What is the remainder of a positive integer N when it is divided by 2?

1. N contains odd numbers as factors
2. N is a multiple of 15

Stmt 1. Integers with odd factors include such numbers as 6 and 9. Both 6 ( 2 * 3 ) and 9 ( 3 * 3 ), in which case 6/2 has no remainder while 9/2 has a reminader of 1. So Insuff.

Stmt 2. Multiples of 15 are 15, 30, 45 etc . Thus ,15/2 has 1 as a remainder, 30/2 has as a 0 remainder. So Insuff.

Merging the stmts will similarly yield varied remainders. So Insuff. Thus E.

If, however, stmt 1 stated that N has odd number of factors, the answer would be C

If I am interpreting the first statement correctly -- Odd numbers as factors. In that case IMO A.


What is the OA?

@Rahul
the option1 says it as factors as odd numbers as factors (3,5,7 etc)
in any case the prodcut of odd no is odd and the remainder shd be 1 when divided by 2

hence OA should be A


Please advise


@Haaress
6 does not have odd factors. 2 is not considered as a odd no

Rahul@gurome wrote:(1) If an odd integer when divided by 2 will always leave 1 as the remainder.
An even integer leaves a remainder 0 when divided by 2. We have no information whether N is even or odd.
So, (1) is NOT SUFFICIENT.

(2) Multiples of 15 are 15, 30, 45... Here 15 is odd, 30 is even, so 15 leaves remainder of 1 and 30 leaves a remainder 0.
So, (2) is also NOT SUFFICIENT.

Combining (1) and (2) also, we don't whether N is even or odd. So it is also NOT SUFFICIENT.

The correct answer is (E).

outreach wrote:
@Haaress
6 does not have odd factors. 2 is not considered as a odd no

The stmt states that N contains odd numbers as factors, meaning that a integer such as 6 has factor, 1, 2, 3, and 6. So 3 is an odd factor in 6.

Hope that helps!

the answer should be E
(1) from 1 st we are given that N is square of the integer, as only square of the integer has odd number of factors
so remainder can be 0 or 1
1=2*0+1
4=2*2+0
9=2*4+1....
so insufficient
(2) from 2 st we are given that N is a multiple of 15
15=2*7+1
30=2*15+0
also insufficient
both:N is a square of the integer and multiple of 15
so it can be
15^2=2*a+1. or
15^2*2^2=2*b+0
so as we have 1, or 0 as remainders the answer is E

clock60 wrote: (1) from 1 st we are given that N is square of the integer, as only square of the integer has odd number of factors
so remainder can be 0 or 1
1=2*0+1
4=2*2+0
9=2*4+1....

I think the inference you are using is not correct. N cannot surely be concluded as a square number just because it has odd number of factors. In that case 15 (1*3*5) should be a square number.
A possible inference that can be drawn is that N is surely not a prime number. But, that doesn't help us much.

Also, the actual question posted doesn't say that the number of factors is odd - it simply says that it has factor(s) that are odd number(s).

anirban_lax wrote:

clock60 wrote: (1) from 1 st we are given that N is square of the integer, as only square of the integer has odd number of factors
so remainder can be 0 or 1
1=2*0+1
4=2*2+0
9=2*4+1....

I think the inference you are using is not correct. N cannot surely be concluded as a square number just because it has odd number of factors. In that case 15 (1*3*5) should be a square number.
A possible inference that can be drawn is that N is surely not a prime number. But, that doesn't help us much.

Also, the actual question posted doesn't say that the number of factors is odd - it simply says that it has factor(s) that are odd number(s).

hi friend
am not strong in math, but in your example-15 has even number of factors
1,3,5,15
as second notice i think you are right i misread the question but it is slightly ambiguous
if n contains only odd numbers as factors the answer should be A

1.What is the remainder of a positive integer N when it is divided by 2?
1> N contains odd numbers as factors
2>N is a multiple of 15

IMO A :
Stmtn 1 says : N contains odd numbers as factors (Not odd number of factors) in that case the remainder is always 1.

square of a integer contains odd factors,but not odd numbers

ex 2^2 = 4 (factors 1,2,4) which are not odd
3^2 = 9 (factors 1,3,9) which are odd and remainder is 1