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Which of the following statements is true?

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Which of the following statements is true? [#permalink]

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New post 27 Aug 2010, 08:15
3
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

40% (01:54) correct 60% (01:35) wrong based on 113 sessions

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Which of the following statements is true?

A. \(3\sqrt{7}<2\sqrt{15}<\frac{5\sqrt{13}}{sqrt{5}}<\frac{39}{5}\)

B. \(2\sqrt{15}<\frac{39}{5}<3\sqrt{7}<\frac{5\sqrt{13}}{sqrt{5}}\)

C. \(2\sqrt{15}<3\sqrt{7}<\frac{39}{5}<\frac{5\sqrt{13}}{sqrt{5}}\)

D. \(2\sqrt{15}<3\sqrt{7}<\frac{5\sqrt{13}}{sqrt{5}}<\frac{39}{5}\)

E. \(2\sqrt{15}<\frac{5\sqrt{13}}{sqrt{5}}<3\sqrt{7}<\frac{39}{5}\)

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Re: Which of the following statements is true? [#permalink]

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New post 27 Aug 2010, 09:06
Answer should be C

Make all the Fraction with same denominator that way it would be much easier as only one option lefts.....!!!!
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Re: Which of the following statements is true? [#permalink]

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New post 14 Sep 2010, 05:18
any quick way to solve this plsss...???
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Re: Which of the following statements is true? [#permalink]

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New post 14 Sep 2010, 10:54
utin wrote:
any quick way to solve this plsss...???


hi,
By observing carefully we can see that all answer choice compare 4 different value types of which 3 are in some form of sqrt......

well for a question like this strategy should be to take all the value inside square root and then compare each..

39/5 will be approx 8 which will be sqrt of 64 and then u can compare all the values easily.......

hope it helps u

thanx
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Re: Which of the following statements is true? [#permalink]

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New post 14 Sep 2010, 12:50
sandeep800 wrote:
utin wrote:
any quick way to solve this plsss...???


hi,
By observing carefully we can see that all answer choice compare 4 different value types of which 3 are in some form of sqrt......

well for a question like this strategy should be to take all the value inside square root and then compare each..

39/5 will be approx 8 which will be sqrt of 64 and then u can compare all the values easily.......

hope it helps u

thanx


Nice idea. I was going decimal route which will be bad.
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Re: Which of the following statements is true? [#permalink]

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New post 14 Sep 2010, 12:56
saxenashobhit wrote:
sandeep800 wrote:
utin wrote:
any quick way to solve this plsss...???


hi,
By observing carefully we can see that all answer choice compare 4 different value types of which 3 are in some form of sqrt......

well for a question like this strategy should be to take all the value inside square root and then compare each..

39/5 will be approx 8 which will be sqrt of 64 and then u can compare all the values easily.......

hope it helps u

thanx


Nice idea. I was going decimal route which will be bad.


Thanx shobhit..sometime pattern of answer choices gives us the way to solve!!! :)
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Re: Which of the following statements is true? [#permalink]

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New post 14 Sep 2010, 19:30
1
B. you have to be careful while doing such approximations.

If you bring everything under a squareroot it becomes obvious.

so it becomes sqrt(63), sqrt(60), sqrt(65), [39/5=sqrt(7.8*7.8) = sqrt(60.84)]

You should be careful while thinking of 7.8 as 8... just watch out ...coz in this case if you would get B as the answer. Not C.
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Re: Which of the following statements is true? [#permalink]

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New post 14 Sep 2010, 21:23
hemanthp wrote:
B. you have to be careful while doing such approximations.

If you bring everything under a squareroot it becomes obvious.

so it becomes sqrt(63), sqrt(60), sqrt(65), [39/5=sqrt(7.8*7.8) = sqrt(60.84)]

You should be careful while thinking of 7.8 as 8... just watch out ...coz in this case if you would get B as the answer. Not C.

Thanx hemanth for pointing out that!!i actually dint solved the question..was just trying to tell the strategy we can use here....
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Re: Which of the following statements is true? [#permalink]

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New post 15 Sep 2010, 09:40
hemanthp wrote:
B. you have to be careful while doing such approximations.

If you bring everything under a squareroot it becomes obvious.

so it becomes sqrt(63), sqrt(60), sqrt(65), [39/5=sqrt(7.8*7.8) = sqrt(60.84)]

You should be careful while thinking of 7.8 as 8... just watch out ...coz in this case if you would get B as the answer. Not C.


This is where i was stuck.
Thanks Hemanthp :)
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Re: Which of the following statements is true? [#permalink]

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New post 25 Dec 2017, 04:34
3
Squaring each term and then comparing makes life easy

\((3 \sqrt{7})^2\) = \(9 * 7\) = \(63\)

\((2 \sqrt{15})^2\) = \(4 * 15\) = \(60\)

\((39/5)^2\) = 1521/25 = \(60.x\) (some decimal)

\((5 \sqrt{13} / \sqrt{5})^2\) = \(25 * 13 / 5\) = \(65\)

60 < 60.x < 63 < 65

Answer (B)
Re: Which of the following statements is true?   [#permalink] 25 Dec 2017, 04:34
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