What is the remainder when integer n is divided by two?

Question

(1) When n is divided by 5 the remainder is even.
(2) When n is divided by 4 the remainder is even.

vitaliyGMAT · Answer

(1) N=5x, N=5x + 2 or N=5x + 4. N can be even or odd depending on x. Insufficient.

(2) N=4x or N=4x+2. In both cases we'll get even numbers. Sufficient.

B.

Mo2men · Answer

(1) When n is divided by 5 the remainder is even.

n=5q + even

Let q=any odd number.......... n=odd+even =odd .........When dividing n by 2, the reminder is 1 such as 7/2 , 17/2...etc)

Let q = any even number.......n= even+even= even.....When dividing n by 2, the reminder is 0

Insufficient

(2) When n is divided by 4 the remainder is even.

n=4q + even

n is always even ..Thus When dividing n by 2, the reminder is 0.

Sufficient

Answer is B

JeffTargetTestPrep · Answer

We need to determine the remainder when integer n is divided by 2. Keep in mind that the only possible remainders when an integer is divided by 2 are 0 and 1.

Statement One Alone:

When n is divided by 5 the remainder is even.

The information in statement one is not sufficient to answer the question. For example, if n = 7, then the remainder when n is divided by 2 is 1; however, when n = 10, the remainder when n is divided by 2 is 0.

Statement Two Alone:

When n is divided by 4, the remainder is even.

Division of n by 4 produces an even remainder, so we know that n is even. If n is even, the remainder when n is divided by 2 will always be 0. Statement two alone is sufficient to answer the question.

Answer: B

rudraashutosh · Answer

Cases 1 when dividing N by 5 gets even remainder --> N = 7 or 9
Since 
7/5=Rem 2 & 9/5=Rem 4
Now dividing 7 or 9 by 2 gives is 1.
Hence statement 1 alone is sufficient .

Now let's get to statement 2 
And we have only one case that is 6 ,
On dividing 6 by 4 gives us 2(even remainder).
 
Hence , answer would be D.
Each statement alone is sufficient.

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What is the remainder when integer n is divided by two?

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