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

 It is currently 25 Sep 2018, 20:28

### 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

# M16-35

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49496

### Show Tags

16 Sep 2014, 01:00
3
23
00:00

Difficulty:

85% (hard)

Question Stats:

62% (01:35) correct 38% (02:06) wrong based on 160 sessions

### HideShow timer Statistics

If $$x$$, $$a$$, and $$b$$ are positive integers such that when $$x$$ is divided by $$a$$, the remainder is $$b$$ and when $$x$$ is divided by $$b$$, the remainder is $$a-2$$, then which of the following must be true?

A. $$a$$ is even
B. $$x+b$$ is divisible by $$a$$
C. $$x-1$$ is divisible by $$a$$
D. $$b=a-1$$
E. $$a+2=b+1$$

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 49496

### Show Tags

16 Sep 2014, 01:00
7
6
Official Solution:

If $$x$$, $$a$$, and $$b$$ are positive integers such that when $$x$$ is divided by $$a$$, the remainder is $$b$$ and when $$x$$ is divided by $$b$$, the remainder is $$a-2$$, then which of the following must be true?

A. $$a$$ is even
B. $$x+b$$ is divisible by $$a$$
C. $$x-1$$ is divisible by $$a$$
D. $$b=a-1$$
E. $$a+2=b+1$$

When $$x$$ is divided by $$a$$, the remainder is $$b$$: $$x=aq+b$$ and $$remainder=b \lt a=divisor$$ (remainder must be less than divisor);

When $$x$$ is divided by $$b$$, the remainder is $$a-2$$: $$x=bp+(a-2)$$ and $$remainder=(a-2) \lt b=divisor$$.

So we have that: $$a-2 \lt b \lt a$$, as $$a$$ and $$b$$ are integers, then it must be true that $$b=a-1$$ (there is only one integer between $$a-2$$ and $$a$$, which is $$a-1$$ and we are told that this integer is $$b$$, hence $$b=a-1$$).

_________________
Manager
Joined: 05 Jul 2015
Posts: 104
GMAT 1: 600 Q33 V40
GPA: 3.3

### Show Tags

19 Feb 2016, 15:49
1
Slightly different approach:

x=aq+b
x=bq+a-2

aq+b=bq+a-2
factor out q's
re-arranging gives: 2b=2a-2
Divide by 2
b=a-1
Ans D
Current Student
Joined: 12 Nov 2015
Posts: 59
Location: Uruguay
Concentration: General Management
Schools: Goizueta '19 (A)
GMAT 1: 610 Q41 V32
GMAT 2: 620 Q45 V31
GMAT 3: 640 Q46 V32
GPA: 3.97

### Show Tags

08 Mar 2016, 14:41
Would it work to pick numbers?
Math Expert
Joined: 02 Sep 2009
Posts: 49496

### Show Tags

09 Mar 2016, 11:25
Avigano wrote:
Would it work to pick numbers?

Considering 3 variables and constraints, picking numbers won't be the best way for this problem.
_________________
Intern
Joined: 22 Mar 2016
Posts: 2
Schools: Sloan '20 (A)
GMAT 1: 770 Q50 V47
GPA: 3.42

### Show Tags

28 Mar 2016, 18:19
I think this is a high-quality question and I agree with explanation.
Manager
Joined: 21 Sep 2015
Posts: 79
Location: India
GMAT 1: 730 Q48 V42
GMAT 2: 750 Q50 V41

### Show Tags

20 Jun 2016, 16:55
I think this is a high-quality question and I agree with explanation.
_________________

Appreciate any KUDOS given !

Intern
Joined: 12 Jan 2014
Posts: 1

### Show Tags

05 Jul 2016, 01:02
Slightly different approach:

x=aq+b
x=bq+a-2

aq+b=bq+a-2
factor out q's
re-arranging gives: 2b=2a-2
Divide by 2
b=a-1
Ans D

Is this correct? I find it extremely confusing.
Math Expert
Joined: 02 Sep 2009
Posts: 49496

### Show Tags

05 Jul 2016, 06:48
1
gmatprepeugene2014 wrote:
Slightly different approach:

x=aq+b
x=bq+a-2

aq+b=bq+a-2
factor out q's
re-arranging gives: 2b=2a-2
Divide by 2
b=a-1
Ans D

Is this correct? I find it extremely confusing.

When you say "factor out q's" where does q go? It cannot just disappear.

But more importantly, the quotient should not be the same. If you check the solution above you'll see that it's x=aq+b in one case and x=bp+(a-2). We don't know whether q = p.
_________________
Intern
Joined: 18 Mar 2016
Posts: 3

### Show Tags

07 Jul 2016, 04:35
Hi ,

Please check this and correct me if i am wrong

X= aq + b,

x= bp + (a-2).

so substituting values

a=4,q=1,b=2,x=6,p=3, a-2=0.

6 = 4(1) + 2---------------------x =aq + b

6 = 2(3) + (2-2)------------------x = bp + (a-2)

but D doesnt satisfy the above b = a-1 . b is not equal to a-1.

Thanks
John
Math Expert
Joined: 02 Sep 2009
Posts: 49496

### Show Tags

07 Jul 2016, 04:44
sidjohn wrote:
Hi ,

Please check this and correct me if i am wrong

X= aq + b,

x= bp + (a-2).

so substituting values

a=4,q=1,b=2,x=6,p=3, a-2=0.

6 = 4(1) + 2---------------------x =aq + b

6 = 2(3) + (2-2)------------------x = bp + (a-2)

but D doesnt satisfy the above b = a-1 . b is not equal to a-1.

Thanks
John

If a-2=0, then a=2 but you consider a=4 in the first case.
_________________
Intern
Joined: 18 Mar 2016
Posts: 3

### Show Tags

07 Jul 2016, 05:03
hahaha crazy me.tnx buneul.
Intern
Joined: 12 Oct 2014
Posts: 9
Location: India
GMAT 1: 700 Q48 V38
GPA: 3.2

### Show Tags

11 Sep 2016, 04:41
1
I think this is a high-quality question and I agree with explanation.
Current Student
Joined: 14 Jul 2016
Posts: 6
Location: India
GMAT 1: 730 Q50 V39
GPA: 3.4

### Show Tags

28 Sep 2016, 09:59
Avigano wrote:
Would it work to pick numbers?

I used numbers x=5 a=3 and b=2. Worked like a charm. But I also admit I may have got lucky.
Intern
Joined: 26 Apr 2013
Posts: 5
GMAT 1: 660 Q48 V33

### Show Tags

26 Nov 2016, 13:23
Bunuel wrote:
gmatprepeugene2014 wrote:
Slightly different approach:

x=aq+b
x=bq+a-2

aq+b=bq+a-2
factor out q's
re-arranging gives: 2b=2a-2
Divide by 2
b=a-1
Ans D

Is this correct? I find it extremely confusing.

When you say "factor out q's" where does q go? It cannot just disappear.

But more importantly, the quotient should not be the same. If you check the solution above you'll see that it's x=aq+b in one case and x=bp+(a-2). We don't know whether q = p.

Hi Bunuel, I am extremely sorry but I didnt understand how we got rid of the quotients and got the below equation. Can you please help me understand it

aq+b=bq+a-2
factor out q's
re-arranging gives: 2b=2a-2
Math Expert
Joined: 02 Sep 2009
Posts: 49496

### Show Tags

27 Nov 2016, 01:40
1
vtomar20 wrote:
Bunuel wrote:
gmatprepeugene2014 wrote:
Slightly different approach:

x=aq+b
x=bq+a-2

aq+b=bq+a-2
factor out q's
re-arranging gives: 2b=2a-2
Divide by 2
b=a-1
Ans D

Is this correct? I find it extremely confusing.

When you say "factor out q's" where does q go? It cannot just disappear.

But more importantly, the quotient should not be the same. If you check the solution above you'll see that it's x=aq+b in one case and x=bp+(a-2). We don't know whether q = p.

Hi Bunuel, I am extremely sorry but I didnt understand how we got rid of the quotients and got the below equation. Can you please help me understand it

aq+b=bq+a-2
factor out q's
re-arranging gives: 2b=2a-2

This is an incorrect method by gmatprepeugene2014, which is pointed out in my post.
_________________
Intern
Joined: 11 Apr 2016
Posts: 45
Location: India
Concentration: Marketing, Technology

### Show Tags

30 Mar 2017, 04:30
brunel : This is a very good question, thanks for a lucid explanation!!!
Intern
Joined: 07 Mar 2017
Posts: 2
Location: Indonesia
Schools: Haas '20 (D)
GMAT 1: 640 Q42 V35
GPA: 3.77

### Show Tags

06 Apr 2017, 21:54
1
Key takeway that really helps *thanks Bunuel for showing this* is remainder must be less than divisor
Intern
Joined: 23 Aug 2014
Posts: 8

### Show Tags

25 May 2017, 02:44
DJ1986 wrote:
Slightly different approach:

x=aq+b
x=bq+a-2

aq+b=bq+a-2
factor out q's
re-arranging gives: 2b=2a-2
Divide by 2
b=a-1
Ans D

There is a problem with approach. Its nowhere mentioned that the quotient "q" is same in both the cases as assumed here. This makes this approach incorrect.
Intern
Joined: 15 May 2017
Posts: 1

### Show Tags

29 May 2017, 04:06
1
I think this is a high-quality question and I don't agree with the explanation. Question says " when x is divided by a, the remainder is b" so that would mean that x+b is divisible by a.
So the option "x+b is divisible by a" is also correct
Re M16-35 &nbs [#permalink] 29 May 2017, 04:06

Go to page    1   2    Next  [ 31 posts ]

Display posts from previous: Sort by

# M16-35

Moderators: chetan2u, Bunuel

## Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.