices, the results will be possible values for n:
3+30 = 33.
12+30 = 42.
18+30 = 48.
22+30 = 52.
28+30 = 58.

Of the resulting options for n, only 52 and 58 yield a remainder of 4 when divided by 6.
Eliminate A, B and C.
Between 52 and 58, only 58 yields a remainder of 3 when divided by 5.
Eliminate D.

The correct answer is E.
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by RBBmba@2014 » Fri Mar 27, 2015 6:21 am
Thanks Mitch for your reply. I posted another remainder problem here. Could you please let me know whether there is any such faster approach to solve that one ?

As for your solution to the above problem - does this work fine because of the reason that 30 is LCM of 5 & 6 ?

Had it been any other number than 30, will the approach you shown work ? I guess, NOT. Right ?

Correct me please if wrong!
Last edited by RBBmba@2014 on Fri Mar 27, 2015 10:17 pm, edited 1 time in total.
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by Brent@GMATPrepNow » Fri Mar 27, 2015 7:09 am
RBBmba@2014 wrote:Positive integer n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5. If n is greater than 30, what is the remainder that n leaves after division by 30?

(A) 3

(B) 12

(C) 18

(D) 22

(E) 28
Here's another approach:
We'll check the ANSWER CHOICES to see which one matches the given information.

NOTE: Each of the answer choices represents the remainder when n is divided by 30.
So, for example, answer choice A suggests that, when n is divided by 30, the remainder is 3.
In other words, n is 3 greater than some multiple of 3
So, we can write: n = 30k + 3 (for some integer k)
If this is the correct answer, then this value of n will satisfy the given information (n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5)
Let's check whether this is true.
n = 30k + 3 = 6(5k) + 3, which means n is 3 greater than some multiple of 6.
This means that n divided by 6 would leave remainder 3, but we're told that the remainder is supposed to be 4.
So, we can ELIMINATE A.

Answer choice B
This means that n = 30k + 12 (for some integer k)
n = 30k + 12 = 6(5k + 2), which means n is a MULTIPLE of 6.
This means that n divided by 6 would leave remainder 0, but we're told that the remainder is supposed to be 4.
So, we can ELIMINATE B.

Answer choice C
This means that n = 30k + 18 (for some integer k)
n = 30k + 18 = 6(5k + 3), which means n is a MULTIPLE of 6.
This means that n divided by 6 would leave remainder 0, but we're told that the remainder is supposed to be 4.
So, we can ELIMINATE C.

Answer choice D
This means that n = 30k + 22 (for some integer k)
n = 30k + 22 = 30k + 18 + 4 = 6(5k + 3) + 4. So, n is 4 greater than some multiple of 6, which means that n divided by 6 would leave remainder 4. This part checks out.
What about the other piece of given information (n leaves a remainder of 3 after division by 5)?
n = 30k + 22 = 30k + 20 + 2 = 5(6k + 4) + 2, which means that n divided by 5 would leave remainder 2. We're told that the remainder is supposed to be 3.
So, we can ELIMINATE D.

Answer = E

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Brent
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by RBBmba@2014 » Sat Mar 28, 2015 10:54 am
RBBmba@2014 wrote: Mitch - As for your solution to the above problem - does this work fine because of the reason that 30 is LCM of 5 & 6 ?

Had it been any other number than 30, will the approach you shown work ? I guess, NOT. Right ?

Correct me please if wrong!
Mitch - just a quick confirmation reqd. Could you please share your thoughts on this ?

Much thanks in advance.
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by GMATGuruNY » Mon Mar 30, 2015 1:42 pm
RBBmba@2014 wrote:
RBBmba@2014 wrote: Mitch - As for your solution to the above problem - does this work fine because of the reason that 30 is LCM of 5 & 6 ?

Had it been any other number than 30, will the approach you shown work ? I guess, NOT. Right ?

Correct me please if wrong!
Mitch - just a quick confirmation reqd. Could you please share your thoughts on this ?

Much thanks in advance.
Positive integer n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5.
Options for n = 28, 58, 88, 118...

If the question stem asked for the remainder after division by a number other than 30, there would be no correct answer.
Revised question stem:
What is the remainder that n leaves after division by 31?
If n=58, then 58/31 = 1 R27.
If n=88, then 88/31 = 2 R26.
If n=108, then 108/31 = 3 R25.
Since the remainder can be different values, there is no correct answer to the revised question stem.

Thus, your query seems moot.
The question stem would not ask for the remainder after division by a number other than 30.
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Re: Positive integer n leaves a remainder of 4 after division by

by Scott@TargetTestPrep » Sat Jul 25, 2020 1:07 pm
RBBmba@2014 wrote: ↑
Fri Mar 27, 2015 3:58 am
 Positive integer n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5. If n is greater than 30, what is the remainder that n leaves after division by 30?

(A) 3

(B) 12

(C) 18

(D) 22

(E) 28

OA: E

Experts - what is the smartest way to solve this type of problems,consuming minimum time ?
Solution:

Notice that 4 is 2 less than 6 and 3 is also 2 less than 5; thus, a number that has both requirements (i.e., a remainder of 4 after division by 6 and a remainder of 3 after division by 5) is 2 less than the LCM of 6 and 5. Since the LCM of 6 and 5 is 30, that number will be 28. Although we are given that n is greater than 30, we can modify the number by adding 30 to it. That is, n = 28 + 30 = 58, and the remainder when 58 is divided by 30 is 28 (note that 58/6 = 9 R 4 and 58/5 = 11 R 3, satisfying the requirements).

Answer: E
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