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If |a| = b, is a+b > ab (1) a = -b (2) a = -3

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Bunuel
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If |a| = b, is a+b > ab (1) a = -b (2) a = -3 [#permalink] New post   04 Aug 2020, 00:27
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If |a| = b, is a+b > ab

(1) a = -b

(2) a = -3



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B
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Re: If |a| = b, is a+b > ab (1) a = -b (2) a = -3 [#permalink] New post   04 Aug 2020, 00:54
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I think (B) is the right answer.

Let's talk about (A):
Here we can take the value of 'a' to be '0' too. So, that makes (A) insufficient since we cannot say a definitive 'Yes' or 'No'
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Re: If |a| = b, is a+b > ab (1) a = -b (2) a = -3 [#permalink] New post   04 Aug 2020, 00:57
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Given: |a| = b,
To find: is a+b > ab

(1) a = -b
Case 1 : A = 0
B = 0
0+0 = 0*0 (Wrong)

Case 2: A = -2
B = 2
-2+2 > -2*+2
0>-4 (correct)
Insufficient

(2) a = -3
B = 3 (|-3| = 3)
-3+3 > -3*+3
0 > -9
Sufficient

IMO B

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Re: If |a| = b, is a+b > ab (1) a = -b (2) a = -3 [#permalink] New post   04 Aug 2020, 02:12
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Bunuel wrote:
If |a| = b, is a+b > ab

(1) a = -b

(2) a = -3


Solution


Step 1: Analyse Question Stem


    • |a| = b
      o This means b is a non-negative number.
    • We need to find the value of a+b > ab

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE


Statement 1: a = -b
    • Since, b is a non-negative number, so there can be two cases:
      o Case 1: b = 0
         In that case, a = 0,
         So, a+b = 0 and a*b = 0
         Here, a+b = a*b
      o Case 1: b is positive
         In that case, a is negative, and a = -b
         So, a+b = 0 and a*b = -\(b^2\)
         Here, a+b > a*b,
    • We are getting contradictory results.
Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D.

Statement 2: a = -3
    • So, b = |-3| = 3
      o This means, a+b = 3 – 3 = 0, and a*b = -9
      o Therefore, a+b > a*b
Hence, statement 2 is sufficient.
Thus, the correct answer is Option B.
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Re: If |a| = b, is a+b > ab (1) a = -b (2) a = -3 [#permalink] New post   04 Aug 2020, 20:07
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Bunuel wrote:
If |a| = b, is a+b > ab

(1) a = -b

(2) a = -3


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Statement 1:
We can plug in to get "is \(0 > -b^2\) ?" is the question. Simplify one more step we would be asking "is \(b^2 > 0\) ?". This is always true UNLESS b = 0, which is possible. Then this is insufficient as we might have that case.

Statement 2:
If a = -3 then we must have b = |-3| = 3. We know both values of a and b now so it must be sufficient.

Ans: B
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Re: If |a| = b, is a+b > ab (1) a = -b (2) a = -3 [#permalink] New post   05 Aug 2020, 00:05
|a| = b (given)
Is a+b>ab?

Statements:

(1) a=-b
a+b>ab for all cases except b=0
Insufficient

(2) a = -3
Therefore, b = 3
ab = -9
a+b = 0 > -9
Sufficient

Answer is Option (B)
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Re: If |a| = b, is a+b > ab (1) a = -b (2) a = -3 [#permalink] New post   05 May 2023, 07:16
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Re: If |a| = b, is a+b > ab (1) a = -b (2) a = -3 [#permalink]
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