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If the remainder is 1 when m is divided by 2 and the remainder is 3

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Joined: 02 Sep 2009
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If the remainder is 1 when m is divided by 2 and the remainder is 3 [#permalink]

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02 Jun 2017, 20:17
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If the remainder is 1 when m is divided by 2 and the remainder is 3 when n is divided by 4, which of the following must be true?

(A) m is even
(B) n is even
(C) m + n is even
(D) mn is even
(E) m/n is even

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Re: If the remainder is 1 when m is divided by 2 and the remainder is 3 [#permalink]

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02 Jun 2017, 21:22
m = 2x + 1, where x is a non negative integer
n = 4y + 3, where y is a non negative integer

We can see that individually, both m and n are odd integers
So when we add them, (m+n) MUST be even

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Re: If the remainder is 1 when m is divided by 2 and the remainder is 3 [#permalink]

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02 Jun 2017, 22:13
1
Bunuel wrote:
If the remainder is 1 when m is divided by 2 and the remainder is 3 when n is divided by 4, which of the following must be true?

(A) m is even
(B) n is even
(C) m + n is even
(D) mn is even
(E) m/n is even

Let the quotient of $$\frac{m}{2}$$ be x
m = 2x + 1 ----------------(i)

Let the quotient of $$\frac{n}{4}$$ be y
n = 4y + 3 -----------------(ii)

m + n = 2x + 1 + 4y + 3 = 2x + 4y + 4

Therefore m + n is even.
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Re: If the remainder is 1 when m is divided by 2 and the remainder is 3 [#permalink]

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02 Jun 2017, 23:19
It is clear from the question that both m and n are odd and not even - if m was even - the remainder with 2 would be zero. and if n was even - it will either leave a remainder of 2 or 0 with four. This rules out option A and B. D and E are rejected as the product or quotient of two odd numbers will be odd. However, odd + odd = even, hence Answer C
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Re: If the remainder is 1 when m is divided by 2 and the remainder is 3 [#permalink]

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03 Jun 2017, 03:09
Bunuel wrote:
If the remainder is 1 when m is divided by 2 and the remainder is 3 when n is divided by 4, which of the following must be true?

(A) m is even
(B) n is even
(C) m + n is even
(D) mn is even
(E) m/n is even

Values of "m"can be 1, 3, 5, 7 and so on to get the remainder "1"

Values of "n" can be 3, 7, 11,15 and so on to get the remainder "3"

After analyzing both we know that m & n are odd.

So m + n is even. (C)
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Re: If the remainder is 1 when m is divided by 2 and the remainder is 3 [#permalink]

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03 Jun 2017, 03:21
f the remainder is 1 when m is divided by 2 and the remainder is 3 when n is divided by 4, which of the following must be true?
f the remainder is 1 when m is divided by 2
-m=2x+1 (odd )
remainder is 3 when n is divided by 4
-n=4y+3
-n=4Y+2+1
n=2(2y+1)+1 odd
m is an odd no , n is an odd no

so only c is correct answer choice
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Re: If the remainder is 1 when m is divided by 2 and the remainder is 3 [#permalink]

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03 Jun 2017, 03:41
clearly from the question,,,
m is odd, n is of the form 4K-3 , hence odd
both m and n are odd implies m+n = even
ans C
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Re: If the remainder is 1 when m is divided by 2 and the remainder is 3 [#permalink]

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03 Jun 2017, 09:37
Bunuel wrote:
If the remainder is 1 when m is divided by 2 and the remainder is 3 when n is divided by 4, which of the following must be true?

(A) m is even
(B) n is even
(C) m + n is even
(D) mn is even
(E) m/n is even

Breakdown and solve -

Quote:
the remainder is 1 when m is divided by 2

Possible values of m = { 1, 3 , 5 , 7................ } ======> ODD Numbers

Quote:
the remainder is 3 when n is divided by 4

Possible values of n = { 3, 7 , 11................ } ======> ODD Numbers

So, Both m & n are Odd numbers...

Now, $$m + n = ODD + ODD = Even$$

Thus, answer will be (C) m + n is even

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Re: If the remainder is 1 when m is divided by 2 and the remainder is 3 [#permalink]

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03 Jun 2017, 10:47
Bunuel wrote:
If the remainder is 1 when m is divided by 2 and the remainder is 3 when n is divided by 4, which of the following must be true?

(A) m is even
(B) n is even
(C) m + n is even
(D) mn is even
(E) m/n is even

let both m and n=3
m+n=6 (even)
C
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Re: If the remainder is 1 when m is divided by 2 and the remainder is 3 [#permalink]

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03 Jun 2017, 11:38
m is odd as it not divisible by
n is odd as it is not divisible by 4.
If n is even it would have given remainder of 2 , For example 10/4 remainder is 2
when it is odd 7/4 remainder is 3.
m+n is even
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Re: If the remainder is 1 when m is divided by 2 and the remainder is 3 [#permalink]

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14 Aug 2017, 22:25
My approach was similar to what other clubbers has done above.

"If the remainder is 1 when m is divided by 2" - Clearly m is odd - 1, 3,5,7 etc...

"the remainder is 3 when n is divided by 4" - n 3, 7, 11 etc...

We have M and N both Odd.

A. Not possible. Already saw m is odd
B. Not Possible. Already saw n is odd
C. Possible. Sum of ANY two odd numbers is Even (eg. 1+1 = 2)
D. Not possible. Product of two odd can never be Even. It can only be odd.
E. Not Possible. Since Both M and N are odd there are no factors of 2 in both the numbers. Hence their quotient can never be an Even number

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Re: If the remainder is 1 when m is divided by 2 and the remainder is 3 [#permalink]

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18 Aug 2017, 09:16
1
Bunuel wrote:
If the remainder is 1 when m is divided by 2 and the remainder is 3 when n is divided by 4, which of the following must be true?

(A) m is even
(B) n is even
(C) m + n is even
(D) mn is even
(E) m/n is even

We can create the following two equations:

m = 2Q + 1

2Q is an even number, and adding 1 to an even number yields an odd number. Thus, we see that m must be odd.

And

n = 4S + 3

4S is an even number, and adding the odd number 3 to it yields an odd number. Thus, we see that n must be odd.

From the rules of arithmetic, we know that odd + odd = even. Therefore, we know that the sum of m and n is even.

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Re: If the remainder is 1 when m is divided by 2 and the remainder is 3   [#permalink] 18 Aug 2017, 09:16
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