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

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

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Question Stats:

59% (01:53) correct 41% (02:08) wrong based on 80 sessions

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

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New post 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)

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

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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.




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

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New post 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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New post 19 Oct 2017, 20:10
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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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