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

Question

(1) When n is divided by 13, the remainder is 3
(2) n + 2 is a multiple of 7

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GMATinsight · Answer

Question: Remainder when n is divided by 2?

If n is even then remainder is 0 and if n is odd then remainder is 1 so we only need to know whether n is even or odd

Question: Is n even?

Statement 1 : When n is divided by 13, the remainder is 3

i.e.  n = 13a+3

but n may be 16 or 29 hence

NOT SUFFICIENT

Statement 2 : n + 2 is a multiple of 7 
i.e.  n = 7b-2 
i.e. n+2 = 7 or 14 
i.e n - 5 or 14 hence

NOT SUFFICIENT

COmbining the statements

n = 13a+3  and  n = 7b-2

13a+3 = 7b-2

i.e. 13a + 5 = 7b

FOr, a = 5, b=10, n = 68 EVEN
FOr, a = 12, b=23, n = 159 ODD

NOT SUFFICIENT

Answer: Option E

RaghavKhanna · Answer

n = 13k + 3

when
k=0, n=3, => mod(n/2)=1
k=1, n=16, => mod(n/2)=0

Since, we get different values of remainder,
=> St.1 is insufficient.

St.2:
n+2 = 7k
=> n = 7k+5

When,
k=0, n=5, => mod (n/2) = 1
k=1, n=12, => mod (n/2) = 0

Since, we get different values of remainder,
=> St.2 is insufficient.

Combining st.1 and st.2

=> 13a + 3 = 7b + 5
=> a = (7b+2)/13

Min. value of b for which a is integer = 9
ie; b = 9, => a = 5
=> Minimum value of n = 68

General form of the number will be:
n = LMC (7,13)K + 68

k = 0, n = 68, => mod (n/2) = 0
k = 1, n = 159, => mod(n/2) = 1

Again, we get different values of remainder.

=> St. 1 and 2 together are also insufficient.

=> Answer: E

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yashikaaggarwal · Answer

When a no. Is divided by 2. It either leave remainder 0 or 1

Statement 1: When n is divided by 13, the remainder is 3
Therefore value of n = 3,16,29,42.............
When odd/2 leaves 1 as remainder
When even/2 leaves 0 as remainder
(Not sufficient)

Statement 2: n + 2 is a multiple of 7
N+2=7x
Where x is a positive natural no. = 1,2,3.........
X = 1
07 = N+2 => N = 5
X = 2
14 = N+2 => N = 12
X = 3
21 = N+2 => N = 19
Values of N = 5,12,19,26.......
When odd/2 leaves 1 as remainder
When even/2 leaves 0 as remainder
(Not sufficient).

Statement 1&2 together: Set values of N = 3,5,12,16,19,26,29,42,26......
When odd/2 leaves 1 as remainder
When even/2 leaves 0 as remainder
(Not sufficient)

Answer is E

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dimri10 · Answer

I DO HOPE IT IS E 
 1. N/13 THEN R=3. IT COULD BE 3 SO 3/2 HAS A REMAINDER OR 16 WHICH HAS NO REMINDER AT ALL. NOT SUFFICIENT
2. N+2 IS 7X SO N CAN BE 5 OR 12 . 5 LEAVES A RAMAINDER BUT 12 NOT. NOT SUFFICIENT

BOTH:
n=13K+3
n=7W-2
2n=13K+7w+1
n=6.5K+3.5w+1 (since N is an integer- K and W could be only even numbers so that N will be an integer-- ------ 0.5*3 etc. is a fraction. 0.5*4 or *6 or * 8 is a whole number)

now if K and W are i.e, 2 N is odd ( 6.5*2+ 3.5*2+1), so when N is divided by 2, N will have a remainder.

but if K is 2 and W is 4, i.e, N is even (6.5*2+ 3.5*4+1), so he won't have a reminder.

81 and 146, i.e applies to both statements

Ahmed9955 · Answer

How to think for a=12

I checked by putting values for a and got for a=5 -> n=68 but to reach a=12 n-159 would be lengthy and time consuming. How to do I think that it'll further give a value with a different remainder?

ueh55406 · Answer

(1) When n is divided by 13, the remainder is 3

n is of the form:

n=13q+3 -----> if we divide 13q+3 by 2, we will get multiple values for remainders.

if  q=;1 n=13+3=16  in that case remainder will be 0.
if  q=2;n=26+3=29  in this case remainder will be 1.

clearly Not sufficient.

(2) n + 2 is a multiple of 7.

this means,  7q=n+2 , where q is any integer: 1,2,3,4...

n=7q-2

7q-2 / 2  gives multiple remainders as well.

if q=1;   n=7*2-2= 12 . in this case, when divided by 2, remainder will be 0
if q=3;  n=7*3-2=19 .in this case, when divided by 2, remainder will be 1

Not sufficient.

1+2 together.

n=13q+3  and n+2 is a multiple of 7

therefore,  n+2= 13q+3+2 ---->  n+2=13q+5  is also a multiple of 7. again, q can be any integer=1,2,3,4...

you don't need to "solve" further it's clear we're kinda in a circle now. since q can be any integer this will not give one single result.

Hence, E.

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

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