If a^2=b, is the value of a between 0 and 1?

If a = -0.5, b =0.25
a = 0.5 , b = 0.25 ...

Well MY reaction after reading your post ....

I will edit my response...!

This graph helped me understand this question:



You can clearly see b as the red diagonal and a^{2} as the blue curve

(1) b is between 0 and 1
You can see that where the red line is between 0 and 1, the blue curve is between -1 and 1

(2) a > b
You can see the only portion of the graph where the red line is above the blue curve is between 0 and 1

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.

If a^2=b, is the value of a between 0 and 1?

(1) b is between 0 and 1
(2) a>b


There is nothing to transform in the original condition and the question. WE have 2 variable (a,b) and 1 equation (a^2=b), thus we need 1 more to match the number of variables and equations. Since there is 1 each in 1) and 2), D is likely the answer.

In case of 1), if b=0.04 then the answer is no if a=-0.2 and yes if a=0.2 Thus it is not sufficient.
In case of 2), a>b=a^2, a>a^2, 0>a^2-a, 0>a(a-1), 0<a<1, therefore the answer is yes.
Thus the answer is B.

Is 1>a>0 ?

1) 1>b>0
\(a^2\) = b
a > 0 or a < 0
a = \(\frac{1}{2}\) , b = \(\frac{1}{4}\) Yes
a = \(\frac{-1}{2}\) , b = \(\frac{1}{4}\) No
Insufficient.

2) a>b
This basically means a cannot be less than 0.
and since \(a^2\) = b
=> a > \(a^2\)
=> 1>a>0
B is sufficient.

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