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

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.

Practice Questions Question: 4 Page: 330 Difficulty: medium/hard

Re: In the triangle [#permalink]
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 \(\frac{x}{y}>1\)

Re: In the triangle [#permalink]
02 Apr 2016, 03:28

2

This post received KUDOS

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

Re: In the triangle [#permalink]
10 Apr 2016, 19:37

3

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Expert's post

Let's not overthink this one.

Concept: In any triangle:

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

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Re: In the triangle [#permalink]
16 Aug 2016, 07:41

3

This post received KUDOS

Expert's post

Carcass wrote:

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]
27 May 2018, 23:18

1

This post received KUDOS

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!