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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42 GPA: 3.82

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[Math Revolution GMAT math practice question]

Is ab>bc?

1) abc=0
2) a>c

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Math Expert V
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Posts: 7995
Re: Is ab>bc?  [#permalink]

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1
Is ab>bc?
ab-bc>0.......b(a-c)>0?
So
if b>0, a>c
If b<0, a<c
If b=0, NOT possible

1) abc=0
If b=0, NO..
But if $$b\neq{0}$$, Ans can be yes or no
b=5, a=4 and c=0......yes
b=5, a=0 and c=4......no
Insufficient

2) a>c
Insufficient

Combined..
We still do not know anything about which is 0 and what is b
Insufficient

E
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Math Revolution GMAT Instructor V
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Re: Is ab>bc?  [#permalink]

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=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

When we modify the question, $$ab > bc$$ is equivalent to $$ab – bc > 0$$ or $$b(a-c) > 0$$. Even though we know $$a – c > 0$$ from condition 2), we don’t know if $$b$$ is positive or negative. Thus, both conditions together are not sufficient.

Conditions 1) & 2):
If $$a = 1, b =1$$ and $$c = 0$$, then $$ab > bc$$ and the answer is ‘yes’.
If $$a = 1, b =-1$$ and $$c = 0$$, then $$ab < bc$$ and the answer is ‘no’.
Since we don’t have a unique solution, both conditions together are not sufficient.

Therefore, E is the answer.

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MathRevolution wrote:
[Math Revolution GMAT math practice question]

Is ab>bc?

1) abc=0
2) a>c

My approach kindly assist me where am i going wrong.

Rephrasing the question

ab>bc
therefore ab-bc>0 or b(a-c)>0 or a>c ( dividing both sides by b )

my question why cant we divide both sides by 'b' to get the equation as : a-c>0
Eg: b(a-c)/b > 0/b :- Now since 0/b =0 and b(a-c)/b cancels out 'b' wont the equation be (a-c)>0

or ab/b>bc/b = a>c

So there is no need for B here.
Stmt 1: ac =0 ( I haven't considered B in this statement as i managed to cancel it as per the above equation )
a=0 or c=0 clearly insufficient.
a-c>0 If a=0 and c=2 then we have (0-2)>0 NO
If a=2 and c=0 then we have (2-0)>0 Yes

Stmt 2: a>c

Without Plugging in values : ab>bc then divide both sides by 'b' to get a>c. Sufficient.

the same is confirmed when plugging in values as well.
If a and c both are negative a=-2 and c=-4 then we have (-2>-4). So -2-(-4)= -2+4>0 YES
If a and c are both positive a=4 and c=2 then we have (4-2)>0 YES

As per my approach i get B as the answer.
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8023
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Is ab>bc?  [#permalink]

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Avinasht123 wrote:
MathRevolution wrote:
[Math Revolution GMAT math practice question]

Is ab>bc?

1) abc=0
2) a>c

My approach kindly assist me where am i going wrong.

Rephrasing the question

ab>bc
therefore ab-bc>0 or b(a-c)>0 or a>c ( dividing both sides by b )

my question why cant we divide both sides by 'b' to get the equation as : a-c>0
Eg: b(a-c)/b > 0/b :- Now since 0/b =0 and b(a-c)/b cancels out 'b' wont the equation be (a-c)>0

or ab/b>bc/b = a>c

So there is no need for B here.
Stmt 1: ac =0 ( I haven't considered B in this statement as i managed to cancel it as per the above equation )
a=0 or c=0 clearly insufficient.
a-c>0 If a=0 and c=2 then we have (0-2)>0 NO
If a=2 and c=0 then we have (2-0)>0 Yes

Stmt 2: a>c

Without Plugging in values : ab>bc then divide both sides by 'b' to get a>c. Sufficient.

the same is confirmed when plugging in values as well.
If a and c both are negative a=-2 and c=-4 then we have (-2>-4). So -2-(-4)= -2+4>0 YES
If a and c are both positive a=4 and c=2 then we have (4-2)>0 YES

As per my approach i get B as the answer.

If we have a = 4 and c = 2, then a > c.
Put b = -1.
ab = (4)(-1) = -4
bc = (-1)2 = -2
Then ab < bc since -4 < -2.
The answer is no.
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Re: Is ab>bc?  [#permalink]

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MathRevolution wrote:
Is ab>bc?

1) abc=0
2) a>c

(1+2) Insufficient:

Take (a,b,c) = (1,1,0) <YES>
Take (a,b,c) = (1,0,0) <NO>

The above follows the notations and rationale taught in the GMATH method.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
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Re: Is ab>bc?  [#permalink]

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Avinasht123 wrote:
MathRevolution wrote:
[Math Revolution GMAT math practice question]

Is ab>bc?

1) abc=0
2) a>c

My approach kindly assist me where am i going wrong.

Rephrasing the question

ab>bc
therefore ab-bc>0 or b(a-c)>0 or a>c ( dividing both sides by b )

my question why cant we divide both sides by 'b' to get the equation as : a-c>0
Eg: b(a-c)/b > 0/b :- Now since 0/b =0 and b(a-c)/b cancels out 'b' wont the equation be (a-c)>0

or ab/b>bc/b = a>c

So there is no need for B here.
Stmt 1: ac =0 ( I haven't considered B in this statement as i managed to cancel it as per the above equation )
a=0 or c=0 clearly insufficient.
a-c>0 If a=0 and c=2 then we have (0-2)>0 NO
If a=2 and c=0 then we have (2-0)>0 Yes

Stmt 2: a>c

Without Plugging in values : ab>bc then divide both sides by 'b' to get a>c. Sufficient.

the same is confirmed when plugging in values as well.
If a and c both are negative a=-2 and c=-4 then we have (-2>-4). So -2-(-4)= -2+4>0 YES
If a and c are both positive a=4 and c=2 then we have (4-2)>0 YES

As per my approach i get B as the answer.
Only one thing : don't divide by a variable unless you are sure it is a positive integer and not equal to zero.

Thank you = Kudos
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Thank you =Kudos
The best thing in life lies on the other side of the pain.
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When dividing by a variable is considered, you must consider two cases separately:

First case: you have an EQUATION involved. In this case, you may divide whenever the variable cannot assume the zero value.

Example: $$ab - {b^3}c = d{b^2}\,\,\,\, \Rightarrow \,\,\,\,a - {b^2}c = db$$ IF you can guarantee that b is different from zero.

Second case: you have an INEQUATION involved, that is, an inequality. In this case, you ALSO may divide whenever the variable cannot assume the zero value BUT

(i) if the variable can assume only positive values, the inequality sign is kept.
(ii) if the variable can assume only negative values, the inequality sign is reversed.

(If you cannot control the sign of the variable, you cannot be sure the inequality sign will be kept or reversed.)

Example: $$ab - {b^3}c > d{b^2}\,\,\,\, \Rightarrow \,\,\,\,\left\{ \begin{gathered} a - {b^2}c > db\,\,\,\,\,\,\left( {b > 0} \right) \hfill \\ a - {b^2}c < db\,\,\,\,\,\,\left( {b < 0} \right) \hfill \\ \end{gathered} \right.$$

Please note that it doesn´t matter if the variable takes only integer values or not. This is irrelevant for all the discussion above.

Regards,
fskilnik.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
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Posts: 935

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Thank you for the kudos, Avinasht123 !

If you have any other "conceptual" doubt, please feel free to post it in this forum and send to me a private message, including the link to that post.

I will be happy to help you understand the "theoretical subtleties" (there are many!) that belong to the GMAT content. And, yes, I will always be GMAT-focused, although I love the mathematics that goes far beyond the exam.

May I give you a suggestion? If you are that "rare type" of student who wants to understand the subject deeply, so that an outstanding performance is a "sub-product" of your knowledge and competence, try my method through a complete test drive you will obtain as soon as you register on my site (http://www.gmath.net).

It´s not (just a matter of) business (although I really "earn my living" teaching quant GMAT since 2000): I really believe in the bold statement above. (Yes, bold in the two senses, LoL.)

Success in your studies and in your MBA admission process!
Fabio.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net Is ab>bc?   [#permalink] 27 Aug 2018, 05:31
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