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Founder  Joined: 18 Apr 2015
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Which is greater x/y or 1 [#permalink]
Expert's post 00:00

Question Stats: 85% (00:24) correct 14% (00:36) wrong based on 261 sessions
Attachment: #GRepracticequestion Which is greater x frac y or 1.jpg [ 4.28 KiB | Viewed 7905 times ]

 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
[Reveal] Spoiler: OA

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Founder  Joined: 18 Apr 2015
Posts: 13719
GRE 1: Q160 V160 Followers: 305

Kudos [?]: 3553 , given: 12681

Expert's post
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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Intern Joined: 28 Mar 2016
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but isn't x opposite 50 degrees which is larger than 40 degrees which is the angle y is opposite?
Director  Joined: 16 May 2014
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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 $$\frac{x}{y}>1$$

Attachment: gre1.PNG [ 6.84 KiB | Viewed 13535 times ]

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If you find this post helpful, please press the kudos button to let me know !  Intern Joined: 31 Mar 2016
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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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Expert's post
Yup precisely!
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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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Last edited by skypetutor on 29 Sep 2017, 16:29, edited 1 time in total.
Intern Joined: 30 Jul 2016
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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 $$A$$
Intern Joined: 30 Jul 2016
Posts: 8
Followers: 0

Kudos [?]: 1 , given: 3

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?? GRE Instructor Joined: 10 Apr 2015
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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

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Thanks for confirming by suspicion. The first solution provided for this was incorrect.... Intern Joined: 08 Apr 2018
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1
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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!
Founder  Joined: 18 Apr 2015
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Expert's post
Sorry for the silly mismatch. Fixed.

Regards
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Director Joined: 09 Nov 2018
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skypetutor wrote:
Let's not overthink this one.

Concept: In any triangle:

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

right
Intern Joined: 14 Sep 2019
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skypetutor wrote:
Let's not overthink this one.

Concept: In any triangle:

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

Imo, this is the easiest approach to this question.
GRE Instructor Joined: 10 Apr 2015
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Expert's post
soumya1989 wrote:
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 $$\frac{x}{y}>1$$

Attachment:
gre1.PNG

For the sake of those just beginning to prepare for the GRE, I should mention that trigonometric ratios (sine, cosine, etc) are not required for the GRE General Test.
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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 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 $$A$$

i think the example u took it will be $$\frac{3}{2}$$ not $$\frac{2}{3}$$. if it is $$\frac{2}{3}$$ for x and y respectively than the answer are not going to correct for answer A.
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Intern Joined: 11 Nov 2019
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Re: Which is greater x/y or 1 [#permalink]
it's quite very simple
Intern Joined: 11 Nov 2019
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Re: Which is greater x/y or 1 [#permalink]
It's so funny as I never expected to get it right Re: Which is greater x/y or 1   [#permalink] 11 Nov 2019, 14:03
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