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# Which of the following statements is true?

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Manager
Joined: 16 Mar 2009
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Location: Bologna, Italy
Which of the following statements is true?  [#permalink]

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27 Aug 2010, 07:15
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Difficulty:

95% (hard)

Question Stats:

42% (02:41) correct 58% (02:06) wrong based on 123 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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Manager
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Re: Which of the following statements is true?  [#permalink]

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27 Aug 2010, 08:06
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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14 Sep 2010, 04:18
any quick way to solve this plsss...???
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Re: Which of the following statements is true?  [#permalink]

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14 Sep 2010, 09:54
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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14 Sep 2010, 11:50
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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Senior Manager
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Re: Which of the following statements is true?  [#permalink]

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14 Sep 2010, 11:56
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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14 Sep 2010, 18:30
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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14 Sep 2010, 20:23
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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Joined: 16 Aug 2009
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Re: Which of the following statements is true?  [#permalink]

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15 Sep 2010, 08:40
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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25 Dec 2017, 03:34
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? &nbs [#permalink] 25 Dec 2017, 03:34
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# Which of the following statements is true?

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