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Which is greater a or b

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Carcass
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Which is greater a or b [#permalink] New post   04 Mar 2020, 04:18
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Quantity A
Quantity B
a
b



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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B
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uchihaitachi
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Re: Which is greater a or b [#permalink] New post   04 Mar 2020, 06:11
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We use the concept of slope here. If the angle had been 45 degrees then a = b.

\(Slope = \frac{rise}{run} = \frac{b}{a}\)

Since the angle is greater than 45 so, \(rise > run\).

OA,B

Carcass wrote:
Attachment:
#greprepclub Which is greater a or b.jpg


Quantity A
Quantity B
a
b



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.

Kudos for the right answer and explanation
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Asif123
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Re: Which is greater a or b [#permalink] New post   04 Mar 2020, 08:04
How you confirm that Angle is greater than 45 and rise is greater than run?
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Re: Which is greater a or b [#permalink] New post   04 Mar 2020, 09:34
It is given in the question that the angle is 50 degrees.

So slope is also equivalent to tan(theta). Basic trigonometry. Tan(45) = 1. Tan(50) is greater than Tan(45).


Asif123 wrote:
How you confirm that Angle is greater than 45 and rise is greater than run?
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Re: Which is greater a or b [#permalink] New post   09 Jun 2020, 05:30
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An easier way to explain the answer:
1- imagine a triangle, with angles 50, 90 , 40. The length of the side that is opposite to 50 is greater than the side with angle 40.

Y represents the length of the side opposite to 50, and the x represents the side that is opposite to 40.
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Which is greater a or b [#permalink] New post   09 Jun 2020, 06:03
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Carcass wrote:
Attachment:
#greprepclub Which is greater a or b.jpg


Quantity A
Quantity B
a
b



We can use the following property:
Image


Create a right triangle by drawing a perpendicular line from the point to the x-axis
Image


Since 40° is the smallest angle, the side opposite 40° must be the shortest side.
So, the side with length a must be the shortest.

This means a < b

Answer: B

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Re: Which is greater a or b [#permalink] New post   05 Sep 2023, 14:50
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y = x creates a 45 degree angle. If the angle is greater than 45 degrees, you know that the point (a, b) will be higher since a bigger angle corresponds to a larger side. Therefore, b > a and B is the correct answer.
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Re: Which is greater a or b [#permalink] New post   03 Jan 2024, 00:51
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Point (a,b) lies on point thus we can simply put it in line equation y=mx+c
and as we can clearly see the slop is positive thus slop will be greater than 1 (because +ve slope 1 is at 45 degree)

thus b = a+c thus b > a
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