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# Which of the following must be true?

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Which of the following must be true?  [#permalink]

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Updated on: 29 Sep 2016, 01:23
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55% (hard)

Question Stats:

62% (02:31) correct 38% (03:03) wrong based on 56 sessions

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Which of the following must be true?

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“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.”

Originally posted by AsadAbu on 28 Sep 2016, 14:59.
Last edited by AsadAbu on 29 Sep 2016, 01:23, edited 1 time in total.
Senior Manager
Joined: 23 Feb 2015
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Re: Which of the following must be true?  [#permalink]

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Updated on: 29 Sep 2016, 01:20
Hi Bunuel,
In the question, there is no indication that the ''y'' of R and the ''y'' of Q are same. So, why did we say that its correct choice is B?
Thanks Expert...
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“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.”

Originally posted by AsadAbu on 28 Sep 2016, 15:02.
Last edited by AsadAbu on 29 Sep 2016, 01:20, edited 1 time in total.
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Re: Which of the following must be true?  [#permalink]

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28 Sep 2016, 15:59
For triangle Q we know the area is 50 1/2 (b*h)=1/2(10*10)

And for triangle P I got the area was 25√3 so I'm lost how they can all be equal
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Re: Which of the following must be true?  [#permalink]

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29 Sep 2016, 00:16
Area of 1st triangle = (√3/4)*A^2 which gives us Area = 25√3

Area of 2nd triangle = (1/2)b*h = 50

We will have to calculate Y from 2nd triangle and it comes out to 5√5

Area of 3rd Triangle = (1/2)b*h, where as per figure b and h are equal to Y

So, area of 3rd Triangle = (1/2) Y * Y = (1/2) 5√5*5√5 = 125/2

So, as per my understanding it would be option B.

Pls help if its correct.
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Re: Which of the following must be true?  [#permalink]

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29 Sep 2016, 01:08
iMyself : Are we sure the OA is correct? I got B as the answer.
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Re: Which of the following must be true?  [#permalink]

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29 Sep 2016, 01:22
abhimahna wrote:
iMyself : Are we sure the OA is correct? I got B as the answer.

I'm sorry for my mistake. I've edited it again.
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“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.”

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Re: Which of the following must be true?  [#permalink]

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28 Feb 2017, 04:29
(I) area of triangle P = √3*10*10/4 = 25√3 =25*1.73
(II) area of triangle Q = ½ *10*10 = 50 = 25*2 and y = 5√5
(III) area of triangle R = ½ *y*y = 125/2 = 25 *2.5

Therefore we can say that III>II>I . option B
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Re: Which of the following must be true? &nbs [#permalink] 28 Feb 2017, 04:29
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