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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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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
Hence C answer



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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
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)
Adding (i) and (ii) ie; Adding m and n we get
m + n = 2x + 1 + 4y + 3 = 2x + 4y + 4
Therefore m + n is even. 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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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 4K3 , 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 NumbersQuote: the remainder is 3 when n is divided by 4 Possible values of n = { 3, 7 , 11................ } ======> ODD NumbersSo, 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 Final 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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18 Aug 2017, 09:16
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. Answer: C
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