Is it (a² - b) or a(a - b)?koby_gen wrote:Is 2a < a x a - b ?
(1) 0 < a < 2
(2) -2 < b < 0
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Inequalities
Source: Beat The GMAT — Data Sufficiency |
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Anurag@Gurome
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smackmartine
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I go for E
2a<a^2 -b
1) Insufficient as we do n't have values for b
2) Insufficient as we do n't have values for a
combining 1) and 2)
if a=1 and b= -1
2< 1-(-1) ---> 2<2 ( cannot happen) so--> NO
if a=1 and b= -1.5
2< 1-(-1.5) --> 2< 2.5 ---> Yes
As we can prove both Yes and No , so answer should be E
2a<a^2 -b
1) Insufficient as we do n't have values for b
2) Insufficient as we do n't have values for a
combining 1) and 2)
if a=1 and b= -1
2< 1-(-1) ---> 2<2 ( cannot happen) so--> NO
if a=1 and b= -1.5
2< 1-(-1.5) --> 2< 2.5 ---> Yes
As we can prove both Yes and No , so answer should be E
(a² - b)Anurag@Gurome wrote:Is it (a² - b) or a(a - b)?koby_gen wrote:Is 2a < a x a - b ?
(1) 0 < a < 2
(2) -2 < b < 0
Thanks
I'm getting E.
Statement asks if 2a < a^2 - b. You could rephrase as 2a < (a + b)(a - b) if you want.
Statement 1: Tells nothing about the value of B. Insufficient.
Statement 2: Tells nothing about the value of A. Insufficient.
Combined, we could plug in a = 1 and b = -1. 2(1) < 1^2 - (-1). In this case, 2 = 2, and the answer to the initial question is NO. However, we could also plug in a = 1/2 and b = -1, in which case 2(1/2) < 1^2 -(-1) = 1 < 2, in which case the answer to the question is YES.
Thus, INSUFFICIENT.
Statement asks if 2a < a^2 - b. You could rephrase as 2a < (a + b)(a - b) if you want.
Statement 1: Tells nothing about the value of B. Insufficient.
Statement 2: Tells nothing about the value of A. Insufficient.
Combined, we could plug in a = 1 and b = -1. 2(1) < 1^2 - (-1). In this case, 2 = 2, and the answer to the initial question is NO. However, we could also plug in a = 1/2 and b = -1, in which case 2(1/2) < 1^2 -(-1) = 1 < 2, in which case the answer to the question is YES.
Thus, INSUFFICIENT.
Consider f(a) = a²-2a-b
the minimum value is for a=1, f(1)=-1-b, knowing the sign of -1-b will give the answer
1) 0<a<2 ----> not help to know the sign of -1-b
2) -2<b<0 ----> -1<-1-b<1, -1-b could be both sign, Hence NOT SUFF
1&2-----> NOT SUFF
Answer is E
the minimum value is for a=1, f(1)=-1-b, knowing the sign of -1-b will give the answer
1) 0<a<2 ----> not help to know the sign of -1-b
2) -2<b<0 ----> -1<-1-b<1, -1-b could be both sign, Hence NOT SUFF
1&2-----> NOT SUFF
Answer is E
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prachich1987
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Hi Anurag,Anurag@Gurome wrote:Is it (a² - b) or a(a - b)?koby_gen wrote:Is 2a < a x a - b ?
(1) 0 < a < 2
(2) -2 < b < 0
is there any other approach apart from "putting values" for inequality questions?
Thanks!
Prachi
Prachi
1. 0< a< 2 ; this mean that " a" is +ve so a can be 0.5, 1, 1.5 or 1.9, however no "b" info. therefore INSUFF.
2. -2 < b<0 ; b is -ve, "'b" can be -1.5,-1,-0.5 , no "a" info, so INSUFF.
Combining (1) &(2)
2a < a x a - b ?
a = 0.5, b = -0.5
1<0.25 + 0.5 ;
a = 0.5, b = -1
1 < 0.25 +1 ..... different result from above.
So E is the answer.
2. -2 < b<0 ; b is -ve, "'b" can be -1.5,-1,-0.5 , no "a" info, so INSUFF.
Combining (1) &(2)
2a < a x a - b ?
a = 0.5, b = -0.5
1<0.25 + 0.5 ;
a = 0.5, b = -1
1 < 0.25 +1 ..... different result from above.
So E is the answer.
