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# st=square_root 10

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st=square_root 10 [#permalink]  18 Jan 2016, 07:48
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Question Stats:

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st=$$\sqrt{10}$$

 Quantity A Quantity B $$s^2$$ $$\frac{10}{t^2}$$

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

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Re: st=square_root 10 [#permalink]  18 Jan 2016, 07:57
Expert's post
Solution

Do not being intimidated by the question

st=$$\sqrt{10}$$. Squaring both sides we do have $$s^2t^2$$ = $$(\sqrt{10}^2)$$

So $$s^2t^2=10$$.Indeed $$s^2=\frac{10}{t^2}$$

The answer is $$C$$
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Re: st=square_root 10 [#permalink]  09 Feb 2019, 14:48
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Expert's post
Carcass wrote:
st=$$\sqrt{10}$$

 Quantity A Quantity B $$s^2$$ $$\frac{10}{t^2}$$

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

GIVEN: st = √10

Divide both sides by t to get: s = (√10)/t

Square both sides to get: s² = (√10)²/t²

Simplify to get: s² = 10/t²

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

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Re: st=square_root 10 [#permalink]  11 Feb 2019, 03:41
Does it must be obvious to understant that s and t are diferent numbers?
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Re: st=square_root 10 [#permalink]  11 Feb 2019, 05:14
Expert's post
Malbash212 wrote:
Is it must that s and t are different numbers?

No, they can be same too..
If s=t, st=$$s^2=\sqrt{10}$$

A= $$s^2=\sqrt{10}$$
B= $$\(\frac{10}{t^2}$$=$$\frac{10}{s^2}$$=$$\frac{10}{\sqrt{10}}$$=\)$$\sqrt{10}$$

So A=B, even when s=t.
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

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Re: st=square_root 10 [#permalink]  11 Feb 2019, 06:41
Expert's post
Malbash212 wrote:
Does it must be obvious to understant that s and t are diferent numbers?

Many students believe that if we have two DIFFERENT variables (e.g., x and y), then those two variables cannot have the same value.
This belief, however, is incorrect.

Cheers,
Brent
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Re: st=square_root 10   [#permalink] 11 Feb 2019, 06:41
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