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Is (A/B)^3 < (AB)^3 ? (1) A > 0 (2) AB > 0
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11 Sep 2019, 21:10
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Competition Mode Question Is \((\frac{A}{B})^3 < (AB)^3\) ? (1) \(A > 0\) (2) \(AB > 0\)
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Re: Is (A/B)^3 < (AB)^3 ? (1) A > 0 (2) AB > 0
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Updated on: 11 Sep 2019, 22:08
IMO answer is option E (If the questions mentioned A and B are integers, then answer would have been option B) Posted from my mobile device
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Originally posted by EncounterGMAT on 11 Sep 2019, 21:23.
Last edited by EncounterGMAT on 11 Sep 2019, 22:08, edited 2 times in total.



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Re: Is (A/B)^3 < (AB)^3 ? (1) A > 0 (2) AB > 0
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11 Sep 2019, 21:46
Statement 1 is insufficient since we know nothing about B. When A=3; and b=2 (A/B)^3= 27/8 > (AB)^3=216 When A=3 and B=2, (AB)^3 > (A/B)^3
2 is also insufficient bcos AB>0 means either both A and B are greater than 0 or both A and B are negative. When A=3 and B=2, (AB)^3 > (A/B)^3 When A=3 and B=1/2, (A/B)^3 > (AB)^3 Hence insufficient.
1+2 is still insufficient. Because we know A and B must be positive in order for both conditions to be satisfied. Meanwhile, when A=3 and B=2, as we saw already, (AB)^3 > (A/B)^3 However when A=3 and B=1/2, (A/B)^3 > (AB)^3
Hence the answer is E.
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Re: Is (A/B)^3 < (AB)^3 ? (1) A > 0 (2) AB > 0
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11 Sep 2019, 23:56
is (A/B)^3 < (AB)^3 ?
STATEMENT (1) A > 0 but we don't have any information about B if A = 4 B =\(\frac{1}{4}\) then (A/B)^3 > (AB)^3is (A/B)^3 < (AB)^3 ? NO
if A = 4 B = \(\frac{1}{4}\) then (A/B)^3 < (AB)^3is (A/B)^3 < (AB)^3 ? YES
from here we can't get a definite answer so, INSUFFICIENT
STATEMENT (2) AB > 0 from here we know A and B are either positive or negative if A = 4 B = \(\frac{1}{4}\) then (A/B)^3 > (AB)^3is (A/B)^3 < (AB)^3 ? NO
if A = 4 B = 2 then (A/B)^3 < (AB)^3is (A/B)^3 < (AB)^3 ? YES
from here we can't get a definite answer so, INSUFFICIENT
combining both statements together we know AB>0 and A>0 this tells us B>0
if A = 4 B = \(\frac{1}{4}\) then (A/B)^3 > (AB)^3is (A/B)^3 < (AB)^3 ? NO
if A = 4 B = 2 then (A/B)^3 < (AB)^3is (A/B)^3 < (AB)^3 ? YES
from here we can't get a definite answer so, INSUFFICIENT
E is the correct answer



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Re: Is (A/B)^3 < (AB)^3 ? (1) A > 0 (2) AB > 0
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12 Sep 2019, 00:04
(A/B)^3 < (AB)^3 ?
(1) A>0 Let's A = 1, B = 2; insert A,B value, we've got 1/8 < 8. NO But A = 1, B = 2; 1/8 < 8. Yes
So, A is sufficient
(2) AB>0 Let's A = 1, B = 2; insert A,B value, we've got 1/8 < 8. Yes But A = 2, B = 1; 8 < 8 No. So, 2 alone is not suffcient
(1) + (2); A>0 and AB >0, thus both A,B > 0 If A = 1, B =2; 1/8 < 8 Yes. If A =2 , B =1 ; 8 < 8 No.
Not sufficient. Therefore E is the answer



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Re: Is (A/B)^3 < (AB)^3 ? (1) A > 0 (2) AB > 0
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12 Sep 2019, 00:19
Is \((\frac{A}{B})^3 < (AB)^3\) ? No relation between A and B is given so many possibilities exist. (1) \(A > 0\) Here either \(B > A\) for both integer value and noninteger value of positive B. Example: Let A = 2 & B = 3 then \((\frac{2}{3})^3 < (2*3)^3\) YES OR \(A > B\) for either positive value of B or negative value of B. Example: Let A = 2 & B = 1 then \((\frac{2}{1})^3 < (2*1)^3\) NO INSUFFICIENT. (2) \(AB > 0\) Two cases are possible here: (a) Both A and B are +ve Take A = 2 & B = 3 then \((\frac{2}{3})^3 < (2*3)^3\) YES (b) Both A and B are ve Take \(A = \frac{1}{2}\) & \(B = \frac{1}{3}\) then \(((\frac{1}{2})/(\frac{1}{3}))^3 < ((\frac{1}{2})*(\frac{1}{3}))^3\) NO INSUFFICIENT. Together 1) and 2) We have \(A > 0\) and \(B > 0\) Again Take A = a2 & B = 3 then \((\frac{2}{3})^3 < (2*3)^3\) YES And Take \(A = \frac{1}{2}\) & \(B = \frac{1}{3}\) then \(((\frac{1}{2}/\frac{1}{3})^3 < ((\frac{1}{2})*(\frac{1}{3}))^3\) NO INSUFFICIENT. Answer (E).
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Re: Is (A/B)^3 < (AB)^3 ? (1) A > 0 (2) AB > 0
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12 Sep 2019, 00:54
Is \((\frac{A}{B})^{3}<(AB)^{3}\)?
\(A^{3}(B^{3}(\frac{1}{B})^{3}\))>0
\(A^{3}*(B\frac{1}{B})*(B^{2}+B*\frac{1}{B}+(\frac{1}{B})^{2}\))>0
\((B^{2}+B*\frac{1}{B}+(\frac{1}{B})^{2}\)) is always greater than zero. > \(A^{3}*(B\frac{1}{B})\)>0 ??? (1) A > 0
(2) AB > 0
Statement1: A > 0 > (B\(\frac{1}{B}\))>0 ???
If B=2, then 2\(\frac{1}{2}\)>0 (Yes) If B=\(\frac{1}{2}\), then \(\frac{1}{2}\)2>0 (NO)
Insufficient.
Statement2: AB > 0 > Both A and B are Positive or Negative: \(A^{3}*(B\frac{1}{B})\)>0
if A=B=2, then > \(2^{3}(2\frac{1}{2})\)>0 (yes) if A=B=\(\frac{1}{2}\), then > \((\frac{1}{2})^{3}(\frac{1}{2}2)\)>0 (NO)
Insufficient.
Taken together 1 and 2, A>0 and AB>0 > B>0.
\(A^{3}*(B\frac{1}{B})\)>0 > (B\(\frac{1}{B}\))>0 ???
if B=2, then > (2\(\frac{1}{2}\))>0 (yes) if B=\(\frac{1}{2}\), then >(\(\frac{1}{2}\)2)>0 (NO)
Insufficient
The answer is E.



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Re: Is (A/B)^3 < (AB)^3 ? (1) A > 0 (2) AB > 0
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12 Sep 2019, 02:28
#1 A>0 so A is +ve but no relation of B with A insufficient #2 AB>0 so either both AB are +ve or ve also they can be same value /integer/ fraction no given info insufficient from 1 &2 we can say that AB are +ve but whether A=B ; A>B or B<A cannot be determined IMO E
Is(AB)3<(AB)3 ?
(1) A>0
(2) AB>0



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Re: Is (A/B)^3 < (AB)^3 ? (1) A > 0 (2) AB > 0
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12 Sep 2019, 03:34
IMO it's E. Because even after combining if we take A=100 and B=1 then NO is the answer. And if A=100 and B=2 then YES is the answer.
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Re: Is (A/B)^3 < (AB)^3 ? (1) A > 0 (2) AB > 0
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12 Sep 2019, 04:32
Quote: Is \((A/B)^3<(AB)^3\)?
(1) A>0 (2) AB>0 rephrase: \((A/B)^3<(AB)^3…A/B<AB…A/B<AB\); Is \(A/B<AB\)? case 1: \(A,B=(1,2)…A/B<AB…1/2<2:true\) case 2: \(A,B=(10,1)…A/B<AB…10<10:false\) (1) A>0: case 1 and 2, insufi. (2) AB>0: case 1 and 2, insufi. (1&2) A,B>0: case 1 and 2, insufi. Answer (E)



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Re: Is (A/B)^3 < (AB)^3 ? (1) A > 0 (2) AB > 0
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12 Sep 2019, 07:35
Is (A/B)^3 <(AB)^3 ?
(1) A>0 if A>0, then \((A/B)^3<(AB)^3\) \(A^3/B^3<A^3*B^3\) \(1/B^3<B^3\) if B = 1, \(1/1^3<1^3\) is not possible if B = 2, \(1/2^3<2^3\) is possible so, no unique answer
(2) AB>0 A>0 & B>0 (I) or A<0 & B<0 (II) condition (I) is same as (1), so no unique answer we don't have to check condition (II)
(1) & (2) A>0 (from 1), so B>0 again no unique solution if we take B = 1 or 2 So, answer is E




Re: Is (A/B)^3 < (AB)^3 ? (1) A > 0 (2) AB > 0
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