It is currently 20 Jan 2018, 23:05

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43334

Kudos [?]: 139627 [1], given: 12794

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

Show Tags

02 Jun 2017, 19:17
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

92% (00:45) correct 8% (00:47) wrong based on 143 sessions

HideShow timer Statistics

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
[Reveal] Spoiler: OA

_________________

Kudos [?]: 139627 [1], given: 12794

DS Forum Moderator
Joined: 21 Aug 2013
Posts: 671

Kudos [?]: 214 [0], given: 299

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

Show Tags

02 Jun 2017, 20:22
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

Kudos [?]: 214 [0], given: 299

Director
Joined: 04 Dec 2015
Posts: 696

Kudos [?]: 356 [0], given: 261

Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
Re: If the remainder is 1 when m is divided by 2 and the remainder is 3 [#permalink]

Show Tags

02 Jun 2017, 21:13
1
This post was
BOOKMARKED
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.

Kudos [?]: 356 [0], given: 261

Manager
Joined: 06 Nov 2016
Posts: 100

Kudos [?]: 21 [0], given: 15

Location: India
GMAT 1: 710 Q49 V37
GPA: 2.8
Re: If the remainder is 1 when m is divided by 2 and the remainder is 3 [#permalink]

Show Tags

02 Jun 2017, 22:19
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

Kudos [?]: 21 [0], given: 15

Senior Manager
Joined: 13 Apr 2013
Posts: 259

Kudos [?]: 94 [0], given: 682

Location: India
Schools: ISB '19
GMAT 1: 480 Q38 V22
GPA: 3.01
WE: Engineering (Consulting)
Re: If the remainder is 1 when m is divided by 2 and the remainder is 3 [#permalink]

Show Tags

03 Jun 2017, 02:09
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)
_________________

"Success is not as glamorous as people tell you. It's a lot of hours spent in the darkness."

Kudos [?]: 94 [0], given: 682

Intern
Joined: 01 May 2017
Posts: 17

Kudos [?]: 1 [0], given: 4

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

Show Tags

03 Jun 2017, 02:21
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

Kudos [?]: 1 [0], given: 4

Director
Joined: 21 Mar 2016
Posts: 549

Kudos [?]: 9 [0], given: 99

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

Show Tags

03 Jun 2017, 02:41
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

Kudos [?]: 9 [0], given: 99

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3242

Kudos [?]: 1179 [0], given: 327

Location: India
GPA: 3.5
Re: If the remainder is 1 when m is divided by 2 and the remainder is 3 [#permalink]

Show Tags

03 Jun 2017, 08:37
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

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Kudos [?]: 1179 [0], given: 327

Director
Joined: 07 Dec 2014
Posts: 884

Kudos [?]: 308 [0], given: 17

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

Show Tags

03 Jun 2017, 09:47
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

Kudos [?]: 308 [0], given: 17

VP
Status: Learning
Joined: 20 Dec 2015
Posts: 1107

Kudos [?]: 104 [0], given: 607

Location: India
Concentration: Operations, Marketing
GMAT 1: 670 Q48 V36
GRE 1: 314 Q157 V157
GPA: 3.4
WE: Manufacturing and Production (Manufacturing)
Re: If the remainder is 1 when m is divided by 2 and the remainder is 3 [#permalink]

Show Tags

03 Jun 2017, 10:38
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
_________________

We are more often frightened than hurt; and we suffer more from imagination than from reality

Kudos [?]: 104 [0], given: 607

Manager
Joined: 12 Jun 2016
Posts: 224

Kudos [?]: 49 [0], given: 152

Location: India
WE: Sales (Telecommunications)
Re: If the remainder is 1 when m is divided by 2 and the remainder is 3 [#permalink]

Show Tags

14 Aug 2017, 21:25
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

_________________

My Best is yet to come!

Kudos [?]: 49 [0], given: 152

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1821

Kudos [?]: 1050 [1], given: 5

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

Show Tags

18 Aug 2017, 08:16
1
KUDOS
Expert's post
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.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 1050 [1], given: 5

Re: If the remainder is 1 when m is divided by 2 and the remainder is 3   [#permalink] 18 Aug 2017, 08:16
Display posts from previous: Sort by