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Senior Manager  Joined: 12 Oct 2008
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What is the remainder when the positive integer n is divided  [#permalink]

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Question Stats: 46% (01:35) correct 54% (01:41) wrong based on 582 sessions

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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.
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Re: What is the remainder when the positive integer n is divided  [#permalink]

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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.

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.
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Re: What is the remainder when the positive integer n is divided  [#permalink]

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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.
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Re: What is the remainder when the positive integer n is divided  [#permalink]

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2
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.

(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
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Re: What is the remainder when the positive integer n is divided  [#permalink]

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1
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
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Re: What is the remainder when the positive integer n is divided  [#permalink]

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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
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Re: please explain the answer how the authore arrives to that  [#permalink]

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naaga wrote:
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

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.

P. S. naaga please always tag your questions.
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Re: please explain the answer how the authore arrives to that  [#permalink]

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Answer should be B.

If divided by 10 ,and the remainder is odd, then remainder will always be 1 when divided by 2
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Re: please explain the answer how the authore arrives to that  [#permalink]

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Clear B. 2) tells me precisely that n is odd. Hence reminder is 1 when n is divided by 2.
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Re: please explain the answer how the authore arrives to that  [#permalink]

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1. in suff
no will be like 6,8,11,13

2. suff - no will be always odd-11,13 15 , 17

so b is the answer
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Re: What is the remainder when the positive integer n is divided  [#permalink]

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Ans is B

As per statement one the number can be either odd or even. but when u divide by 10 you will get odd integer only when you divide a odd integer

So Ans is B
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Re: What is the remainder when the positive integer n is divided  [#permalink]

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Bunuel wrote:
naaga wrote:
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

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.

P. S. naaga please always tag your questions.

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?
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What is the remainder when the positive integer n is divided  [#permalink]

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unceldolan wrote:
Bunuel wrote:
naaga wrote:
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

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.

P. S. naaga please always tag your questions.

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?

Those are possible values of n, not the possible values of the remainders upon division n by 5.
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Re: What is the remainder when the positive integer n is divided  [#permalink]

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1. n can be 3, then the reminder will be 1, or n can be 8, and the remainder is 0. NS
2. n is odd, thus, the remainder when n is divided by 2 will always be 1.
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Re: What is the remainder when the positive integer n is divided  [#permalink]

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St 1 Insuff, becuase if we divide 10/5 --> remainder 0 but 8/5 = 3

St2 Suff - All-odd /10 will give odd Int as remainder (Suff)

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Re: What is the remainder when the positive integer n is divided  [#permalink]

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statement 1
n/5 gives odd remainder, since 2 is not a factor of 5 we can't say about the remainder of n/2. not sufficient.

statement 2
n/10 gives odd remainder, since 2 is factor of 10(2*5),so n/2 will have same remainder which is odd.

hence B is answer.
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Re: What is the remainder when the positive integer n is divided  [#permalink]

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Bunuel wrote:
naaga wrote:
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

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.

P. S. naaga please always tag your questions.

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?
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Re: What is the remainder when the positive integer n is divided  [#permalink]

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SUNILAA wrote:
Bunuel wrote:
naaga wrote:
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

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.

P. S. naaga please always tag your questions.

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?

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
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Re: What is the remainder when the positive integer n is divided  [#permalink]

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Bunuel wrote:
naaga wrote:
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

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.

P. S. naaga please always tag your questions.

for statement 2:
when n=13 ; 13/10 remainder=3 (odd no) 13/2 r=1
when n=15 ; 15/10 r=5 (odd no) 15/2 r= 1
when n=17 ; 17/10 r=7 (odd no) 17/2 r=1
when n=19 ; 19/10 r=9 (odd no) 19/2 r=1
when n= 21 : 21/10 r=1 (odd no) 21/2 r=1

in all no we are getting r=1 so statement 2 is sufficient. so it doesn't matter that we are getting different values of n we need to get same remainder when n divided by 2? is my thought process correct?is my way to solve the quest correct?
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Re: What is the remainder when the positive integer n is divided  [#permalink]

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SUNILAA wrote:
Bunuel wrote:
naaga wrote:
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

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.

P. S. naaga please always tag your questions.

for statement 2:
when n=13 ; 13/10 remainder=3 (odd no) 13/2 r=1
when n=15 ; 15/10 r=5 (odd no) 15/2 r= 1
when n=17 ; 17/10 r=7 (odd no) 17/2 r=1
when n=19 ; 19/10 r=9 (odd no) 19/2 r=1
when n= 21 : 21/10 r=1 (odd no) 21/2 r=1

in all no we are getting r=1 so statement 2 is sufficient. so it doesn't matter that we are getting different values of n we need to get same remainder when n divided by 2? is my thought process correct?is my way to solve the quest correct?

We are not asked to find the value of n. The question asks: what is the remainder when the positive integer n is divided by 2? For all possible values of n, from (2), the reminder is 1. So, (2) is sufficient to answer the question.
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