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# How to answer this sort of question

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19 May 2014, 10:23
Hi guys,

I'm currently enrolled in a GMAT study course through Kaplan, and have professors on my campus teaching us how to do some of the quant problems. The other day, my quant professor answered a question, and I was curious if he was correct. He gets things wrong on occasion, and this is something that could get my in trouble if he's incorrect.

It was a data sufficiency problem:

Is the integer x divisible by 3?

(1) The last digit in x is 3.
(2) x+5 is divisible by 6.

So if x were 13, if you used both parts it would be 18, so yes, it is.
If x were 23, if you used both parts it would be 28, so no it isn't.

What my professor said is that it is answer (C) because you can say it is, or you can say it isn't with both parts. I assumed it would be answer (E) because using both, you can get a correct answer, but you can also get an incorrect answer, so I assumed you couldn't know. So is he correct in saying it is (C)? and if so, are there a lot of problems similar to this in Data sufficiency where you can figure out the final answer, but it can be wrong or right, and that means it's answer (C)?

Thanks!

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19 May 2014, 12:34
This post was a computer error and should be deleted.
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Last edited by mikemcgarry on 19 May 2014, 12:37, edited 1 time in total.

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19 May 2014, 12:34
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ethanr wrote:
Hi guys,

I'm currently enrolled in a GMAT study course through Kaplan, and have professors on my campus teaching us how to do some of the quant problems. The other day, my quant professor answered a question, and I was curious if he was correct. He gets things wrong on occasion, and this is something that could get my in trouble if he's incorrect.

It was a data sufficiency problem:

Is the integer x divisible by 3?

(1) The last digit in x is 3.
(2) x+5 is divisible by 6.

So if x were 13, if you used both parts it would be 18, so yes, it is.
If x were 23, if you used both parts it would be 28, so no it isn't.

What my professor said is that it is answer (C) because you can say it is, or you can say it isn't with both parts. I assumed it would be answer (E) because using both, you can get a correct answer, but you can also get an incorrect answer, so I assumed you couldn't know. So is he correct in saying it is (C)? and if so, are there a lot of problems similar to this in Data sufficiency where you can figure out the final answer, but it can be wrong or right, and that means it's answer (C)?

Thanks!

Dear ethanr
I'm happy to respond.

First of all, this "ask experts" forum is not the place for questions about math or verbal content. This questions should have been posted in the math forum. Also, before post anything in the math forum, search for it, because pretty much every math practice question from every source has already been posted. For example, this question has been posted here:
is-the-integer-x-divisible-by-3-1-the-last-digit-in-x-is-41567.html

The answer to this question is definitely (B).

Statement #1: The last digit in x is 3.
Well, the numbers with a last digit of three include {13, 23, 33, 43, 53, 63, 73, ...} Some of those (33 & 63) are divisible by 3, and others aren't. From this fact alone, the last digit, we can make no determination of whether x is divisible by 3. This statement, alone and by itself, is insufficient.

Statement #2: x+5 is divisible by 6.
Fact #1: any multiple of 6 is automatically a multiple of 3. (In general, any multiple of N is also a multiple of any factor of N.)
Thus, (x + 5) is a multiple of 3.
Fact #2: we can add 3 to any multiple of 3, or subtract 3 from any multiple of 3, and the result will still be a multiple of 3.
Thus, (x + 5) - 3 = (x + 2) is a multiple of 3, and so is (x + 2) - 3 = (x - 1). If (x + 2) and (x - 1) are multiples of three, then there is absolutely no way that x can be a multiple of 3. The answer to the prompt question is a definitive "no." Because we could answer the prompt question definitively, this means that this statement, alone and by itself, is sufficient.

First statement insufficient. Second statement sufficient. Answer = (B)

If you tutor couldn't get this, it sounds as if he might not be able to help you prepare for GMAT-level math. Feel free to send me a private message if you would like my input on future problems.

Does all this make sense?
Mike
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19 May 2014, 14:43
I've been clicking around the forum and just realized I posted it in the wrong spot. My apologies.

Ok that makes sense. I completely read that wrong, and was thinking you could adjust x to whatever you wanted, and would that work. So x=1 would work, but I just misunderstood the question.

Thanks for your help, that makes sense.

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19 May 2014, 20:18
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Expert's post
ethanr wrote:
Hi guys,

I'm currently enrolled in a GMAT study course through Kaplan, and have professors on my campus teaching us how to do some of the quant problems. The other day, my quant professor answered a question, and I was curious if he was correct. He gets things wrong on occasion, and this is something that could get my in trouble if he's incorrect.

It was a data sufficiency problem:

Is the integer x divisible by 3?

(1) The last digit in x is 3.
(2) x+5 is divisible by 6.

So if x were 13, if you used both parts it would be 18, so yes, it is.
If x were 23, if you used both parts it would be 28, so no it isn't.

What my professor said is that it is answer (C) because you can say it is, or you can say it isn't with both parts. I assumed it would be answer (E) because using both, you can get a correct answer, but you can also get an incorrect answer, so I assumed you couldn't know. So is he correct in saying it is (C)? and if so, are there a lot of problems similar to this in Data sufficiency where you can figure out the final answer, but it can be wrong or right, and that means it's answer (C)?

Thanks!

Also, the answer to your question "are there a lot of problems similar to this in Data sufficiency where you can figure out the final answer, but it can be wrong or right," is this:
Sufficiency means "is the data given to you sufficient to get a single clean unique answer?"

Look at the question stem: Is x divisible by 3?
How will you answer it? There are 3 ways:
"Definitely Yes" or "Definitely No" or "May be - which means sometimes it is and sometimes it is not"

For sufficiency, you need a single definite answer. If the statements tell you that x is definitely divisible by 3, then great the statement is sufficient. If it tells you that it is definitely NOT divisible by 3, then again, the statement is sufficient.

It is NOT sufficient in case of the "May be" answer.

Similarly, say a question stem says "What is the value of x?"
If the statement gives you x = 3 or 5, it is NOT sufficient. You need a unique value. 3 or 5 is not good enough. You need to know which one.

And yes, I agree with Mike, you might need to look elsewhere for GMAT coaching. He might be great at Quant but GMAT is a different game. These are the very basics of DS and half of your Quant section depends on them.

Also, here is how I would solve this question:

(1) The last digit in x is 3.
We know that a number of divisible by 3 when the sum of all its digits is divisible by 3. Just knowing that the last digit is 3 doesn't help. We need to know the sum of all digits. 13 is not divisible by 3 but 33 is. So here we get "May be". x could be divisible by 3, it may not be. This statement alone is not sufficient.

(2) x+5 is divisible by 6.
This means x+5 is a multiple of 6.
x + 5 = 6a
x = 6a - 5 = 6a - 3 - 2 = 3(2a - 1) - 2
Note that the highlighted part is a multiple of 3. x is 2 less than a multiple of 3. This means that x cannot be a multiple of 3. For x to be a multiple of 3, it must be 3/6/9... less or more than another multiple of 3. This statement alone is sufficient.

The logic of this is explained here:
http://www.veritasprep.com/blog/2011/09 ... c-or-math/
http://www.veritasprep.com/blog/2011/09 ... h-part-ii/
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Last edited by VeritasPrepKarishma on 20 May 2014, 10:01, edited 1 time in total.

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20 May 2014, 09:49
Dear Karishma

I tried doing this qs by taking numbers....

Statement 1: insufficient
a. x=3..... Yes
b. x=13.... No

Statment:
a. x+5= 6p.... if x = 1...x+5=6...divisible by 3&6
b. x cannot be 2,3,4,5,6 as it doesnt satisfy the x+5 = 6p...
next will be x= 7.. x+5=12... yes for 6,3 both

shouldnt it be B?

please explain what i am doing wrong.
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20 May 2014, 10:04
NGGMAT wrote:
Dear Karishma

I tried doing this qs by taking numbers....

Statement 1: insufficient
a. x=3..... Yes
b. x=13.... No

Statment:
a. x+5= 6p.... if x = 1...x+5=6...divisible by 3&6
b. x cannot be 2,3,4,5,6 as it doesnt satisfy the x+5 = 6p...
next will be x= 7.. x+5=12... yes for 6,3 both

shouldnt it be B?

please explain what i am doing wrong.

The answer is (B) and I have explained why above. I had forgotten to write "Answer (B)" so I have added it now.
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20 May 2014, 10:20
ok. but your explanation says x is not divisible by 3 and mine is by 3. please explain what is wrong with what i have done as that is how i generally answer these qs.
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20 May 2014, 11:22
NGGMAT wrote:
ok. but your explanation says x is not divisible by 3 and mine is by 3. please explain what is wrong with what i have done as that is how i generally answer these qs.

Dear NGGMAT,
I see you received a high quality explanation from the brilliant Karishma, but I am happy to answer this follow-up question.

In (B), the cases that work include:
when x = 7, (x + 5) = 12
when x = 13, (x + 5) = 18
when x = 19, (x + 5) = 24
etc.
In each of those cases, the (x+5) number is divisible by 6, as required, and therefore is divisible by 3. BUT, the question is not asking about the (x + 5) value. It is asking about the value of x itself, and each case {7, 13, 19, ...}, x is not and cannot be divisible by three. I think that might be your confusion, between the value of (x+5) and the value of x itself.

I will also add: GMAT DS is a demanding question type. Plugging-in numbers is one possible strategy, but hardly the only, and certainly not the best in a large number of cases. In fact, the GMAT specifically constructs math questions to punish and trap those students who always plug in numbers. It's relatively easy to create mathematical "rules" that work for all of the small numbers one might plug in, but then doesn't work when the numbers are larger.

Does all this make sense?
Mike
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20 May 2014, 11:58
mikemcgarry wrote:
NGGMAT wrote:
ok. but your explanation says x is not divisible by 3 and mine is by 3. please explain what is wrong with what i have done as that is how i generally answer these qs.

Dear NGGMAT,
I see you received a high quality explanation from the brilliant Karishma, but I am happy to answer this follow-up question.

In (B), the cases that work include:
when x = 7, (x + 5) = 12
when x = 13, (x + 5) = 18
when x = 19, (x + 5) = 24
etc.
In each of those cases, the (x+5) number is divisible by 6, as required, and therefore is divisible by 3. BUT, the question is not asking about the (x + 5) value. It is asking about the value of x itself, and each case {7, 13, 19, ...}, x is not and cannot be divisible by three. I think that might be your confusion, between the value of (x+5) and the value of x itself.

I will also add: GMAT DS is a demanding question type. Plugging-in numbers is one possible strategy, but hardly the only, and certainly not the best in a large number of cases. In fact, the GMAT specifically constructs math questions to punish and trap those students who always plug in numbers. It's relatively easy to create mathematical "rules" that work for all of the small numbers one might plug in, but then doesn't work when the numbers are larger.

Does all this make sense?
Mike

OH! I GOT IT NOW!... so silly of me.... unfortunately, i have to give my exam next week... i have been getting between 47-49 in Quant in all the mocks but am not very sure if that will happen on real Gmat...
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Re: How to answer this sort of question   [#permalink] 20 May 2014, 11:58
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