What is the remainder when the positive integer n is divided

Question

What is the remainder when the positive integer n is divided by 2?

(1) When n is divided by 5, the remainder is an odd integer.
(2) When n is divided by 10, the remainder is an odd integer.

IanStewart · Accepted Answer

Without testing numbers:

First, there are only two remainders possible when you divide n by 2: 0 and 1. The remainder is 0 if n is even, and 1 if n is odd. So the question is really just asking "is n odd?"

Remember the quotient/remainder definition. When we divide n by d, we have n = qd + r, where r is the remainder and q the quotient.

From S1, n = 5q + r, where r is odd. So n = 5q + odd, and n could be even if q is odd, and n could be odd if q is even. Insufficient.

From S2, n = 10q + r where r is odd. So n = even + odd = odd. Sufficient.

Bunuel · Answer

What is the remainder when the positive integer n is divided by 2?

Question basically asks whether n is odd or even: if it's odd then the remainder will be 1 and if it's even then the remainder will be zero.

(1) When n is divided by 5, the remainder is an odd integer --> n=5q+odd, so n could be odd (1, 3, 11, 13, 21, 23, ...) as well as even (6, 8, 16, 18, ... ). Not sufficient.

(2) When n is divided by 10, the remainder is an odd integer --> n=10p+odd=even+odd=odd. Sufficient.

Answer: B.

pm4553 · Answer

(1) Let n = 8, remainder 3.....so, 8/2 = remainder = 0
 Let n = 16, remainder 1....so 16/2 = remainder = 0
Suff
(2) n = can be 10,30,50,70,90,110,130 etc
All these numbers are divisible by 2, remainder = 0
Suff

D

P.S > I hope i'm not missing something

pmenon · Answer

I think its B.

From stat 1, n could be 6 or 11. Both numbers give different remainders when divided by 2.Insuff.

From stat 2, n can be 11, 21, 31, etc. In all cases, it gives a remainder of 1 when divided by 2. Suff.

bigtreezl · Answer

n is +ive int, rem when n/2?

1)n/5, rem is odd
 
test numbers 13,21,28

13/2 rem=1, 21/2 rem=1, 28/2 rem=0, insuff

2)n/10, rem is odd

test numbers 13, 21, 27

13/2 rem=1, 21/2 rem=1, 27/2 rem =1, suff

B

sojafon · Answer

1) n = 5q + odd

^This doesn't tell us whether q is divisible by 2 or not. So this info is insufficient.

2) n = 10q + odd,
= 2(5q) + odd

^We can see that the remainder is odd. So this info is sufficient. B

unceldolan · Answer

Bunuel,

how can the remainder of n/5 be 11 or 6 and so on? Isn't it always between 1 and 4? e.g. 9/ 5 = 1+4 or 23 / 5 = 1+3.
What am I getting wrong here?

Bunuel · Answer

Those are possible values of n, not the possible values of the remainders upon division n by 5.

SUNILAA · Answer

when n=13 ; 13/5 remainder=3(odd no) ; 13/2 remainder =1
when n=14 ; 14/5 remainder =1 ( odd no); 14/2 remainder= 0
when n= 16 ; 16/5 remainder =1 (odd no); 16/2 remainder = 0
when n=18 ; 18/5 remainder=3 (odd no) ; 18/2 remainder =0 
when n= 21 ; 21/5 remainder =1 (odd no) ; 21/2 reaminder= 1

in all no we are nt getting a definite value of n so how statement 2 is sufficient?

Bunuel · Answer

14 divided by 5 gives the remainder of 4, not 1. Also, you are analyzing statement (1) there, which is not sufficient.

Statement (2) says: When n is divided by  10 , the remainder is an odd integer

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

What is the remainder when the positive integer n is divided

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

What is the remainder when the positive integer n is divided

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards