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# w > 45

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w > 45 [#permalink]  07 Dec 2017, 03:19
Expert's post
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Question Stats:

56% (00:36) correct 43% (00:47) wrong based on 97 sessions
Attachment:

cg.png [ 7.33 KiB | Viewed 3202 times ]

$$w > 45$$

 Quantity A Quantity B m + n 2m

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: w > 45 [#permalink]  07 Dec 2017, 15:19
Since w > 45, the slope of the line must be > 1. Hence the Y coordinate, will be greater than the X coordinate, when both are positive. Hence 2m<n+m

For instance f(x)= 2x

For every positive x value one enters, y will always be greater.

EDIT: Sorry, mixed up A and B in my answer

Last edited by simon1994 on 08 Dec 2017, 05:03, edited 3 times in total.
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Re: w > 45 [#permalink]  07 Dec 2017, 20:31
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my answer is n+m > 2m,
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Re: w > 45 [#permalink]  08 Dec 2017, 04:02
Expert's post

Please provide always the explanation. It helps the community.

Thank you
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Re: w > 45 [#permalink]  18 Sep 2018, 12:08
When slope is linear, it equals 1 and divides the plane into two 45 degree angles and x=y. However, here w > 45, which means slope is more than 1 because it is more steep. In such cases, y coordinates > x coordinates.
n>m. I.E. n+m>2m

If you are good at drawing or visualization, it usually helps in GRE with coordinate geometry especially because planes are to scale.
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Re: w > 45 [#permalink]  21 Oct 2018, 23:01
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Expert's post
Carcass wrote:
Attachment:
The attachment cg.png is no longer available

$$w > 45$$

 Quantity A Quantity B m + n 2m

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.

Refer the attached figure..

At 45, $$m=n$$..
but at $$w>45$$, $$n>m....n+m>m+m...n+m>2m....A>B$$
Attachments

11.png [ 5.61 KiB | Viewed 2204 times ]

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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

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Re: w > 45 [#permalink]  14 Jun 2019, 11:10
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Expert's post
Carcass wrote:
Attachment:
The attachment cg.png is no longer available

$$w > 45$$

 Quantity A Quantity B m + n 2m

Attachment:

Z5.png [ 18.89 KiB | Viewed 1183 times ]

To get a better idea of what's going on here, let's see what happens when the angle is EXACTLY 45 degrees
Attachment:

Z1.png [ 3.42 KiB | Viewed 1183 times ]

If we drop a line from a point ON the line, we see we get an ISOSCELES RIGHT triangle.

This means that, for any point ON the line, ....
Attachment:

Z2.png [ 4.94 KiB | Viewed 1183 times ]

....the x-coordinate and the y-coordinate will be EQUAL

So, some other points on this line will look like this:
Attachment:

Z3.png [ 3.89 KiB | Viewed 1184 times ]

KEY CONCEPT: If w > 45, then the line will pass through the red region
Attachment:

Z4.png [ 3.35 KiB | Viewed 1185 times ]

We already know that, for any point ON THE BLUE LINE, the x-coordinate and the y-coordinate will be EQUAL
If the red region lies ABOVE THE BLUE LINE, what important thing can we say about the coordinates of ANY point in the red region???

We can say that, for any point in the red region, the y-coordinate will be greater than the x-coordinate

So, if w > 45, then we know that n > m

Given:
Quantity A: m + n
Quantity B: 2m

Subtract m from both quantities to get:
Quantity A: n
Quantity B: m

Since we now know that n > m, we can see that the correct answer is A

Cheers,
Brent
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Re: w > 45   [#permalink] 14 Jun 2019, 11:10
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