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d > c

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d > c [#permalink] New post 15 Sep 2017, 08:40
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Question Stats:

48% (01:05) correct 52% (10:35) wrong based on 25 sessions



Attachment:
triangle.jpg
triangle.jpg [ 25.59 KiB | Viewed 1074 times ]


\(d > c\)

Quantity A
Quantity B
a
d - b


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: d > c [#permalink] New post 16 Sep 2017, 08:10
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I focus on the third angle of the first triangle from above. This angle, that we can call x, is equal to 180°-a-b since the sum of the internal angles of a triangle is 180° but it is also equal to 180°-c since the flat angle is 180°. Thus, we have that x = 180°-a-b and x = 180°-c. Equating these two expressions we get 180°-a-b = 180°-c, from which we get that angle c =is equal to angle a plus angle b. More interestingly, we can rewrite the expression a+b = c as a = c-b. Since we know that d > c, and we have to compare a with d-b it is straightforward to deduce that since a = c-b then it must be lower than d-b given that d is a larger integer to which we subtract the same quantity b. Then the answer is B.
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Re: d > c [#permalink] New post 13 Nov 2018, 17:09
Please explain with pictures.
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Re: d > c [#permalink] New post 15 Nov 2018, 13:11
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Carcass wrote:



Attachment:
triangle.jpg


\(d > c\)

Quantity A
Quantity B
a
d - b


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.


Let's first focus on the red triangle below.
Since all 3 angles must add to 180°, we can conclude that the 3rd angle must equal 180 - (a + b)
Image


Now focus on the highlighted line below.
Image

Since angles on a line must add to 180°, we can write: [180 - (a + b)] + c = 180
Simplify left side to get: 180 - a - b + c = 180
Subtract 180 from both sides to get: -a - b + c = 0
Add a to both sides: -b + c = a
Add b to both sides: c = a + b we'll use this information shortly....

GIVEN:
Quantity A: a
Quantity B: d - b

Add b to both quantities to get:
Quantity A: a + b
Quantity B: d

Since already concluded that c = a + b, we can replace a + b with c to get:
Quantity A: c
Quantity B: d

Finally, we're told that d > c, so the correct answer is B

Cheers,
Brent
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Re: d > c [#permalink] New post 27 Nov 2018, 11:51
Answer: B
Consider the top triangle:
a + b + (180-c) = 180
a + b = c


Consider the middle triangle:
c + (180-d) + a2 = 180
(The angle just under a is called a2)


We have :
a + b = c
c + (180-d) + a2 = 180
We substitute c in second expression with first expression:

(a+ b) + (180-d) + a2 = 180
a + a2 = d-b

As a2 can’t be 0, d-b is bigger than a, the answer is B.
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Re: d > c   [#permalink] 27 Nov 2018, 11:51
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