If x = 4 and y = 16, then root[(x+y)/(xy)] is closet to : Problem Solving (PS)

Bunuel

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Re: PT #11 PS 3 Q 13 [#permalink]

07 Mar 2012, 00:53

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eybrj2 wrote:

If x = 4 and y = 16, then \sqrt{x + y/xy} is closet to which of the following?

A. 1/3
B. 1/2
C. 3/4
D. 7/8
E 1

\(\sqrt{\frac{x+y}{xy}}=\sqrt{\frac{4+16}{4*16}}=\sqrt{\frac{20}{4*16}}=\sqrt{\frac{5}{16}}\approx{\sqrt{\frac{4}{16}}}=\sqrt{\frac{1}{4}}=\frac{1}{2}\).

Answer: B.

P.S. Please format the questions correctly. Thank you.
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sidoknowia

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Re: If x = 4 and y = 16, then root[(x+y)/(xy)] is closet to [#permalink]

16 Oct 2016, 18:35

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Bunuel wrote:

eybrj2 wrote:

If x = 4 and y = 16, then \sqrt{x + y/xy} is closet to which of the following?

A. 1/3
B. 1/2
C. 3/4
D. 7/8
E 1

\(\sqrt{\frac{x+y}{xy}}=\sqrt{\frac{4+16}{4*16}}=\sqrt{\frac{20}{4*16}}=\sqrt{\frac{5}{16}}\approx{\sqrt{\frac{4}{16}}}=\sqrt{\frac{1}{4}}=\frac{1}{2}\).

Answer: B.

P.S. Please format the questions correctly. Thank you.

Hi Bunuel,

in your final step

\sqrt{\frac{5}{16}} = 2.73 / 4

2.73 is approx 3,
then answer becomes 3/4.

Why are we not solving it in this way?

Bunuel

Math Expert

Joined: 02 Sep 2009

Posts: 92747

Re: If x = 4 and y = 16, then root[(x+y)/(xy)] is closet to [#permalink]

17 Oct 2016, 03:05

Expert Reply

sidoknowia wrote:

Bunuel wrote:

eybrj2 wrote:

If x = 4 and y = 16, then \sqrt{x + y/xy} is closet to which of the following?

A. 1/3
B. 1/2
C. 3/4
D. 7/8
E 1

\(\sqrt{\frac{x+y}{xy}}=\sqrt{\frac{4+16}{4*16}}=\sqrt{\frac{20}{4*16}}=\sqrt{\frac{5}{16}}\approx{\sqrt{\frac{4}{16}}}=\sqrt{\frac{1}{4}}=\frac{1}{2}\).

Answer: B.

P.S. Please format the questions correctly. Thank you.

Hi Bunuel,

in your final step

\sqrt{\frac{5}{16}} = 2.73 / 4

2.73 is approx 3,
then answer becomes 3/4.

Why are we not solving it in this way?

\(\sqrt{5}\approx 2.24\), not 2.73
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dave13

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If x = 4 and y = 16, then root[(x+y)/(xy)] is closet to [#permalink]

17 Feb 2018, 13:36

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eybrj2 wrote:

If x = 4 and y = 16, then \(\sqrt{\frac{x+y}{xy}}\) is closet to which of the following?

A. 1/3
B. 1/2
C. 3/4
D. 7/8
E. 1

Hi Bunuel , why my solution is not correct ? Any idea ?

\(\sqrt{\frac{4+16}{4*16}}\) = \(\frac{sqrt4 +sqrt16}{sqrt64}\) = \(\frac{3}{4}\)

Theory
Exponents and Roots on the GMAT: Tips and hints
Cyclicity and the remainders on the GMAT

Bunuel

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Posts: 92747

Re: If x = 4 and y = 16, then root[(x+y)/(xy)] is closet to [#permalink]

17 Feb 2018, 15:17

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dave13 wrote:

eybrj2 wrote:

If x = 4 and y = 16, then \(\sqrt{\frac{x+y}{xy}}\) is closet to which of the following?

A. 1/3
B. 1/2
C. 3/4
D. 7/8
E. 1

Hi Bunuel , why my solution is not correct ? Any idea ?

\(\sqrt{\frac{4+16}{4*16}}\) = \(\frac{sqrt4 +sqrt16}{sqrt64}\) = \(\frac{3}{4}\)

Generally \(\sqrt{x+y} \neq \sqrt{x}+\sqrt{y}\). Does \(\sqrt{1+4}\) equal to \(\sqrt{1}+\sqrt{4}\)?

8. Exponents and Roots of Numbers

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PrernaMurada

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Re: If x = 4 and y = 16, then root[(x+y)/(xy)] is closet to [#permalink]

18 Feb 2018, 00:45

((x+y)/xy)^0.5
Substituting the value of x and y,Given expression=(20/4*16)^0.5
5^0.5/4=2.23/4 which is approximately 0.5

Theory
Exponents and Roots on the GMAT: Tips and hints
Cyclicity and the remainders on the GMAT

dave13

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Posts: 1162

Re: If x = 4 and y = 16, then root[(x+y)/(xy)] is closet to [#permalink]

18 Feb 2018, 03:43

Bunuel wrote:

dave13 wrote:

eybrj2 wrote:

If x = 4 and y = 16, then \(\sqrt{\frac{x+y}{xy}}\) is closet to which of the following?

A. 1/3
B. 1/2
C. 3/4
D. 7/8
E. 1

Hi Bunuel , why my solution is not correct ? Any idea ?

\(\sqrt{\frac{4+16}{4*16}}\) = \(\frac{sqrt4 +sqrt16}{sqrt64}\) = \(\frac{3}{4}\)

Generally \(\sqrt{x+y} \neq \sqrt{x}+\sqrt{y}\). Does \(\sqrt{1+4}\) equal to \(\sqrt{1}+\sqrt{4}\)?

8. Exponents and Roots of Numbers

Questions
Units digits, exponents, remainders problems
Tough and tricky DS exponents and roots questions with detailed solutions
Tough and tricky PS exponents and roots questions with detailed solutions
Exponents DS Questions
Exponents PS Questions
Roots DS Questions
Roots PS Questions

Check below for more:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread

Hope it helps.

Hello Bunuel, i have one question which i dont understnd

What would equal \(0^0\) = 1? or = 0 ?

many thanks

Bunuel

Math Expert

Joined: 02 Sep 2009

Posts: 92747

Re: If x = 4 and y = 16, then root[(x+y)/(xy)] is closet to [#permalink]

18 Feb 2018, 05:25

Expert Reply

dave13 wrote:

Hello Bunuel, i have one question which i dont understnd

What would equal \(0^0\) = 1? or = 0 ?

many thanks

0^0, in some sources equals to 1, some mathematicians say it's undefined. But you won't need this for the GMAT because the case of 0^0 is not tested on the GMAT.
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Abhishek009

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Re: If x = 4 and y = 16, then root[(x+y)/(xy)] is closet to [#permalink]

08 May 2020, 01:21

eybrj2 wrote:

If x = 4 and y = 16, then \(\sqrt{\frac{x+y}{xy}}\) is closet to which of the following?

A. 1/3
B. 1/2
C. 3/4
D. 7/8
E. 1

\(\sqrt{\frac{x+y}{xy}}\)

= \(\sqrt{\frac{20}{64}}\)

= \(\sqrt{\frac{10}{32}}\)

= \(\sqrt{\frac{5}{16}}\)

~ \(\sqrt{\frac{4}{16}}\)

~ \(\sqrt{\frac{1}{4}}\)

~ \(\frac{1}{2}\), Answer must be (B)
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Hoozan

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Re: If x = 4 and y = 16, then root[(x+y)/(xy)] is closet to [#permalink]

23 Oct 2020, 03:53

Quote:

\(\sqrt{5}\approx 2.24\), not 2.73

Bunuel why isn't 2.24/4 not close to 3/4?

Bunuel

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Joined: 02 Sep 2009

Posts: 92747

Re: If x = 4 and y = 16, then root[(x+y)/(xy)] is closet to [#permalink]

23 Oct 2020, 07:09

Expert Reply

Hoozan wrote:

Quote:

\(\sqrt{5}\approx 2.24\), not 2.73

Bunuel why isn't 2.24/4 not close to 3/4?

2.24/4 = 0.56 while 3/4 = 0.75.
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BrentGMATPrepNow

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Re: If x = 4 and y = 16, then root[(x+y)/(xy)] is closet to [#permalink]

20 Apr 2022, 10:28

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eybrj2 wrote:

If x = 4 and y = 16, then \(\sqrt{\frac{x+y}{xy}}\) is closet to which of the following?

A. 1/3
B. 1/2
C. 3/4
D. 7/8
E. 1

Before test day, be sure to memorize the following approximations:
√2 ≈ 1.4
√3 ≈ 1.7
√5 ≈ 2.2

Useful property: \(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\)

Given: \(\sqrt{\frac{x+y}{xy}}\)

Substitute values: \(\sqrt{\frac{4+16}{(4)(16)}}\)

Simplify: \(\sqrt{\frac{20}{64}}\)

Apply above property: \(\frac{\sqrt{20}}{\sqrt{64}}\)

Rewrite numerator and simplify denominator: \(\frac{2\sqrt{5}}{8}\)

Substitute 2.2 for √5 to get: \(\frac{(2)(2.2)}{8} ≈ \frac{4.4}{8} \)

Since 1/2 closest answer choice to \(\frac{4.4}{8}\), the correct answer is B

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Re: If x = 4 and y = 16, then root[(x+y)/(xy)] is closet to [#permalink]

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