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

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Manager
Joined: 21 Feb 2012
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Location: India
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]

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10 May 2012, 05:34
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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
[Reveal] Spoiler: OA

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Math Expert
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Re: If 4 students were added to a dance class, would the teacher [#permalink]

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10 May 2012, 05:48
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Expert's post
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.

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Re: If 4 students were added to a dance class, would the teacher [#permalink]

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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.

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Re: If 4 students were added to a dance class, would the teacher [#permalink]

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23 Aug 2012, 07:49
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.
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Re: If 4 students were added to a dance class, would the teacher [#permalink]

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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.

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Re: If 4 students were added to a dance class, would the teacher [#permalink]

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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.
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Re: If 4 students were added to a dance class, would the teacher [#permalink]

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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.

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Re: If 4 students were added to a dance class, would the teacher [#permalink]

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23 Aug 2012, 11:06
Thanks guys.

I am clear with the explanation.

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Re: If 4 students were added to a dance class, would the teacher [#permalink]

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24 Jul 2015, 00:42
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Re: If 4 students were added to a dance class, would the teacher [#permalink]

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16 Apr 2017, 04:50
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).

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Re: If 4 students were added to a dance class, would the teacher   [#permalink] 16 Apr 2017, 04:50
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