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# M23-24

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Intern
Joined: 17 May 2016
Posts: 29
GMAT 1: 740 Q46 V46

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13 Apr 2017, 07:23
1
Hi All,

Must Known for GMAT,

IF YOU CAN DRAW THE FIGURE, IT MEANS THAT YOU KNOW ALL PROPERTIES

From Stem : $$width * length = 80$$

Statement 1 : $$width + length = 42$$

We have two equations, with two variables so we can solve and find the two sides : 40 and 2 ==> SUFFICIENT

Statement 2 : Shorter side is 2

So we have $$2 * length = 80$$
Therefore length = 40 and thus we can draw the figure and know all the angles. ==> SUFFICIENT

Senior Manager
Joined: 15 Nov 2016
Posts: 282

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26 Apr 2017, 03:12
What does "angle between the diagonal of the rectangle and its longer side", can someone draw it out for me please?
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Intern
Joined: 30 May 2013
Posts: 29
GMAT 1: 600 Q50 V21
GMAT 2: 640 Q49 V29

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13 Jul 2017, 07:30
dyg wrote:
Hi Bunuel,

I found the lentgh of side but since they are 2 and 40 I thought we cant determine the angle. Now I got the point. I just wanna ask something to you. In geometry (generally) is it possible to find value of an angle if we know the lenght of the sides?

Hi,
Just to satisfy the query of many friends -
Knowing all the sides of a triangle helps in identifying the angle between any two sides. How : Here it follows:
Calculate the area using Heros Formula : Area= √s(s-a)(s-b)(s-c) where s = sum of all the sides / 2 and a,b,c are the length of the sides. ------ (1)
Also Area = 1/2 ab sinx where x is angle between side a and b. -----(2)
Equate (1) & (2) to extract the value of sinx or x.
Intern
Joined: 03 Jan 2015
Posts: 8
GMAT 1: 690 Q50 V33

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14 Jul 2017, 18:20
1
I think this is a high-quality question and I don't agree with the explanation. When we solve wstatement-1, we will get 2 values either (l,b) = (40,2) or (2,40), so accordingly angle will also be different. So, not sufficient. Answer must be option B. Kindly correct if I am wrong.
Math Expert
Joined: 02 Sep 2009
Posts: 50585

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15 Jul 2017, 01:55
1
mohitpoddar wrote:
I think this is a high-quality question and I don't agree with the explanation. When we solve wstatement-1, we will get 2 values either (l,b) = (40,2) or (2,40), so accordingly angle will also be different. So, not sufficient. Answer must be option B. Kindly correct if I am wrong.

We need to find the angle between the diagonal of the rectangle and its longer side. So, it does not matter whether it's (40,2) or (2,40). In any case we should find the angle between the diagonal and the side of length 40.
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Location: India
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15 Jul 2017, 09:21
1st Sufficient as Perimeter 2(L + B) = 84
L+B = 42
only possible values of L&B such that L+B=42 and L*B=40 is L=40 ,B=2

2nd Sufficient as shorter side = 2 , longer must be 40 to make L*B=80

OA D
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20 Jul 2017, 02:03
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

Area of rectangle = 80
Let length of rectangle = L
and breadth of rectangle = B
=> LB = 80

1. Perimeter =84
=> 2(L+B) = 84
=> L+B = 42
=> B = 42-L

Now , L* (42-L) = 80
=> L^2 - 42L +80 = 0
=> L^2 - 40L - 2L +80 = 0
=> (L-2)(L-40) = 0
=> L = 2 , 40
If Length = 2 , then breadth = 40 and vice versa

Now , diagonal can be calculated using Pythagoras theorem .
If we know sides of a triangle , we can calculate the angle using trigonometry.
Sufficient

(2) The shorter side of the rectangle is 2
Sufficient - same as B = 2 and L = 40

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Intern
Joined: 29 Jul 2016
Posts: 6

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25 Aug 2017, 12:32
I like this Magoosh explanation in regards to determining the uniqueness of a triangle. In short, if we can determine unique values for SAS, SSS, and etc (see link for full list), then we can determine everything about a triangle since we are essentially breaking the problem down into two triangles.

https://magoosh.com/gmat/2012/gmat-data ... nce-rules/
Intern
Joined: 03 Sep 2016
Posts: 15

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27 Aug 2017, 03:11
Hi,

Statement 1 gives L=40 or 2 B= 2 or 40. Does not changing length and breadth impact the angle?
Math Expert
Joined: 02 Sep 2009
Posts: 50585

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27 Aug 2017, 03:15
Sanjay2043 wrote:
Hi,

Statement 1 gives L=40 or 2 B= 2 or 40. Does not changing length and breadth impact the angle?

Explained above:

We need to find the angle between the diagonal of the rectangle and its longer side. So, it does not matter whether it's (40,2) or (2,40). In any case we should find the angle between the diagonal and the side of length 40.
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Intern
Joined: 09 Jun 2016
Posts: 22

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05 Sep 2017, 00:16
Bunuel wrote:
dyg wrote:
Hi Bunuel,

I found the lentgh of side but since they are 2 and 40 I thought we cant determine the angle. Now I got the point. I just wanna ask something to you. In geometry (generally) is it possible to find value of an angle if we know the lenght of the sides?

Yes, knowing the lengths of all the sides is enough to get the angels.

Hi Bunuel,

1. I guess this is true for parallelograms and polygons as well? That knowing the sides is enough to know the angles. I guess Yes , because if we actually start drawing it on paper, we will be able to measure the angles with a protractor?

2. Another question, what if it was a PS question and we actually have to find the angles. I know trigo so I can use that but how do you do it without trigo? Is the ratio of angles of a triangle equal to the ratio of opp sides in all cases?
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Math Expert
Joined: 02 Sep 2009
Posts: 50585

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05 Sep 2017, 00:22
abhishek911 wrote:
Bunuel wrote:
dyg wrote:
Hi Bunuel,

I found the lentgh of side but since they are 2 and 40 I thought we cant determine the angle. Now I got the point. I just wanna ask something to you. In geometry (generally) is it possible to find value of an angle if we know the lenght of the sides?

Yes, knowing the lengths of all the sides is enough to get the angels.

Hi Bunuel,

1. I guess this is true for parallelograms and polygons as well? That knowing the sides is enough to know the angles. I guess Yes , because if we actually start drawing it on paper, we will be able to measure the angles with a protractor?

2. Another question, what if it was a PS question and we actually have to find the angles. I know trigo so I can use that but how do you do it without trigo? Is the ratio of angles of a triangle equal to the ratio of opp sides in all cases?

1. Yes, it's true for convex polygons.

2. For PS either you won't be asked such question or it would be special triangle involved (30-60-90, 45-45-90).
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Joined: 09 Jun 2016
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05 Sep 2017, 01:47
Sure. Thanks!

Sent from my iPhone using GMAT Club Forum
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Manager
Joined: 23 Jun 2016
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15 Nov 2017, 21:31
from 1, what is the quick way to derive side lengths?
x + y = 42
x * y = 80

How do we get 40,2?
Manager
Joined: 23 Jun 2016
Posts: 110

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16 Nov 2017, 06:51
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?
Math Expert
Joined: 02 Sep 2009
Posts: 50585

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16 Nov 2017, 06:55
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, 06:59
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: 50585

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16 Nov 2017, 07:03
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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Location: Spain
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15 Jan 2018, 02:17
Bunuel wrote:
dyg wrote:
Hi Bunuel,

I found the lentgh of side but since they are 2 and 40 I thought we cant determine the angle. Now I got the point. I just wanna ask something to you. In geometry (generally) is it possible to find value of an angle if we know the lenght of the sides?

Yes, knowing the lengths of all the sides is enough to get the angels.

Thank you very much
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Joined: 08 Jun 2015
Posts: 435
Location: India
GMAT 1: 640 Q48 V29
GMAT 2: 700 Q48 V38
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19 Mar 2018, 08:34
+1 for option D
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Re: M23-24 &nbs [#permalink] 19 Mar 2018, 08:34

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# M23-24

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