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In the triangle

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In the triangle [#permalink] New post 12 Jan 2016, 09:38
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Question Stats:

81% (00:22) correct 18% (00:30) wrong based on 55 sessions
Image

Quantity A
Quantity B
\(\frac{x}{y}\)
\(1\)


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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Question: 4
Page: 330
Difficulty: medium/hard
[Reveal] Spoiler: OA

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Re: In the triangle [#permalink] New post 12 Jan 2016, 09:42
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Solution

A bit of logic comes in handy in this question

You do have an angle of 50°, the other one is 90° and the third is 40°, to sum up 180°

As such, X must greater than Y i.e. for instance \(\frac{2}{3}\) because the 3 sides are \(y < x < z\)

A proper fraction is always less than 1.

So the best answer is \(A\)
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Re: In the triangle [#permalink] New post 29 Mar 2016, 09:54
but isn't x opposite 50 degrees which is larger than 40 degrees which is the angle y is opposite?
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Re: In the triangle [#permalink] New post 30 Mar 2016, 06:14
Expert's post
Sagnik you are absolutely right. The fraction \(\frac{x}{y}\) is definitely > 1.


Solution


Lets take the Sine rule which states that:
\(\frac{x}{sin(X)}\) = \(\frac{y}{sin(Y)}\) = \(\frac{z}{sin(Z)}\)

So in this triangle XYZ we can write,
\(\frac{x}{sin(50^0)}\) = \(\frac{y}{sin(40^0)}\)
or, \(\frac{x}{y}\) = \(\frac{sin(50^0)}{sin(40^0)}\)
and we know \(sin(50^0)>sin(40^0)\).
Therefore \(\frac{x}{y}>1\)

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Re: In the triangle [#permalink] New post 02 Apr 2016, 03:28
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to simplify, in a 90 - 45 - 45 triangle, the sides opposite 45 are equal. Now when one angle is 50 degrees the side opposite it will be longer than side opposite 40 degrees. So x > y and x/y > 1
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Re: In the triangle [#permalink] New post 02 Apr 2016, 09:38
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Yup precisely!
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Re: In the triangle [#permalink] New post 10 Apr 2016, 19:37
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Let's not overthink this one.

Concept: In any triangle:

largest side = opposite largest angle
smallest side = opposite smallest angle

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Last edited by skypetutor on 29 Sep 2017, 16:29, edited 1 time in total.
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Re: In the triangle [#permalink] New post 13 Aug 2016, 08:25
Carcass wrote:
Solution

A bit of logic comes in handy in this question

You do have an angle of 50°, the other one is 90° and the third is 40° to sum up 180°

As such, X must less than Y i.e. for instance \(\frac{2}{3}\) because the 3 sides are \(x < y < z\)

A proper fraction is always less than 1.

So the best answer is \(A\)
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Re: In the triangle [#permalink] New post 13 Aug 2016, 08:26
Carcass wrote:
Solution

A bit of logic comes in handy in this question

You do have an angle of 50°, the other one is 90° and the third is 40° to sum up 180°

As such, X must less than Y i.e. for instance \(\frac{2}{3}\) because the 3 sides are \(x < y < z\)

A proper fraction is always less than 1.

So the best answer is \(A\)



Carcass,

why is x < y < z ??
x = 50 , y = 40, and the hypotenuse is 90....
So why must x be less than y??
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Re: In the triangle [#permalink] New post 16 Aug 2016, 07:41
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Carcass wrote:
Image

Quantity A
Quantity B
x/y
1




skypetutor is absolutely right.
The side lengths are related to their opposite angles
The 3 angles are 40, 50 and 90.
We have: 40 < 50 < 90
So, the side lengths are: y < x < hypotenuse

Since y < x, we can be certain that x/y > 1

Answer: A

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Re: In the triangle [#permalink] New post 18 Aug 2016, 16:09
Thanks for confirming by suspicion. The first solution provided for this was incorrect....
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Re: In the triangle [#permalink] New post 27 May 2018, 23:18
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Carcass wrote:
Solution

A bit of logic comes in handy in this question

You do have an angle of 50°, the other one is 90° and the third is 40° to sum up 180°

As such, X must less than Y i.e. for instance \(\frac{2}{3}\) because the 3 sides are \(x < y < z\)

A proper fraction is always less than 1.

So the best answer is \(A\)


While your answer is correct, your calculation leading to the answer is wrong. x is greater than y (40 degrees) so the fraction will always be greater than 1!
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Re: In the triangle [#permalink] New post 28 May 2018, 10:45
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Sorry for the silly mismatch. Fixed.

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Re: In the triangle   [#permalink] 28 May 2018, 10:45
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