GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 May 2019, 22:32

### 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

# What is the remainder when the two-digit, positive integer x is divide

Author Message
TAGS:

### Hide Tags

Manager
Joined: 04 Oct 2013
Posts: 73
Location: Brazil
GMAT 1: 660 Q45 V35
GMAT 2: 710 Q49 V38
What is the remainder when the two-digit, positive integer x is divide  [#permalink]

### Show Tags

14 Dec 2013, 06:14
4
33
00:00

Difficulty:

25% (medium)

Question Stats:

74% (01:37) correct 26% (01:41) wrong based on 1157 sessions

### HideShow timer Statistics

What is the remainder when the two-digit, positive integer x is divided by 3?

(1) The sum of the digits of x is 5
(2) The remainder when x is divided by 9 is 5
Math Expert
Joined: 02 Sep 2009
Posts: 55231
Re: What is the remainder when the two-digit, positive integer x is divide  [#permalink]

### Show Tags

14 Dec 2013, 06:21
15
22
What is the remainder when the two-digit, positive integer x is divided by 3?

(1) The sum of the digits of x is 5 --> x can be 14, 41, 23, 32, or 50. Each of this numbers gives the remainder of 2 when divided by 3. Sufficient.

(2) The remainder when x is divided by 9 is 5 --> $$x = 9q + 5 = 9q + 3 + 2 =3(3q+1)+2$$ --> the remainder when x is divided by 3 is 2. Sufficient.

_________________
##### General Discussion
Manager
Status: Work hard in silence, let success make the noise
Joined: 25 Nov 2013
Posts: 131
Location: India
Concentration: Finance, General Management
GMAT 1: 540 Q50 V15
GMAT 2: 640 Q50 V27
GPA: 3.11
WE: Consulting (Computer Software)
Re: What is the remainder when the two-digit, positive integer x is divide  [#permalink]

### Show Tags

14 Dec 2013, 10:47
3
1. Possible choices - 14,41,23,32,50. All give remainder 2 when divided by 3. So, sufficient.
2. Take for example 14 or any other no. which gives remainder 5 when divided by 9, it will always give remainder 2 when divided by 3. So, sufficient.

So, the correct answer is D.
_________________
Sahil Chaudhary
If you find this post helpful, please take a moment to click on the "+1 KUDOS" icon.
My IELTS 7.5 Experience
From 540 to 640...Done with GMAT!!!
http://www.sahilchaudhary007.blogspot.com
Manager
Joined: 15 Aug 2013
Posts: 53
Re: What is the remainder when the two-digit, positive integer x is divide  [#permalink]

### Show Tags

14 Dec 2013, 18:51
2
1
A no is divisile by 3 if the sum of the digits is divisible by 3. The remainder any no with 3 can be found by just dividing the sum of digits(of that no) with 3. If it is zero, the no is divisible by 3, otherwise the remainder obtained is same as what we would have got if we divide the no by 3.
1) sum of digits of x is 5. Hence, the remainder obtained by dividing x by 3 is same as remainder obtained by dividing 5 by 3, i.e. 2.
2) x = 9k + 5. => 3*3x + 3 + 2 = 3(3x + 1)+ 2. Now if we divide this by3, the remainder will be 2.

Hence, each statement is sufficient. Ans- D
SVP
Joined: 06 Sep 2013
Posts: 1660
Concentration: Finance
Re: What is the remainder when the two-digit, positive integer x is divide  [#permalink]

### Show Tags

30 Jan 2014, 16:51
Bunuel wrote:
What is the remainder when the two-digit, positive integer x is divided by 3?

(1) The sum of the digits of x is 5 --> x can be 14, 41, 23, 32, or 50. Each of this numbers gives the remainder of 2 when divided by 3. Sufficient.

(2) The remainder when x is divided by 9 is 5 --> $$x = 9q + 5 = 9q + 3 + 2 =3(3q+1)+2$$ --> the remainder when x is divided by 3 is 2. Sufficient.

What is the logic in statement 1? How come all numbers that add to 5 give remainder 2? Bunuel, I look forward to your response

PS. Actually, now that I think about it is because they are 2 more than multiples of 3? I guess thats the reason

Cheers
J
Math Expert
Joined: 02 Sep 2009
Posts: 55231
Re: What is the remainder when the two-digit, positive integer x is divide  [#permalink]

### Show Tags

30 Jan 2014, 22:30
jlgdr wrote:
Bunuel wrote:
What is the remainder when the two-digit, positive integer x is divided by 3?

(1) The sum of the digits of x is 5 --> x can be 14, 41, 23, 32, or 50. Each of this numbers gives the remainder of 2 when divided by 3. Sufficient.

(2) The remainder when x is divided by 9 is 5 --> $$x = 9q + 5 = 9q + 3 + 2 =3(3q+1)+2$$ --> the remainder when x is divided by 3 is 2. Sufficient.

What is the logic in statement 1? How come all numbers that add to 5 give remainder 2? Bunuel, I look forward to your response

PS. Actually, now that I think about it is because they are 2 more than multiples of 3? I guess thats the reason

Cheers
J

Yes, the first statement gives the numbers which are 2 more than multiples of 3.
_________________
Intern
Joined: 21 Feb 2015
Posts: 26
Re: What is the remainder when the two-digit, positive integer x is divide  [#permalink]

### Show Tags

30 Mar 2015, 18:47
Kuddos chacha (awesome explanation)
Senior Manager
Joined: 23 Sep 2015
Posts: 371
Location: France
GMAT 1: 690 Q47 V38
GMAT 2: 700 Q48 V38
WE: Real Estate (Mutual Funds and Brokerage)
Re: What is the remainder when the two-digit, positive integer x is divide  [#permalink]

### Show Tags

22 Apr 2016, 07:54
1
1
What is the remainder when the two-digit, positive integer x is divided by 3?

(1) The sum of the digits of x is 5 : rule of divisibility by 3 = sum of the digits must be divisible by 3, since 5 is two more than 3, the remainder is 2
(2) The remainder when x is divided by 9 is 5 : Since 9 is a multiple of 3, and leaves a remainder of 5 then we just know that 3 will enter one more time in 5 and leave a remainder of 2

_________________
VP
Status: Learning
Joined: 20 Dec 2015
Posts: 1010
Location: India
Concentration: Operations, Marketing
GMAT 1: 670 Q48 V36
GRE 1: Q157 V157
GPA: 3.4
WE: Engineering (Manufacturing)
Re: What is the remainder when the two-digit, positive integer x is divide  [#permalink]

### Show Tags

09 Jun 2017, 11:53
Imo D
From statement 1
We will get remainder 2 from every number upon division by 3
From statement 2
Again we have remainder​ of 2
Sent from my ONE E1003 using GMAT Club Forum mobile app
_________________
Intern
Joined: 08 Jun 2011
Posts: 18
Re: What is the remainder when the two-digit, positive integer x is divide  [#permalink]

### Show Tags

02 Jul 2017, 10:11
1
No is divisile by 3 => sum of the digits is divisible by 3.
1) sum of digits of x is 5. Hence, the remainder obtained by dividing x by 3 is same as remainder obtained by dividing 5 by 3, i.e. 2.
2) x = 9k + 5. => 3*3x + 3 + 2 = 3(3x + 1)+ 2. Now if we divide this by 3, the remainder will be 2.

Hence, each statement is sufficient. Ans- D
Retired Moderator
Joined: 19 Mar 2014
Posts: 931
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Re: What is the remainder when the two-digit, positive integer x is divide  [#permalink]

### Show Tags

11 Jul 2017, 08:04
nechets wrote:
What is the remainder when the two-digit, positive integer x is divided by 3?

(1) The sum of the digits of x is 5
(2) The remainder when x is divided by 9 is 5

What is the remainder when the two-digit, positive integer x is divided by 3?

(1) The sum of the digits of x is 5

$$14 - 1 + 4 = 5 = 14/3 =$$ Reminder - $$2$$

$$32 - 3 + 2 = 5 - 32/3 =$$ Reminder -$$2$$

As we are getting consistent 2 as the reminder this statement is sufficient.

Hence, (1) ===== is SUFFICIENT

(2) The remainder when x is divided by 9 is 5

Possible numbers when divided by 9 to give 5 as the reminder are:

23, 32, 41..... If we divided them by 3 again we get a consistent reminder of 2

Hence, (2) ===== is SUFFICIENT

You liked the answer? Appreciate with a Kudos
_________________
"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475
Intern
Joined: 23 Jun 2015
Posts: 4
Re: What is the remainder when the two-digit, positive integer x is divide  [#permalink]

### Show Tags

23 Sep 2017, 09:00
Bunuel wrote:
What is the remainder when the two-digit, positive integer x is divided by 3?

......

(2) The remainder when x is divided by 9 is 5 --> $$x = 9q + 5 = 9q + 3 + 2 =3(3q+1)+2$$ --> the remainder when x is divided by 3 is 2. Sufficient.

Hi Bunuel,

What is the rationale behind the manipulation you performed in (2)? Why there has to be a 3q+1? Why can't we just do 3(3q) + 5? (which is wrong..). What did I miss here?

Thanks a lot!
Math Expert
Joined: 02 Sep 2009
Posts: 55231
Re: What is the remainder when the two-digit, positive integer x is divide  [#permalink]

### Show Tags

24 Sep 2017, 01:14
cyy12345 wrote:
Bunuel wrote:
What is the remainder when the two-digit, positive integer x is divided by 3?

......

(2) The remainder when x is divided by 9 is 5 --> $$x = 9q + 5 = 9q + 3 + 2 =3(3q+1)+2$$ --> the remainder when x is divided by 3 is 2. Sufficient.

Hi Bunuel,

What is the rationale behind the manipulation you performed in (2)? Why there has to be a 3q+1? Why can't we just do 3(3q) + 5? (which is wrong..). What did I miss here?

Thanks a lot!

It's not wrong: 3(3q) is divisible by 3 and 5 divided by 3 gives the remainder of 2. In the solution we just re-wrote 9q + 5 so that we directly got (a multiple of 3) + remainder because we separated a number which is less than the divisor (3). Recall that the remainder is always non-negative integer less than divisor $$0\leq{r}<d$$, so $$0\leq{r}<3$$.

Hope it's clear.
_________________
Intern
Joined: 23 Jun 2015
Posts: 4
Re: What is the remainder when the two-digit, positive integer x is divide  [#permalink]

### Show Tags

04 Oct 2017, 12:55
Bunuel wrote:
cyy12345 wrote:
Bunuel wrote:
What is the remainder when the two-digit, positive integer x is divided by 3?

......

(2) The remainder when x is divided by 9 is 5 --> $$x = 9q + 5 = 9q + 3 + 2 =3(3q+1)+2$$ --> the remainder when x is divided by 3 is 2. Sufficient.

Hi Bunuel,

What is the rationale behind the manipulation you performed in (2)? Why there has to be a 3q+1? Why can't we just do 3(3q) + 5? (which is wrong..). What did I miss here?

Thanks a lot!

It's not wrong: 3(3q) is divisible by 3 and 5 divided by 3 gives the remainder of 2. In the solution we just re-wrote 9q + 5 so that we directly got (a multiple of 3) + remainder because we separated a number which is less than the divisor (3). Recall that the remainder is always non-negative integer less than divisor $$0\leq{r}<d$$, so $$0\leq{r}<3$$.

Hope it's clear.

Thanks a lot, Bunuel!
Non-Human User
Joined: 09 Sep 2013
Posts: 10980
Re: What is the remainder when the two-digit, positive integer x is divide  [#permalink]

### Show Tags

26 Nov 2018, 12:14
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.
_________________
Re: What is the remainder when the two-digit, positive integer x is divide   [#permalink] 26 Nov 2018, 12:14
Display posts from previous: Sort by