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

 It is currently 17 Jun 2019, 08:06

### 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

# The smallest number which, when divided by 4, 6 or 7 leaves a remainde

Author Message
Manager
Joined: 08 Oct 2010
Posts: 194
Location: Uzbekistan
Schools: Johnson, Fuqua, Simon, Mendoza
WE 3: 10
The smallest number which, when divided by 4, 6 or 7 leaves a remainde  [#permalink]

### Show Tags

17 Oct 2010, 00:41
1
00:00

Difficulty:

25% (medium)

Question Stats:

77% (00:55) correct 23% (00:52) wrong based on 95 sessions

### HideShow timer Statistics

The smallest number which, when divided by 4, 6 or 7 leaves a remainder of 2, is:

a) 44
b) 62
c) 80
d) 86
e) none of these

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Manager
Joined: 19 Aug 2010
Posts: 62
Re: The smallest number which, when divided by 4, 6 or 7 leaves a remainde  [#permalink]

### Show Tags

17 Oct 2010, 01:01
I first find the smallest possible number which is divisible by 4,6 and 7. With a prime factorization you can easily find that this number is 84.

Therefore, 86 (84+2) will be the smallest possible number which when divided by 4, 6 or 7 leaves a remainder of 2. Hence answer should be D.
Manager
Joined: 15 Apr 2010
Posts: 148
Re: The smallest number which, when divided by 4, 6 or 7 leaves a remainde  [#permalink]

### Show Tags

17 Oct 2010, 01:17
The smallest number which, when divided by 4, 6 or 7 leaves a remainder of 2, is:
a) 44
b) 62
c) 80
d) 86
e) none of these

A number will give a remainder only when it is greater than the multiple of the divisors.
In such problems, always start with the greatest divisor. In our case 7.

Test each number with 7. We are left with 44 & 86.
Now test 44 & 86 with 6. We are left with 44 & 86.
Now test 44 & 86 with 4. We are left with 86.

Alternatively after testing with 7 we can easily see that 44 is a multiple of 4. So we only test 86 with the remaining options.

Hope this helps.
_________________
Give [highlight]KUDOS [/highlight] if you like my post.

Always do things which make you feel ALIVE!!!
Retired Moderator
Joined: 02 Sep 2010
Posts: 755
Location: London
Re: The smallest number which, when divided by 4, 6 or 7 leaves a remainde  [#permalink]

### Show Tags

17 Oct 2010, 01:27
feruz77 wrote:
The smallest number which, when divided by 4, 6 or 7 leaves a remainder of 2, is:
a) 44
b) 62
c) 80
d) 86
e) none of these

Pls, help with a solution method!?

Right, the solutions above are correct in their own way. But the way I think about this is the following :

The set of numbers that are divisible by numbers a,b,c are {LCM,LCMx2,LCMx3,...}
So what we need to know is the LCM of 4,6,7
LCM of these numbers is 84.

So the smallest number leaving remainder 2 will be 86

_________________
Senior Manager
Joined: 13 Oct 2016
Posts: 364
GPA: 3.98
Re: The smallest number which, when divided by 4, 6 or 7 leaves a remainde  [#permalink]

### Show Tags

07 Dec 2016, 02:47
1
1
feruz77 wrote:
The smallest number which, when divided by 4, 6 or 7 leaves a remainder of 2, is:

a) 44
b) 62
c) 80
d) 86
e) none of these

I have another vision of this problem:

In order to leave same remainder upon division by 4, 6 or 7 our number should be in the form:

$$N = LCM (4, 6, 7)*x + 2$$, where $$x >= 0$$

$$N = 84*x + 2$$

And we have AP starting from 2

$$2, 86, 170 ...$$

Smallest number in progression which leaves remainder 2 when divided by all of the 4, 6 and 7 is 2 not 86.

Bunuel please correct me if I'm wrong, may be I missed something.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9325
Location: Pune, India
Re: The smallest number which, when divided by 4, 6 or 7 leaves a remainde  [#permalink]

### Show Tags

07 Dec 2016, 04:47
feruz77 wrote:
The smallest number which, when divided by 4, 6 or 7 leaves a remainder of 2, is:

a) 44
b) 62
c) 80
d) 86
e) none of these

Note that the smallest such number is 2.
When 2 is divided by 4, the quotient is 0 and remainder is 2.
Same logic for 6 and 7 too.

Out of the given options, the next smallest number will be LCM (4, 6, 7) + 2 = 86

_________________
Karishma
Veritas Prep GMAT Instructor

Senior Manager
Joined: 13 Oct 2016
Posts: 364
GPA: 3.98
Re: The smallest number which, when divided by 4, 6 or 7 leaves a remainde  [#permalink]

### Show Tags

07 Dec 2016, 05:03
VeritasPrepKarishma wrote:
feruz77 wrote:
The smallest number which, when divided by 4, 6 or 7 leaves a remainder of 2, is:

a) 44
b) 62
c) 80
d) 86
e) none of these

Note that the smallest such number is 2.
When 2 is divided by 4, the quotient is 0 and remainder is 2.
Same logic for 6 and 7 too.

Out of the given options, the next smallest number will be LCM (4, 6, 7) + 2 = 86

Dear Karishma

But why quotient should not be 0. The question asks about remainder not specifying the quotient. Why the whole number can not go into remainder without splitting into quotient and remainder? I can’t still get why 2 is not appropriate? Question asks about min number.

Senior Manager
Joined: 13 Oct 2016
Posts: 364
GPA: 3.98
Re: The smallest number which, when divided by 4, 6 or 7 leaves a remainde  [#permalink]

### Show Tags

07 Dec 2016, 05:09
Dear Karishma

Little more

The Number is in the form:

N=LCM(a,b,c)*n + 2

Why can't we take n=0?
Senior Manager
Joined: 13 Oct 2016
Posts: 364
GPA: 3.98
Re: The smallest number which, when divided by 4, 6 or 7 leaves a remainde  [#permalink]

### Show Tags

07 Dec 2016, 06:09
let-s-be-the-set-of-all-positive-integers-that-when-divided-by-8-hav-187551.html

In the question above in order to get oficial answer A we need to strat our progression from remainder itself (5) and our quotient is 0.

Can anybody explain why we can't use 2 as our answer here?

I think there should be phrazes like "different from remainder itself", "two digit number" or A<N<B in order to indicate some interval.

Many thanks and kudos for explanation from me.
Manager
Joined: 02 Nov 2013
Posts: 81
Location: India
Re: The smallest number which, when divided by 4, 6 or 7 leaves a remainde  [#permalink]

### Show Tags

07 Dec 2016, 10:53
Another way of looking at the problem,
Going directly to the answer options, two answers can be omitted directly as they are divisible by 4 i.e. 44 and 80. We want the answer where after division from 4 remainder should be 2.
For remaining two should comply the equation 4x+2, 6x+2 and 7x+2.
Senior Manager
Joined: 13 Oct 2016
Posts: 364
GPA: 3.98
The smallest number which, when divided by 4, 6 or 7 leaves a remainde  [#permalink]

### Show Tags

07 Dec 2016, 11:51
feruz77 wrote:
The smallest number which, when divided by 4, 6 or 7 leaves a remainder of 2, is:

a) 44
b) 62
c) 80
d) 86
e) none of these

Dear Prashantrchawla

Your approach is good and 86 definitely leaves remainder 2 when divided by 4, 6 and 7.

But, I have some doubts about this question. I think it’s trickier than it seems. The question does not ask which number from the list leaves remainder … or which smallest two digit number leaves remainder … or something of that sort. It simply and directly asks “what smallest number …” and smallest number is definitely 2 not 86.

But official answer says 86 so let it be. This will remain my personal dilemma .

Thanks for kudos by the way
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9325
Location: Pune, India
Re: The smallest number which, when divided by 4, 6 or 7 leaves a remainde  [#permalink]

### Show Tags

08 Dec 2016, 02:20
1
vitaliyGMAT wrote:
VeritasPrepKarishma wrote:
feruz77 wrote:
The smallest number which, when divided by 4, 6 or 7 leaves a remainder of 2, is:

a) 44
b) 62
c) 80
d) 86
e) none of these

Note that the smallest such number is 2.
When 2 is divided by 4, the quotient is 0 and remainder is 2.
Same logic for 6 and 7 too.

Out of the given options, the next smallest number will be LCM (4, 6, 7) + 2 = 86

Dear Karishma

But why quotient should not be 0. The question asks about remainder not specifying the quotient. Why the whole number can not go into remainder without splitting into quotient and remainder? I can’t still get why 2 is not appropriate? Question asks about min number.

The answer should be 2. The quotient can be 0. I said in my post above that the smallest such number is 2. The options don't have 2 and hence we needed to ignore it. Else, the correct answer is 2 only.
_________________
Karishma
Veritas Prep GMAT Instructor

Senior Manager
Joined: 13 Oct 2016
Posts: 364
GPA: 3.98
Re: The smallest number which, when divided by 4, 6 or 7 leaves a remainde  [#permalink]

### Show Tags

08 Dec 2016, 02:29
Dear Karishma
Thanks a lot for confirmation
Current Student
Joined: 06 Sep 2016
Posts: 129
Location: Italy
Schools: EDHEC (A\$)
GMAT 1: 650 Q43 V37
GPA: 3.2
WE: General Management (Human Resources)
Re: The smallest number which, when divided by 4, 6 or 7 leaves a remainde  [#permalink]

### Show Tags

26 Jan 2018, 09:34
IMO the correct answer should be E as the smallest number is 2!

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: The smallest number which, when divided by 4, 6 or 7 leaves a remainde   [#permalink] 26 Jan 2018, 09:34
Display posts from previous: Sort by