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

 It is currently 23 Sep 2019, 13:32

### 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

# If 4 students were added to a dance class, would the teacher

Author Message
TAGS:

### Hide Tags

Manager
Joined: 21 Feb 2012
Posts: 67
Concentration: Finance, General Management
GMAT 1: 600 Q49 V23
GPA: 3.8
WE: Information Technology (Computer Software)
If 4 students were added to a dance class, would the teacher  [#permalink]

### Show Tags

10 May 2012, 05:34
4
2
00:00

Difficulty:

25% (medium)

Question Stats:

77% (01:33) correct 23% (01:55) wrong based on 203 sessions

### HideShow timer Statistics

If 4 students were added to a dance class, would the teacher be able to divide her students evenly into one or more dance teams of 8?

(1) If 12 students were added, the teacher could divide the students evenly into teams of 8.
(2) The number of students in the class is currently not divisible by 8.

I did not got the explanation already present
Math Expert
Joined: 02 Sep 2009
Posts: 58116
Re: If 4 students were added to a dance class, would the teacher  [#permalink]

### Show Tags

23 Aug 2012, 07:49
2
vkm wrote:
Hi,
I selected E because statement 1 alone is insufficient for all values of X.

From statement 1, if 12 students were added the number of students before lets say = X.
i,e 12+x should be divisible by 8. (x = 4, 12,20,..) should be an even number.

Therefore if i add 4 more students as given in question then i cannot divide the dance team in 8 for all values of X.

First statement says: "if 12 students were added, the teacher could divide the students evenly into teams of 8", which means that x+12 is a multiple of 8. Now, x+12=(x+4)+8=(x+4)+{multiple of 8}. So, we have that the sum of x+4 and some multiple of 8 is a multiple of 8, which means that x+4 must also be a multiple of 8.

To elaborate more:
If integers $$a$$ and $$b$$ are both multiples of some integer $$k>1$$ (divisible by $$k$$), then their sum and difference will also be a multiple of $$k$$ (divisible by $$k$$):
Example: $$a=6$$ and $$b=9$$, both divisible by 3 ---> $$a+b=15$$ and $$a-b=-3$$, again both divisible by 3.

If out of integers $$a$$ and $$b$$ one is a multiple of some integer $$k>1$$ and another is not, then their sum and difference will NOT be a multiple of $$k$$ (divisible by $$k$$):
Example: $$a=6$$, divisible by 3 and $$b=5$$, not divisible by 3 ---> $$a+b=11$$ and $$a-b=1$$, neither is divisible by 3.

If integers $$a$$ and $$b$$ both are NOT multiples of some integer $$k>1$$ (divisible by $$k$$), then their sum and difference may or may not be a multiple of $$k$$ (divisible by $$k$$):
Example: $$a=5$$ and $$b=4$$, neither is divisible by 3 ---> $$a+b=9$$, is divisible by 3 and $$a-b=1$$, is not divisible by 3;
OR: $$a=6$$ and $$b=3$$, neither is divisible by 5 ---> $$a+b=9$$ and $$a-b=3$$, neither is divisible by 5;
OR: $$a=2$$ and $$b=2$$, neither is divisible by 4 ---> $$a+b=4$$ and $$a-b=0$$, both are divisible by 4.

Hope it's clear.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 58116
Re: If 4 students were added to a dance class, would the teacher  [#permalink]

### Show Tags

10 May 2012, 05:48
1
2
If 4 students were added to a dance class, would the teacher be able to divide her students evenly into one or more dance teams of 8?

Say # of the students in the class now is x. The question basically asks whether x+4 is a multiple of 8, because if it is then the teacher would be able to divide x+4 students evenly into teams of 8.

(1) If 12 students were added, the teacher could divide the students evenly into teams of 8 --> x+12=(x+4)+8 is a multiple of 8, so x+4 is also a multiple of 8. Sufficient.

(2) The number of students in the class is currently not divisible by 8. If x=1 then the answer is NO but if x=12 then the asnwer is YES. Not sufficient.

_________________
Intern
Joined: 23 Aug 2012
Posts: 8
GMAT 1: 620 Q47 V29
Re: If 4 students were added to a dance class, would the teacher  [#permalink]

### Show Tags

23 Aug 2012, 05:36
Hi,
I selected E because statement 1 alone is insufficient for all values of X.

From statement 1, if 12 students were added the number of students before lets say = X.
i,e 12+x should be divisible by 8. (x = 4, 12,20,..) should be an even number.

Therefore if i add 4 more students as given in question then i cannot divide the dance team in 8 for all values of X.

Intern
Joined: 05 Mar 2012
Posts: 43
Schools: Tepper '15 (WL)
Re: If 4 students were added to a dance class, would the teacher  [#permalink]

### Show Tags

23 Aug 2012, 08:36
vkm wrote:
Hi,
I selected E because statement 1 alone is insufficient for all values of X.

From statement 1, if 12 students were added the number of students before lets say = X.
i,e 12+x should be divisible by 8. (x = 4, 12,20,..) should be an even number.

Therefore if i add 4 more students as given in question then i cannot divide the dance team in 8 for all values of X.

Evenly divided into =/= divided into even numbers

So for the numbers you picked, bare minimum is 4. so is 4+4 divisible by 8? Yes. If 12, 12+4 divisible by 8? Yes. So on and so forth.
Math Expert
Joined: 02 Sep 2009
Posts: 58116
Re: If 4 students were added to a dance class, would the teacher  [#permalink]

### Show Tags

23 Aug 2012, 09:15
Injuin wrote:
vkm wrote:
Hi,
I selected E because statement 1 alone is insufficient for all values of X.

From statement 1, if 12 students were added the number of students before lets say = X.
i,e 12+x should be divisible by 8. (x = 4, 12,20,..) should be an even number.

Therefore if i add 4 more students as given in question then i cannot divide the dance team in 8 for all values of X.

Evenly divided into =/= divided into even numbers

So for the numbers you picked, bare minimum is 4. so is 4+4 divisible by 8? Yes. If 12, 12+4 divisible by 8? Yes. So on and so forth.

The red part is not correct.

Evenly divisible = divisible.
_________________
Intern
Joined: 05 Mar 2012
Posts: 43
Schools: Tepper '15 (WL)
Re: If 4 students were added to a dance class, would the teacher  [#permalink]

### Show Tags

23 Aug 2012, 09:22
Bunuel wrote:
Injuin wrote:
vkm wrote:
Hi,
I selected E because statement 1 alone is insufficient for all values of X.

From statement 1, if 12 students were added the number of students before lets say = X.
i,e 12+x should be divisible by 8. (x = 4, 12,20,..) should be an even number.

Therefore if i add 4 more students as given in question then i cannot divide the dance team in 8 for all values of X.

Evenly divided into =/= divided into even numbers

So for the numbers you picked, bare minimum is 4. so is 4+4 divisible by 8? Yes. If 12, 12+4 divisible by 8? Yes. So on and so forth.

The red part is not correct.

Evenly divisible = divisible.

That's what I meant. I can't makes the does not equal sign, but I figured =/= was fine. From what vkm stated, he seemed to be under the impression that x+4/8 would be an even number like 2,4,8 as opposed to being simply divisible.
Intern
Joined: 23 Aug 2012
Posts: 8
GMAT 1: 620 Q47 V29
Re: If 4 students were added to a dance class, would the teacher  [#permalink]

### Show Tags

23 Aug 2012, 11:06
Thanks guys.

I am clear with the explanation.
Non-Human User
Joined: 09 Sep 2013
Posts: 12561
Re: If 4 students were added to a dance class, would the teacher  [#permalink]

### Show Tags

15 Aug 2018, 01:07
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: If 4 students were added to a dance class, would the teacher   [#permalink] 15 Aug 2018, 01:07
Display posts from previous: Sort by