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Is a < b? (1) a^3 = ab (2) |b| > |a|

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Is a < b? (1) a^3 = ab (2) |b| > |a|  [#permalink]

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New post 14 Jun 2018, 21:07
2
7
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

40% (01:58) correct 60% (01:37) wrong based on 129 sessions

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Re: Is a < b? (1) a^3 = ab (2) |b| > |a|  [#permalink]

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New post 14 Jun 2018, 21:23
OA - E

Statement 1: a^3 = ab

If a = +ve then b should be +ve. And many values will satisfy this condition. For ex a = 2 and b = 4. In this case a < b.

If a = -ve then b should be positive. Again many values would satisfy this condition. For ex a = -2 and b = 4. In this case too a < b.

But if a = 0, then B can be any value. b = -1 or 1. In one case a>b and in other case a < b. No clear solution.

Statement 2: |b| > |a|

Lets take two values. a = -2 and b = -3. Since in mod b would be greater than a; however a is greater than b.
if a = 2 and b = 3, then b is greater than a. No clear solution.

Combining both.

If a = 0. Then b could be any value. Could be 2 or -2.
For positive value of b it'd be greater than a
but for negative value of b it'd be lesser than a.
Hence no clear solution even after combining.
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Re: Is a < b? (1) a^3 = ab (2) |b| > |a|  [#permalink]

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New post 14 Jun 2018, 22:08

Solution



To find:
    • Whether a < b?

Analysing Statement 1
    • As per the information given in statement 1, a^3 = ab
      o Or, a^3 – ab = 0
      Or, a (a^2 – b) = 0

    • Now, if we assume a = 0, in that case b can be either > 0 or < 0 or = 0
    • As all the possibilities exist for b, we can’t say whether a < b

Hence, statement 1 is not sufficient to answer

Analysing Statement 2
    • As per the information given in statement 2, |b| > |a|
    • If we assume a = 0, then for any negative or positive value of b, |b| > |a|
    • As b can be both positive or negative compared to a = 0, we can’t say whether a < b

Hence, statement 2 is not sufficient to answer

Combining Both Statements
Considering the combined data available in both the statements, we can write
    • For a = 0, b can have either positive or negative value
    • Therefore, we can’t say whether a < b

Hence, the correct answer is option E.

Answer: E
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Re: Is a < b? (1) a^3 = ab (2) |b| > |a|  [#permalink]

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New post 15 Jun 2018, 02:49
1
it should be e

from 1st st. a can be 0 or a square can be equal to b
from 2nd, b can either be less than a or more than a
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Re: Is a < b? (1) a^3 = ab (2) |b| > |a|  [#permalink]

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New post 15 Jun 2018, 05:53
Bunuel wrote:
Is a < b?

(1) a^3 = ab

(2) |b| > |a|


Source: 4Gmat


1) a^3=ab...
a(a^2-b)=0
So either a=0 or a^2=b or both are 0
Insufficient
2) |b|>|a|
So if b>0, yes a<b
If b<0, no
Insufficient

Combined..
We still can't say if b is positive or negative but b is not equal to 0..
Insufficient
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Re: Is a < b? (1) a^3 = ab (2) |b| > |a|  [#permalink]

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New post 20 Jun 2018, 04:37
Answer would be E , I think.
a^3 = ab
a^2 = b

as bcz square can't be negative so b must be positive.
but a can be positve or negative so we can't decide. ( for taking 1 a can be equal to b or by taking any number b is always greater than a . )

| b | > | a |

b > a ( when taking + ve)

or

-b > -a ( when taking -ve )
b < a so we can't decide.
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Re: Is a < b? (1) a^3 = ab (2) |b| > |a|  [#permalink]

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New post 04 Mar 2019, 00:45
Bunuel wrote:
Is a < b?

(1) a^3 = ab

(2) |b| > |a|


Source: 4Gmat


#1
a^3=ab
or say
a^2=b
now a= +/-2 and b=4
in sufficient
#2
|b| > |a|
we can have +/- values of b so in sufficient to conclude that b>a

from 1& 2
we cannot derive anything in common to conclude b>a
IMO E
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Re: Is a < b? (1) a^3 = ab (2) |b| > |a|   [#permalink] 04 Mar 2019, 00:45
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