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

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Intern
Joined: 22 Oct 2012
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If a^2=b, is the value of a between 0 and 1? [#permalink]

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01 Dec 2012, 00:37
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Question Stats:

39% (01:07) correct 61% (01:11) wrong based on 184 sessions

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

(1) b is between 0 and 1
(2) a>b
[Reveal] Spoiler: OA

Last edited by Bunuel on 01 Dec 2012, 05:59, edited 1 time in total.
Edited the question.

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Re: If a*a=b, is the value of a between 0 and 1? [#permalink]

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01 Dec 2012, 04:15
cv3t3l1na wrote:
If a*a=b, is the value of a between 0 and 1?
1. b is between 0 and 1
2. a>b

Why 2. is not sufficient?

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

Last edited by Jp27 on 01 Dec 2012, 07:23, edited 2 times in total.

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Re: If a*a=b, is the value of a between 0 and 1? [#permalink]

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01 Dec 2012, 06:18
Jp27 wrote:
cv3t3l1na wrote:
If a*a=b, is the value of a between 0 and 1?
1. b is between 0 and 1
2. a>b

Why 2. is not sufficient?

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/ If B is between 0 and 1. Root of any value between 0 and 1 will result in a value larger than B but will still be fraction between 0 and 1. Sufficient

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

If a = -0.5, b =0.25
a = 0.5 , b = 0.25 ...
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Re: If a*a=b, is the value of a between 0 and 1? [#permalink]

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01 Dec 2012, 06:45
MacFauz wrote:
Jp27 wrote:
cv3t3l1na wrote:
If a*a=b, is the value of a between 0 and 1?
1. b is between 0 and 1
2. a>b

Why 2. is not sufficient?

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/ If B is between 0 and 1. Root of any value between 0 and 1 will result in a value larger than B but will still be fraction between 0 and 1. Sufficient

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

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

I will edit my response...!

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Re: If a^2=b, is the value of a between 0 and 1? [#permalink]

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01 Dec 2012, 06:54
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Expert's post
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.

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Re: If a^2=b, is the value of a between 0 and 1? [#permalink]

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Re: If a^2=b, is the value of a between 0 and 1? [#permalink]

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02 Sep 2015, 10:02
cv3t3l1na wrote:
If a^2=b, is the value of a between 0 and 1?

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

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

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

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03 Sep 2015, 04:49
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Expert's post
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.
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Re: If a^2=b, is the value of a between 0 and 1? [#permalink]

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03 Aug 2017, 12:50
cv3t3l1na wrote:
If a^2=b, is the value of a between 0 and 1?

(1) b is between 0 and 1
(2) a>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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Re: If a^2=b, is the value of a between 0 and 1?   [#permalink] 03 Aug 2017, 12:50
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