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# For nonnegative integers a, b, and c, what is the value of the product

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Manager
Joined: 28 Jul 2013
Posts: 70
Location: India
Concentration: Marketing, Strategy
GPA: 3.62
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For nonnegative integers a, b, and c, what is the value of the product  [#permalink]

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Updated on: 02 Mar 2015, 02:04
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Question Stats:

69% (01:07) correct 31% (01:16) wrong based on 350 sessions

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For nonnegative integers a, b, and c, what is the value of the product abc?

(1) ab=bc
(2) a≠c

I cannot understand the explanation given by veritas prep. Need help on this one. will post the explanation

Originally posted by sayansarkar on 02 Mar 2015, 01:40.
Last edited by Bunuel on 02 Mar 2015, 02:04, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.
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Re: For nonnegative integers a, b, and c, what is the value of the product  [#permalink]

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02 Mar 2015, 02:10
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For nonnegative integers a, b, and c, what is the value of the product abc?

(1) ab=bc;
ab - bc = 0;
b(a - c) = 0;
Either b =0 or a = c.
If b = 0, then abc = 0 but if b ≠ 0, then the value of abc will depend on the individual values of the variables. Not sufficient.

(2) a≠c. Not sufficient.

(1)+(2) Since from (2) a≠c, then from (1) we'd have that b = 0, making abc equal to 0, irrespective of the values of a and c. Sufficient.

Hope it's clear.
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Joined: 28 Jul 2013
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Location: India
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Re: For nonnegative integers a, b, and c, what is the value of the product  [#permalink]

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02 Mar 2015, 02:30
Thank you Bunuel. Now its clear. I missed the point there
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Joined: 14 Oct 2013
Posts: 45
Re: For nonnegative integers a, b, and c, what is the value of the product  [#permalink]

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05 Mar 2015, 11:44
Bunuel- you stated that "Either b =0 or a = c." when we get to the point of b(a-c)=0 is that always the case, where only one is true, when we have an equation that looks like that? So for example (just making this up)...

12A=9AB
12A-9AB=0
factor out the 3A...
3A(4-3B)=0
So then..only one of these solutions can be true?
A=0 OR B=4/3
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Re: For nonnegative integers a, b, and c, what is the value of the product  [#permalink]

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05 Mar 2015, 11:55
1
Hi soniasawhney,

Both possibilities COULD be true, but it's not grammatically correct (nor mathematically correct) to state:

B=0 AND A=C (as both DO NOT need to be true for the product of B(A-C) to equal 0 - only one of them needs to be true).

If you were taking the notes, then you might find it useful to write....

B=0 or A=C OR BOTH

12A = 9AB
12A - 9AB = 0
3A(4 - 3B) = 0

A=0 or B=4/3 OR BOTH

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** Intern Joined: 14 Oct 2013 Posts: 45 Re: For nonnegative integers a, b, and c, what is the value of the product [#permalink] ### Show Tags 05 Mar 2015, 13:28 ah that makes sense- thank you! Retired Moderator Joined: 19 Mar 2014 Posts: 937 Location: India Concentration: Finance, Entrepreneurship GPA: 3.5 Re: For nonnegative integers a, b, and c, what is the value of the product [#permalink] ### Show Tags 09 Jul 2017, 05:44 1 sayansarkar wrote: For nonnegative integers a, b, and c, what is the value of the product abc? (1) ab=bc (2) a≠c I cannot understand the explanation given by veritas prep. Need help on this one. will post the explanation (1) ab=bc $$ab = bc$$ $$ab - bc = 0$$ $$b(a - c) = 0$$ Either $$b = 0$$ or $$a = c$$ We will get multiple answers based on values of b and a or c. If b = 0 then we will the value of equation as ZERO, however if the a = c then we will get value, based on a or c. Hence, (1) ===== is NOT SUFFICIENT (2) a≠c This does not give us any values of a or b or c Hence, (2) ===== is NOT SUFFICIENT Combining (1) & (2) We get that a≠c which means $$b = 0$$ as per (1) and this gives us the value of ZERO foe abc. Hence, (1) & (2) ===== is SUFFICIENT Hence, Answer is C _________________ "Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent." Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6821 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: For nonnegative integers a, b, and c, what is the value of the product [#permalink] ### Show Tags 10 Jul 2017, 09:59 sayansarkar wrote: For nonnegative integers a, b, and c, what is the value of the product abc? (1) ab=bc (2) a≠c I cannot understand the explanation given by veritas prep. Need help on this one. will post the explanation Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. There are 3 variables and 0 equation. Thus the answer E is most likely. Condition 1) $$ab = bc$$ is equivalent to $$ab - bc = 0$$ or $$b(a-c) = 0$$. Thus $$b = 0$$ or $$a = c$$. If $$b = 0$$, then we have $$abc = 0$$. However, if $$b \ne 0$$ and $$a = c$$, we have the case $$a = b = c = 1$$ with $$abc = 1$$. Since the answer is not unique, this is not sufficient. Condition 2) If $$a = 1$$, $$b = 1$$, $$c = 2$$, then $$abc = 2$$. If $$a = 1$$, $$b = 2$$, $$c = 3$$, then $$abc = 6$$. Since the answer is not unique, this is not sufficient either. Conditions 1) & 2) From the condition 1), $$ab = bc$$ is equivalent to $$ab - bc = 0$$ or $$b(a-c) = 0$$. Thus $$b = 0$$ or $$a = c$$. However, $$b = 0$$, since $$a \ne c$$ by the condition 2) Thus $$abc = 0$$. Therefore, C is the answer. For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80 % chance that E is the answer, while C has 15% chance and A, B or D has 5% chance. Since E is most likely to be the answer using 1) and 2) together according to DS definition. Obviously there may be cases where the answer is A, B, C or D. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: For nonnegative integers a, b, and c, what is the value of the product  [#permalink]

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03 Sep 2018, 09:04
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Re: For nonnegative integers a, b, and c, what is the value of the product &nbs [#permalink] 03 Sep 2018, 09:04
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