Is |a| a? (1) a^2 a (2) a/2 2/a

Question

Competition Mode Question

Is  |a| > a ?

(1)  a^2 < a

(2)  \frac{a}{2}>\frac{2}{a}

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YashKothari94 · Accepted Answer

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, A

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GMATinsight · Answer

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*(a-1) > 0 ie.. a > 1 (NO) or a < 0 (YES) NOT SUFFICIENT Statement 2 : a/2 > 2/a if 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 statements the common range of value sis -2 < a < 0 (YES) SUFFICIENT Answer: Option C

freedom128 · Answer

Q. |a| > a?
In other words, is a < 0 ?

(1) a^2 > a
a*(a-1) > 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^2-4)/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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unraveled · Answer

Is |a| > a?
It is possible only if a < 0

(1) \(a^2 < a\)
\(a^2 < a\)
\(a^2 - a < 0\)
a(a-1) < 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.

minustark · Answer

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

Staphyk · Answer

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

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pabpinor · Answer

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

ArunSharma12 · Answer

Question stem: |a|>a? this is same as is a < 0? statement 1: a2\frac{2}{a} \frac{a^2-4}{2a}>0 \frac{(a-2)(a+2)}{2a}>0 a>2 or -2

lacktutor · Answer

Is |a|>a? --> a < 0 ??? (Statement1) : a^{2} < a a (a-1) <0 0 < a < 1 Always NO Sufficient ( Statement2 ): \frac{a}{2} >\frac{2}{a} \frac{(a^{2}-4 )}{2a} >0 \frac{(a-2)(a+2)}{2a} > 0 --> -2 a >2 Insufficient Answer(A)

AnkithaSrinivas · Answer

chetan2u , in option B

we get 
a/2 - 2/a >0

a power 2 -4 / 2a >0
 since numerator is greater than 0 -> denominator is greater than 0 too

Please help

chetan2u · Answer

\frac{a^2-4}{2a}

numerator is not positive always .

When a is 1,  a^2-4=1-4=-3

lavanya.18 · Answer

These type of questions don't come in GMAT Focus DS questions, right?

Bunuel · Answer

Not anymore.

Pure algebraic questions are no longer a part of the  DS syllabus  of the GMAT.

DS questions in GMAT Focus encompass various types of word problems, such as:

Word Problems 
 Work Problems 
 Distance Problems 
 Mixture Problems 
 Percent and Interest Problems 
 Overlapping Sets Problems 
 Statistics Problems 
 Combination and Probability Problems

While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."

Check  GMAT Syllabus for Focus Edition

You can also visit the  Data Sufficiency forum  and filter questions by  OG 2024-2025, GMAT Prep (Focus), and Data Insights Review 2024-2025 sources  to see the types of questions currently tested on the GMAT.

Hope it helps.

Is |a| > a? (1) a^2 > a (2) a/2 > 2/a

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