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

Question

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

Bunuel · Accepted Answer

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

\(a^2=b\) --> \(a=-\sqrt{b}\) or \(a=\sqrt{b}\).

(1) b is between 0 and 1. If \(b=\frac{1}{4}\), then \(a\) could be \(-\frac{1}{2}\) (answer NO) or \(\frac{1}{2}\) (answer YES). Not sufficient.

(2) a>b --> \(a=\sqrt{b}\) --> \(0<b<1\). Sufficient.

Answer: B.

Jp27 · Answer

Huh? Inside the spoiler you have given OA as B? I guess both a sufficient by itself to answer to question "is the value of a between 0 and 1?" Question rephrase -> a*a = b ; a^2 = b ; a = +/- \sqrt{b} Is 0 < a < 1 Stat1/Given B is between 0 and 1. a= 0.5 then b = 0.25 ; a is in between 0 and 1 a = -0.5 then b = 0.25 ; a is NOT between 0 and 1. InSufficient Stat2/ If a > b & a =\sqrt{b} only values that would satisfy these equations would be value from 0 to 1. Sufficient. So D it is.... Cheers

MacFauz · Answer

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

Jp27 · Answer

Well MY reaction after reading your post :wall

.... I will edit my response...!

omohojo · Answer

This graph helped me understand this question:

https://i.imgur.com/77QDbAI.png

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

MathRevolution · Answer

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.

akshayk · Answer

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.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards