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Is a > a? (1) a^2 > a (2) a/2 > 2/a
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03 Apr 2020, 00:55
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Competition Mode Question Is \(a > a\)? (1) \(a^2 < a\) (2) \(\frac{a}{2}>\frac{2}{a}\) Are You Up For the Challenge: 700 Level Questions
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Re: Is a > a? (1) a^2 > a (2) a/2 > 2/a
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03 Apr 2020, 01:37
Quote: Is a > a? (1) a^2 > a (2) a/2 > 2/a Question: Is a > a? But a > a only if a < 0 i.e. Question REPHRASED: Is a < 0? Statement 1: a^2 > a i.e. a^2  a > 0 i.e. a*(a1) > 0 ie.. a > 1 (NO) or a < 0 (YES) NOT SUFFICIENT Statement 2: a/2 > 2/aif a > 0 then a^2 > 4 i.e. a > 2 if a < 0 then a^2 < 4 i.e. 2 < a < 0 NOT SUFFICIENT COmbining the statementsthe common range of value sis 2 < a < 0 (YES) SUFFICIENT Answer: Option C
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Re: Is a > a? (1) a^2 > a (2) a/2 > 2/a
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03 Apr 2020, 03:02
Is a > a? When can this be true? Only when a is < 0, that is when a is negative. Eg: a=2. 2 > 2? YES (A) \(a^{2}\) < a We know that \(a^{2}\) is always positive. This statement basically tells us that a is a positive decimal. Note that a can't be negative because a negative number cant be greater than a positive number. Therefore, this is sufficient to answer our original question > IS a<0 SUFFICIENT(B) \(a^{2}\) > 4 This is not going to be sufficient. Eg: Let's take \(a^{2}\) to be 16. Therefore, a can be + 4. If a =4 then 4 IS NOT > 4. However, if a = 4, then 4 IS > 4. Hence, APlease give kudos if you found this helpful



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Re: Is a > a? (1) a^2 > a (2) a/2 > 2/a
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03 Apr 2020, 04:17
Quote: Is a > a? (1) a^2 < a (2) a/2 > 2/a a>a, when a<0 (1) sufic a^2a<0 a(a1)<0 0<a<1 (2) insufic a/22/a>0 a^24/2a>0 (a2)(a+2)>0 a>2 or a<2 Ans (A)



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Re: Is a > a? (1) a^2 > a (2) a/2 > 2/a
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03 Apr 2020, 04:17
Q. a > a? In other words, is a < 0 ?
(1) a^2 > a a*(a1) > 0 a<0 or a>1 We don't know which one of the following a<0 (negative) or a>1 is applicable. NOT SUFFICIENT
(2) a/2 > 2/a (a^24)/2a > 0 2<a<0 or a>2 We don't know which one of the following 2<a<0 (negative) or a>2 is applicable. NOT SUFFICIENT
(1)+(2) Superpositioning all possible values of a, we get 2<a<0 (negative) or a>2. HOWEVER, we still don't know which one is applicable: is it 2<a<0 (negative) or a>2 ? NOT SUFFICIENT
FINAL ANSWER IS (E)
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Re: Is a > a? (1) a^2 > a (2) a/2 > 2/a
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03 Apr 2020, 10:47
Is a > a? It is possible only if a < 0 (1) \(a^2 < a\) \(a^2 < a\) \(a^2  a < 0\) a(a1) < 0 0 < a < 1 If a = \(\frac{1}{2}\) \(\frac{1}{2} > \frac{1}{2}\) NO If a = \(\frac{1}{3}\) \(\frac{1}{3} > \frac{1}{3}\) NO SUFFICIENT. (2) \(\frac{a}{2} > \frac{2}{a}\) \(\frac{a}{2} > \frac{2}{a}\) \(\frac{a}{2}  \frac{2}{a}\) > 0 \(\frac{a^2  4}{2a}\) > 0 \(a^2  4 > 0\) \(a^2 > 4\) 2 < x < 2 If a = 1 1 > 1 YES If a = 1 1 > 1 NO INSUFFICIENT. Answer A.
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Re: Is a > a? (1) a^2 > a (2) a/2 > 2/a
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03 Apr 2020, 13:17
from given stmnt we need to determine whether lal>a or say a is ve #1 a2<a a*(a1)<0 a<0 or a<1 i.e 0>a<1 ( a can be ve or fraction from 0 to 1) insufficient #2 a/2>2/a a^24/(2a)>0 (a+2)(a2)/2a>0 possible when either a is 1=a<0 or a >2 insufficient from 1 &2 we get nothing in common IMO E
Is a>a?
(1) a2<a
(2) a/2>2/a



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Re: Is a > a? (1) a^2 > a (2) a/2 > 2/a
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03 Apr 2020, 13:53
The question is asking whether a is negative or not.
1) a^2 < a, this is true for any value between 0 and 1. For any integer value a^2 will be more than a and for values situated in the range 1 <a< 0 also a^2 > a. So a is not negative. Suff. 2) a/2 > 2/a. When a = 3, this is true. Again when a =1, this is also true. Not suff A is the answer



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Re: Is a > a? (1) a^2 > a (2) a/2 > 2/a
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04 Apr 2020, 00:31
Is a > a? (Two cases) (1) Is a > a ?(Null and void case) (11) Is a > a => 2a <0 => a<0 Question becomes Is a<0? Yes? Or Is a>=0? No? (1) a^2< a Let a=1/2 , we have (1/2)^2<1/2 a = +ve here Let a= 2, we have (2)^2 <2 (Not possible) there’s no way a can be negative .: a>0 (Sufficient) Or a <a (Nope!) and a <a —> 2a>0 —> a>0 (Sufficient) (2) a/2 >2/a Let a=8, 8/2 >2/8 a= +ve Let a=1, 1/2 > 2 here a=ve (Not sufficient) A like Actuary Posted from my mobile device
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Re: Is a > a? (1) a^2 > a (2) a/2 > 2/a
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04 Apr 2020, 00:43
Is a>a?
So by asking if the absolute value of a is larger than a what the problem is really asking is if a is negative.
(1) a2<a
This condition tells us that a is not 0, not negative and not positive greater than 1; so a will have to be any value between 0 & 1. By result this tells as that A IS POSITIVE. It is sufficient to find out that a is not smaller than its absolute value. Possible solutions A or D.
(2) a/2>2/a
With the 2nd option we have just to test if it is sufficient by itself, so we have that A has to be positive & larger than 2 OR negative and smaller than 1. As what we seek is to know if it is positive or negative, this question does not provide any more clarity. Not sufficient.
So A is the right answer.
Regards, Pablo



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Re: Is a > a? (1) a^2 > a (2) a/2 > 2/a
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04 Apr 2020, 06:20
Question stem: a>a? this is same as is a < 0?
statement 1: \(a2<a\); \(a(a1)<0\) 0<a<1. this is sufficient as a is always positive.
statement 2: \(\frac{a}{2}>\frac{2}{a}\) \(\frac{a^24}{2a}>0\) \(\frac{(a2)(a+2)}{2a}>0\) a>2 or 2<a<0 a can be positive or negative not sufficient
Ans: A



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Re: Is a > a? (1) a^2 > a (2) a/2 > 2/a
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04 Apr 2020, 07:52
for a>a.......a must be < 0
(1) a^2<a.....this will be satisfied only if 0<a<1.....sufficient to that a not < a.........SUFFICIENT
(2) a/2>2/a.......a>2 and 2<a<0....this is insufficient
OA:A



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Re: Is a > a? (1) a^2 > a (2) a/2 > 2/a
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04 Apr 2020, 09:04
Is a>a?
(1) a2<a
(2) a/2>2/a
stem: a gives positive val,a has to be negative 1) cannot find sign 2) proves a is negative
so b)



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Re: Is a > a? (1) a^2 > a (2) a/2 > 2/a
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05 Apr 2020, 20:05
Is a>aa>a?
ST1: (1) a2<a > Solving we get 0<a<1 > a>0 therefore mod(a) = a .... the question will be false .... hence sufficient
(2) a/2>2/a > Solving we get 2<a<0 OR a>2 > If 2<a<0 then mod(a) > 0 and a is negative Hencethe question will be TRUE ... IF a>2 ... the question will FALSE .... Hence the statement is INSUFICIENT ..
ANS B



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Re: Is a > a? (1) a^2 > a (2) a/2 > 2/a
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05 Apr 2020, 22:42
Is \(a>a? \) > \(a < 0 \)???
(Statement1): \(a^{2} < a\) \(a (a1) <0\) \(0 < a < 1\) Always NO Sufficient (Statement2): \(\frac{a}{2} >\frac{2}{a}\) \(\frac{(a^{2}4 )}{2a} >0\) \(\frac{(a2)(a+2)}{2a} > 0\) > \(2 <a < 0\) > \(a >2 \) Insufficient
Answer(A)



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Re: Is a > a? (1) a^2 > a (2) a/2 > 2/a
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05 Apr 2020, 23:31
The general question can be rephrased into "Is a<0 ?" (1) a^2<a => a(a1)<0 => 0<a<1 The answer is NO (sufficient) (2) a/2>2/a => a/22/a>0 => (a^24)/2a>0 => (a2)(a+2)/2a>0 => 2<a<0 The answer is YES (sufficient) Hence: D
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Is a > a? (1) a^2 > a (2) a/2 > 2/a
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05 Apr 2020, 23:43
Sir, please with your statement ( 2) cross multiplication of inequalities is not allowed ,we don’t even know the sign of (a) GMATinsight wrote: Quote: Is a > a? (1) a^2 > a (2) a/2 > 2/a Question: Is a > a? But a > a only if a < 0 i.e. Question REPHRASED: Is a < 0? Statement 1: a^2 > a i.e. a^2  a > 0 i.e. a*(a1) > 0 ie.. a > 1 (NO) or a < 0 (YES) NOT SUFFICIENT Statement 2: a/2 > 2/aif a > 0 then a^2 > 4 i.e. a > 2 if a < 0 then a^2 < 4 i.e. 2 < a < 0 NOT SUFFICIENT COmbining the statementsthe common range of value sis 2 < a < 0 (YES) SUFFICIENT Answer: Option C Posted from my mobile device
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Is a > a? (1) a^2 > a (2) a/2 > 2/a
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