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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

What is the remainder when a is divided by 4? [#permalink]

Show Tags

19 Dec 2010, 14:22

2

This post received KUDOS

3

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

5% (low)

Question Stats:

81% (01:42) correct
19% (01:07) wrong based on 125 sessions

HideShow timer Statistics

What is the remainder when a is divided by 4?

(1) a is the square of an odd integer. (2) a is a multiple of 3.

According to the book, the answer is A.

But according to me, the answer should be C since if we take the first statement and use the value 1 for a, it gives us 1 for the square of 1, what would be the remainder? When we use 3 for a, the square of a will give us 9 which when divided by 4, gives us remainder of 1.

I'm a little confused regarding the correct answer for the below mentioned question:

What is the remainder when a is divided by 4?

(1) a is the square of an odd integer. (2) a is a multiple of 3.

According to the book, the answer is A.

But according to me, the answer should be C since if we take the first statement and use the value 1 for a, it gives us 1 for the square of 1, what would be the remainder? When we use 3 for a, the square of a will give us 9 which when divided by 4, gives us remainder of 1.

Thanks. Kash.

Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is non-negative integer and always less than divisor).

So according to above, when positive integer \(a\) is less than divisor \(d\) then remainder upon division \(a\) by \(d\) is always equals to \(a\), for example 5 divided by 10 yields reminder of 5. So when 1 is divided by 4 remainder is 1.

Or algebraically: 1 divided by 4 can be expressed as \(1=0*4+1\), so \(r=1\).

Back to the original question:

What is the remainder when a is divided by 4?

(1) a is the square of an odd integer --> \(a=(2k+1)^2=4k^2+4k+1\), first two terms (4k^2 and 4k) are divisible by 4 and the third term (1) when divided by 4 yields the remainder of 1. Sufficient.

Or you can try several numbers for \(a\): \(a=1^1=1\) --> 1 divided by 4 yields remainder of 1; \(a=3^1=9\) --> 9 divided by 4 yields remainder of 1; \(a=5^1=25\) --> 25 divided by 4 yields remainder of 1; ...

(2) a is a multiple of 3 --> clearly insufficient as \(a\) can as well be a multiple of 4, 12 for example, and in this case the remainder will be 0, and it also can not be a multiple of 4, 3 for example, and in this case the remainder will be 3. Not sufficient.

Re: MGMAT's Number Properties Data Sufficiency Question [#permalink]

Show Tags

19 Dec 2010, 14:50

ksear wrote:

Hi everyone,

I'm a little confused regarding the correct answer for the below mentioned question:

What is the remainder when a is divided by 4?

(1) a is the square of an odd integer. (2) a is a multiple of 3.

According to the book, the answer is A.

But according to me, the answer should be C since if we take the first statement and use the value 1 for a, it gives us 1 for the square of 1, what would be the remainder? When we use 3 for a, the square of a will give us 9 which when divided by 4, gives us remainder of 1.

Thanks. Kash.

To answer your specific question, if you divide 1 by 4, the reminder is 1. So the answer is valid.

Re: What is the remainder when a is divided by 4? [#permalink]

Show Tags

07 Aug 2013, 23:10

2

This post received KUDOS

What is the remainder when a is divided by 4?

(1) a is the square of a odd integer. Method #1: a=1 reminder=1; a=9 reminder=1, a=25 reminder=1; a=49 reminder=1... I see a pattern, I am convinced that this is sufficient. Method #2: \(a=(2k+1)^2\) (where k is an integer) \(a=4k^2+4k+1\), \(a=4(k^2+k)+1\) \(a\) is a multiple of four plus one, hence the reminder will be one. Sufficient

(2)a is a multiple of 3. a=3 reminder=3, a=9 reminder=1. Not sufficient.
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Re: What is the remainder when a is divided by 4? [#permalink]

Show Tags

10 Aug 2013, 03:32

ksear wrote:

What is the remainder when a is divided by 4?

(1) a is the square of an odd integer. (2) a is a multiple of 3.

According to the book, the answer is A.

But according to me, the answer should be C since if we take the first statement and use the value 1 for a, it gives us 1 for the square of 1, what would be the remainder? When we use 3 for a, the square of a will give us 9 which when divided by 4, gives us remainder of 1.

Thanks. Kash.

1^2/4 = (4-3)^2/4 = (4^2 - 2.4.3 + 9)/4 = 4 + 6 + 9/4 = 10 + 9/4 so the remainder from 9/4 we have is 1 . That's how we can realize why 1 appears as the remainder when 1^2 is divided by 4.

Re: What is the remainder when a is divided by 4? [#permalink]

Show Tags

08 Apr 2016, 11:23

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...