If a, b, and c are positive integers, is b = ac^(-1/2)

Question

If a, b, and c are positive integers, is  b = \frac{a}{\sqrt{c}} ?

(1)  c = \frac{a^2}{b^2}

(2)  \sqrt{c} = \frac{b}{a}

GMATinsight · Answer

Question : is  b = \frac{a}{\sqrt{c}} ?

Statement 1 :  c = \frac{a^2}{b^2}  
Taking square root both sides
√c = a/b
SUFFICIENT

Statement 2 :  \sqrt{c} = \frac{b}{a}  
@a = b = c = 1 Answer to the question is YES
@a = 1, b=2, c = 4 Answer to the question is NO
NOT SUFFICIENT

Answer: Option A

Bunuel · Answer

Sorry GMATinsight, the question is "If a, b, and c are positive integers, is  b = \frac{a}{\sqrt{c}} ?" NOT "If a, b, and c are positive integers, is  b = \frac{a}{c} ?". Edited.

Nikkb · Answer

(1)  c = \frac{a^2}{b^2} 
=> taking square root
=>  \sqrt{c} = \frac{a}{b} 
=>  b = \frac{a}{\sqrt{c}} 
Sufficient

(2)  \sqrt{c} = \frac{b}{a} 
=>  b =a\sqrt{c} 
In this case :
if c = 1 =>  b =a\sqrt{c}  =>  b = \frac{a}{\sqrt{c}} 
if c = 4 =>  b =a\sqrt{c}  is not same as  b = \frac{a}{\sqrt{c}} 
Insufficient

Answer: A

GmatDaddy · Answer

Given:  a,b,c are +'ve
 To Calculate : b=\frac{a}{\sqrt{c}}

Statement 1: 
 c = \frac{a^2}{b^2} 
Since,  \sqrt{x^2}=|x| 
and a,b,c are all +'ve  
Therefore,  \sqrt{x^2}=x 
Using the above, we can root both sides(Since, all the variables are Positive, there will be no loss of solutions)
 \sqrt{c}=\frac{a}{b} 
Rearranging the terms, we get
 b = \frac{a}{\sqrt{c}} 
 Hence Sufficient.

Statement 2: 
 \sqrt{c} = \frac{b}{a} 
Rearranging the terms, we get:
 b=a\sqrt{c} 
Which is not the term we desire.
 Hence Insufficient.

Answer: A

However, I do not see the need of Value Substitution while evaluating Statement 2.
Can someone throw some light on why did we do that ?

amanvermagmat · Answer

Hello

Value substitution is just one of the techniques which often comes in very handy while solving DS questions, especially for someone who is not so good in algebra and advanced formulas, or if one is not so good in mathematics.

Even for people who are good in formulas/algebra etc, sometimes value substitution saves time. That's why you will often see experts solving questions using this technique.

Although I agree this questions second statement can probably be very easily resolved using what you suggested.

Posted from my mobile device

LeoN88 · Answer

In GMAT if x^2 = 25, the x can be +/-5
But root(25) will have only one answer= 5.

1. Square root both sides:

b = \frac{a}{\sqrt{c}}  Sufficient

2. b= a* root(c)
Yes for all a=b=c=1
No for a!=b!=c!=1. Insufficient.

bumpbot · Answer

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If a, b, and c are positive integers, is b = ac^(-1/2)

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