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

Question

Is |a| > a?

(1) a^2 < a
(2) (a/2) > (2/a)

chetan2u · Answer

HI,
A good Q testing our concepts on MOD and Inequalities..

lets see the INFO from Q

Is|a|>a?..
a can be -ive,0 or positive..
when a is positive, |a|=a, so |a| cannot be >a..
when a=0, both sides again will be 0 and equal..
when a is -ive, |a| is -a and will be positive and thus |a|>a..

we are asked about the THIRD scenario, so we have to find if a is -ive...

lets see the statements

(1) a^2 < a
a^2-a<0..
a(a-1)<0..
if a is negative, a(a-1) will become product of two -ive numbers and thus will be +ive..
so the answer is NO for "is |a|>a?"
Suff

(2) (a/2) > (2/a)
\((\frac{a}{2}) - (\frac{2}{a}) > 0\)..
\(\frac{(a^2-4)}{2a}>0\)..
this means both (a^2-4) and 2a are of same sign..
if a is -ive 2a will be negative, and a^2-4 will be negative with a between 0 and -2... SO -ive value possible
if a is +ive 2a will be +ive, and a^2-4 will be +ive with a >2.. SO +ive value possible
Different solutions possible
Insuff

ans A

rohit8865 · Answer

question basically asking for whether a is negative?? becoz then only I-2I>-2(let a=-2)---------->2>-2 (1) a^2=0 then 0=a^2 2/a (a/2)-(2/a)>0 (a+2)(a-2)/2a>0 sol. range will be -22 so a could be -ve or +ve insuff.. Ans A

RastogiSarthak99 · Answer

is |a| > a?

so |a| will always be positive, but here magnitutde of a is important.

--> St 1 says a^2 < a

so a^2 is always positive, and a^2 < a meaning a is always +ve
use a number
a = 0.5, a^2= 0.25

Test out main equation: |0.5| < 0.5
This is a def no.

--> St 2
a/2>2/a

simplifying it we get a^2>2
use a number a^2 = 4. a = +- 2
|-2| < 2 Yes
|2| < 2 No
In suff

A

SaquibHGMATWhiz · Answer

Solution: Pre Analysis: We are asked if |a| > a or not Which is true only when a is negative and not when it is positive or 0 Thus, we are asked if a is negative number or not Statement 1: a^2 < a a^2 < a is true for the 2nd region of the number line which is 0 \frac{2}{a} ⇒\frac{a^2-4}{2a}>0 2 cases possible: Case 1: both a^2-4<0 and 2a<0 which is true when -20 and 2a>0 which is true when a>2 which means a is positive Thus, statement 2 alone is not sufficient Hence the right answer is Option A

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

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