Problem Solving

√1919/√0.1919 =

A) 0.0001
B) 0.01
C) 100
D) 1000
E) 10,000


why can't you square both and solve?

Hi,
You can square both and solve. But at the end you have to take the square root.

To expand a bit further:

Squaring and then solving is a strategy to be used on EQUATIONS. When you square both sides of an equation, you (usually) maintain the equality that was present in the original equation.

You cannot square an expression and expect the result to be equal to the original. Squaring (usually) changes an expression's value.

So, you can do what Anurag suggested, which is essentially to set up an equation:
√1919/√0.1919 = x
(√1919/√0.1919)^2 = x^2 [SQUARE BOTH SIDES]
1919/0.1919 = x^2
10,000 = x^2
x = 100 [TAKE THE SQUARE ROOT OF BOTH SIDES]

Another approach is to simplify the expression without squaring:
√1919/√0.1919 = x
√(1919/0.1919) = x
√(10,000) = x
x = 100

This approach uses the rule that √a/√b = √(a/b).
Also, in case it is helpful, the reason that 1919/0.1919 = 10,000 is that 1919 = .1919 * 10,000
So, 1919/0.1919 = (0.1919 * 10000)/0.1919
Then cancel the 0.1919 on the top and bottom, which leaves 10,000

Anurag@Gurome wrote:

MBA.Aspirant wrote:√1919/√0.1919 =

A) 0.0001
B) 0.01
C) 100
D) 1000
E) 10,000

Say, x = √1919/√0.1919 = √(1919/0.1919) = √10,000 = 100

Also, x² = (1919/0.1919) = 10,000 = 100
Hence, x = √10,000 = 100

The correct answer is C.

Hi Anurag,
Just want to expand it little further...suppose one took squared approach (second one) and answer choice includes -100 too ...then for which one you would go ?

ArpanaAmishi wrote:

Anurag@Gurome wrote:

MBA.Aspirant wrote:√1919/√0.1919 =

A) 0.0001
B) 0.01
C) 100
D) 1000
E) 10,000

Say, x = √1919/√0.1919 = √(1919/0.1919) = √10,000 = 100

Also, x² = (1919/0.1919) = 10,000 = 100
Hence, x = √10,000 = 100

The correct answer is C.

Hi Anurag,
Just want to expand it little further...suppose one took squared approach (second one) and answer choice includes -100 too ...then for which one you would go ?

I think you can't select "-100" as an answer because actual question asks you about Sq rt of some positive numbers that can only be positive. (FYI-GMAT will never test on negative value of the roots or complex # concepts.)

ArpanaAmishi wrote:

Anurag@Gurome wrote:

MBA.Aspirant wrote:√1919/√0.1919 =

A) 0.0001
B) 0.01
C) 100
D) 1000
E) 10,000

Say, x = √1919/√0.1919 = √(1919/0.1919) = √10,000 = 100

Also, x² = (1919/0.1919) = 10,000 = 100
Hence, x = √10,000 = 100

The correct answer is C.

Hi Anurag,
Just want to expand it little further...suppose one took squared approach (second one) and answer choice includes -100 too ...then for which one you would go ?

Since √y denotes a positive value always . You cant take negative values.
Negative values is only coming into existence as you are squaring the given term.
When you square you add a value -√y also in the range which was earlier not in the range.
so while squaring u need to keep in mind that √y > 0.

Technically speaking without considering √y > 0 and squaring is a wrong method. You always have to consider domain and range when solving problem of under root and inequalities,.


Chk my blog post to understand better : https://mba.webmaggu.com/is-%E2%88%9Ax%C ... x-or-none/