Division and remainder

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saidov.mikhail: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Sat Dec 08, 2012 5:03 am

by saidov.mikhail » Mon Sep 30, 2013 11:14 pm

If n is a positive integer and r is the remainder when 4+7n is divided by s. What is the value of r?

1) n+1 is divisible by 3
2) n > 20

Last edited by saidov.mikhail on Tue Oct 01, 2013 1:00 am, edited 1 time in total.

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Source: Beat The GMAT — Data Sufficiency | Mon Sep 30, 2013 11:14 pm

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by [email protected] » Mon Sep 30, 2013 11:39 pm

Hi saidov.mikhail,

In this question, we need to know something about both "n" and "s"; to figure out the remainder, we need to know what we're dividing by. Since we're never told anything about "s", there's no way to answer this question.

Fact 1 tells us "n" is odd. Nothing about "s" though.
Fact 1 is INSUFFICIENT.

Fact 2 tells us "n" is greater than 20. Nothing about "s" though.
Fact 2 is INSUFFICIENT.

Combined, we know that "n" is odd AND greater than 20. Still nothing about "s" though.

Final Answer: E

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vinay1983: Legendary Member; Posts: 643; Joined: Wed Aug 14, 2013 4:27 amFollowed by: 7 members; Thanked: 48 times

by vinay1983 » Tue Oct 01, 2013 12:21 am

saidov.mikhail wrote:If n is a positive integer and r is the remainder when 4+7n is divided by s. What is the value of r?

1) n+1 is divisible by 2
2) n > 20

We need to know values of n, r and s to arrive at any concrete idea. Let us examine the statements

Statement 1

n+1 is divisible by 2. So n can be 1,3,5,7,9 etc. Plug in values of n in the main equation 4+7n divided by s

so 4+7*1=11 or 4+7*3=25 we need to find "r", but for that we need to know "s", which is not available
Hence Insufficient

Statement 2

n > 20, so "n" can be 21,22,23,24 etc. Plug in the values of "n" in the main equation 4+7n divided by s

so 4+7*21=4+141=145, again to find "r", we need "s", but no mention about it. So insufficient

Combining, still no information about "s".

Hence E for me.

You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!

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saidov.mikhail: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Sat Dec 08, 2012 5:03 am

by saidov.mikhail » Tue Oct 01, 2013 1:03 am

Guys,
I'm very sorry, I made a mistake in original wording (corrected already)

1) n+1 is divisible by 3

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vinay1983: Legendary Member; Posts: 643; Joined: Wed Aug 14, 2013 4:27 amFollowed by: 7 members; Thanked: 48 times

by vinay1983 » Tue Oct 01, 2013 1:07 am

saidov.mikhail wrote:Guys,
I'm very sorry, I made a mistake in original wording (corrected already)

1) n+1 is divisible by 3

I still don't think this will change the outcome of the question.

You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!

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by Brent@GMATPrepNow » Tue Oct 01, 2013 9:30 am

saidov.mikhail wrote:If n is a positive integer and r is the remainder when 4+7n is divided by s. What is the value of r?

1) n+1 is divisible by 3
2) n > 20

You might want to go back and edit your original post again. The question should read:

If n is a positive integer and r is the remainder when 4+7n is divided by 3. What is the value of r?

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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by Brent@GMATPrepNow » Tue Oct 01, 2013 9:49 am

saidov.mikhail wrote:If n is a positive integer and r is the remainder when 4+7n is divided by 3. What is the value of r?

1) n+1 is divisible by 3
2) n > 20

NOTE: I've edited the question so that it matches the original question.

This question could be worded in a nicer way: If n is a positive integer, what is the remainder when 7n+4 is divided by 3?

Target question: What is the remainder when 7n+4 is divided by 3?

Statement 1: n+1 is divisible by 3
Let's take our target expression (7n+4) and rewrite it as 3(2n+1) + (n+1)
This is useful, because we know that 3(2n+1) is divisible by 3.
Now statement 1 tells us that (n+1) is divisible by 3.
There's a nice rule that says, "If A is divisible by k, and B is divisible by k, then (A+B) is divisible by k."
So, we can conclude that 3(2n+1) + (n+1) is divisible by 3
This means that 7n+4 is divisible by 3
In other words, the remainder is zero when 7n+4 is divided by 3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: n > 20
There are several values of n that satisfy this condition. Here are two:
Case a: n = 21, in which case, the remainder is one when 7n+4 is divided by 3
Case b: n = 22, in which case, the remainder is two when 7n+4 is divided by 3
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Tue Oct 01, 2013 9:52 am

saidov.mikhail wrote:If n is a positive integer and r is the remainder when 4+7n is divided by s. What is the value of r?

1) n+1 is divisible by 3
2) n > 20

Dear saidov.mikhail,
I think you have made typo error while typing the question.. I have solved a similar question wherein "r when 4+7n is divided by s" was instead "r when 4+7n is divided by 3"

R A H U L

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Tue Oct 01, 2013 10:02 am

(4 + 7n)/3 => (3 + 6n)/3 + (1+n)3
Part (3 + 6n)/3 is divisible by 3

Statement 1:
(n+1)/3 is divisible.
SUFFICIENT

Statement 2:
n = 20; YES
n = 21; NO
INSUFFICIENT

Answer [spoiler]{A}[/spoiler]

R A H U L

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