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# For real numbers a, b, and c, is ab = bc + 3?

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Math Expert
Joined: 02 Sep 2009
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For real numbers a, b, and c, is ab = bc + 3? [#permalink]

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23 Aug 2016, 08:10
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59% (01:53) correct 41% (02:08) wrong based on 80 sessions

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For real numbers a, b, and c, is ab = bc + 3?

(1) ab = 3b
(2) b + 3 = c
[Reveal] Spoiler: OA

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Kudos [?]: 135519 [2], given: 12697

Intern
Joined: 18 Aug 2013
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Kudos [?]: 6 [0], given: 234

Re: For real numbers a, b, and c, is ab = bc + 3? [#permalink]

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23 Aug 2016, 09:47
(1) ab = 3b => It gives no information about 'c' --> Insufficient

(2) b + 3 = c => It gives no information about 'a' --> Insufficient

Both (1) and (2) together .. Lets substitute these two conditions (1) and (2) in the main eqn (to be proved)

ab = b.(b+3) + 3 = b^2 + 3b + 3

3b = b^2 + 3b + 3 => b^2 = -3 --> For this eqn to be equal, 'b' should be imaginary.

But, we are given that a, b and c are real numbers => These numbers cannot be imaginary ..

Hence, b^ 2 = -3 CANNOT be true for any values of a,b and c.. Option (C)

Kudos [?]: 6 [0], given: 234

Senior Manager
Joined: 23 Apr 2015
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Location: United States
WE: Engineering (Consulting)
Re: For real numbers a, b, and c, is ab = bc + 3? [#permalink]

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23 Aug 2016, 09:55
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Bunuel wrote:
For real numbers a, b, and c, is ab = bc + 3?

(1) ab = 3b
(2) b + 3 = c

Consider 1) $$ab = 3b$$
there are 2 possibilities, $$b = 0$$ or $$b\neq{0}$$ which means $$a = 3$$ or $$a\neq{3}$$ and also $$c$$ is not known.
Not Sufficient , Eliminate A and D

Consider 2) $$b + 3 = c$$
Substituting on the given equation: $$ab = b(b+3) + 3 = b^2 + 3b + 3$$ . Still $$a$$ and $$b$$ are not known.
Not Sufficient , Eliminate B

Consider 1) and 2) together (include that 1) has 2 possibilities based on $$b = 0$$ and $$b\neq{0}$$)
when $$b = 0$$, then $$c=3$$and $$ab = bc +3$$ becomes $$0 = 0 + 3$$ and Hence FAILS
when $$b\neq{0}$$, then $$a = 3$$ and $$ab = bc + 3$$ becomes $$3b = b(b+3) + 3=> b^2 = -3$$
giving values for b which are not real and the Hence Fails,

so answer is C, since when 1) and 2) considered together, the equality FAILS.

PS: this took more than 2 mins, anyone with faster approach please.

+1 for kudos.

Kudos [?]: 118 [2], given: 36

Intern
Joined: 27 Apr 2016
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GPA: 3.5
WE: Information Technology (Computer Software)
Re: For real numbers a, b, and c, is ab = bc + 3? [#permalink]

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03 Sep 2016, 06:35
C is the correct option: Below is the solution

Statement 1: ab=3b i.e b(a-3)=0 . Either b=0 or a=3 : We leave this, as no solution we get
Statement 2: b+3=c No info about anything else, so leave this too

Combining both 1 & 2

If we take b=0 , then c=3 according to statement 2 .
Try inputting this in ab= bc+3 . 0 is not equal to 3 Therefore ruled out

Now take a=3 and b+3 =c
Input these in ab=bc+3 ; b(a-c)=3 ; (c-3)(3-b-3) =3 ; -bc+3b =3 ; b(3-c)=3 : This matches the required where 3=a.

Hence combining the statements gave the answer .

Therefore Option C :D

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Re: For real numbers a, b, and c, is ab = bc + 3? [#permalink]

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19 Oct 2017, 20:10
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: For real numbers a, b, and c, is ab = bc + 3?   [#permalink] 19 Oct 2017, 20:10
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