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# M23-24

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Math Expert
Joined: 02 Sep 2009
Posts: 59588

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16 Nov 2017, 07:55
sevenplusplus wrote:
Bunuel wrote:
Official Solution:

Statement (1) by itself is sufficient. We can find the sides of the rectangle (40 and 2).

how did you find this? Can't sides be fractions?

Check here: https://gmatclub.com/forum/the-area-of- ... 57397.html
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Joined: 23 Jun 2016
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16 Nov 2017, 07:59
Bunuel wrote:
sevenplusplus wrote:
Bunuel wrote:
Official Solution:

Statement (1) by itself is sufficient. We can find the sides of the rectangle (40 and 2).

how did you find this? Can't sides be fractions?

Check here: https://gmatclub.com/forum/the-area-of- ... 57397.html

Thanks. As a general rule, can be assume:
If x + y and x * y both are integers, x & y will be integers?

Sent from my iPhone using GMAT Club Forum mobile app
Math Expert
Joined: 02 Sep 2009
Posts: 59588

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16 Nov 2017, 08:03
sevenplusplus wrote:

Thanks. As a general rule, can be assume:
If x + y and x * y both are integers, x & y will be integers?

Sent from my iPhone using GMAT Club Forum mobile app

No. For example, x+y=3 and xy=1 but if you solve x and y turn out to be irrational numbers.
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29 Aug 2018, 02:43
The stepwise solution is as below:
If the area of a rectangle is 80, what is the angle between the diagonal of the rectangle and its longer side?

Remember word "Rectangle" includes square. In case of square, angle between diagonal and longer side is 45. In case of rectangle, angle between diagonal and longer side is less than 45. We just need to determine

(1) The perimeter of the rectangle is 84

It means 2(m+n) = 84 and mn=80 (given). So m+n=42 and mn=80.
Now substituting m=80/n in m+n=42 can give value of m and n. Hence, n=2 and m=40. So it is not a square and if we know sides of rectangle, the we can definitely calculate angle by drawing it or by trigonometry etc. SUFFICIENT

(2) The shorter side of the rectangle is 2

Hence, m=40 and n=2. Both statement says same thing. SUFFICIENT

OA: D

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12 Apr 2019, 10:11
aren't all angles of rectangle 90degrees, the diagonal will bisect the angle and each angle will be 45?

is this a miracle?
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12 Apr 2019, 10:13
prototypevenom wrote:
aren't all angles of rectangle 90degrees, the diagonal will bisect the angle and each angle will be 45?

is this a miracle?

This would be a case for a rectangle which is a square but not for all other types of rectangles.
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14 Apr 2019, 04:53
Bunuel wrote:
If the area of a rectangle is 80, what is the angle between the diagonal of the rectangle and its longer side?

(1) The perimeter of the rectangle is 84

(2) The shorter side of the rectangle is 2

given
l*b= 80
#1
2*(l+b)=84
so solve
l=40, b= 2
sufficient
#2
b=2 so l = 40
sufficient
IMO D
Re: M23-24   [#permalink] 14 Apr 2019, 04:53

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# M23-24

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