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Is b < a^2 ? (1) b < a (2) b = −2

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Bunuel
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Is b < a^2 ? (1) b < a (2) b = −2 [#permalink] New post   12 Aug 2020, 01:51
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A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

54% (01:07) correct 46% (01:20) wrong based on 93 sessions
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Is b < a^2 ?

(1) b < a
(2) b = −2


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B
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Re: Is b < a^2 ? (1) b < a (2) b = −2 [#permalink] New post   12 Aug 2020, 01:57
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To find: b < a^2

1) b<a
Case 1, B is negative A is positive
B < a^2 (correct)

Case 2, B and A are fraction.
B = 1/4 and A = 1/3
But B > a^2 (Incorrect)
(Invalid)

2) B is negative,
A^2 will be positive.
B<A^2
(Sufficient)

IMO B

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Re: Is b < a^2 ? (1) b < a (2) b = −2 [#permalink] New post   12 Aug 2020, 02:36
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Question: b<a^2

Statement 1: b<a
Case1: b=1 a =2
a^2 = 4
Yes, sufficient
Case2: b=1/3 a=1/2
a^2 = 1/4
No, Not sufficient

Statement2: b=-2
a can be any value 0,1,-2,-1,...
a^2 will be positive always because it is squared

Sufficient

Answer - B
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Re: Is b < a^2 ? (1) b < a (2) b = −2 [#permalink] New post   12 Aug 2020, 02:41
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Bunuel wrote:
Is b < a^2 ?

(1) b < a
(2) b = −2

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IMO B is the correct answer.

(1) We can solve this question by taking example.
If b < 1 and a < 1, for example b = 1/3, a = 1/2. Since a^2 = 1/4 < 1/3 then b > a^2

If b >1 and a > 1, for example b = 2, a = 3. Since a^2 = 9 > 3 then b < a^2

Therefore (1) is INSUFFICIENT.

(2) Since b = -2 < 0 <= a^2 then we can conclude that b < a^2.
Therefore (2) is SUFFICIENT.
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Re: Is b < a^2 ? (1) b < a (2) b = −2 [#permalink] New post   12 Aug 2020, 03:30
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Expert Reply
Bunuel wrote:
Is b < a^2 ?

(1) b < a
(2) b = −2



Solution


Step 1: Analyse Question Stem


    • We need to find if \(b < a^2\)

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


Statement 1: b < a
    • According to this statement, there can be multiple cases, for example, consider the following two cases:
      o Case 1: a = -2 and b = -4, here -4 < -2 i.e. b < a
         Now, \(a^2 = 4\), which is greater than -4
         So, in this case, \(b < a^2\)
      o Case 2: a = 0.5 and b = 0.4, here 0.4 < 0.5 i.e. b < a
         Now, \(a^2 = 0.25\), which is less than 0.4
         So, in this case \( b > a^2\)
    • We are getting contradictory results from the above two cases.
Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D.

Statement 2: b = -2
    • We know that \(a^2\) can be either positive or 0, while b is negative.
      o Therefore, \(b < a^2\)
Hence statement 2 is sufficient.
Thus, the correct answer is Option B.
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Re: Is b < a^2 ? (1) b < a (2) b = −2 [#permalink] New post   12 Aug 2020, 21:57
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Is b < a^2?

Statements:

(1) b<a

b<a^2 for all a greater than 1. But for 0-1, that might not be the case.

Eg. a = 1/3, b= 1/4
But a^2 = 1/9 < b.

Insufficient

(2) b = -2
a^2 is >=0. ALWAYS.

Since b=-2 is negative, a^2 will always be greater than b.

Sufficient

Hence, the answer is Option (B).
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Re: Is b < a^2 ? (1) b < a (2) b = −2 [#permalink]
12 Aug 2020, 21:57
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Bunuel
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