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d > c

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d > c [#permalink] New post   15 Sep 2017, 08:40
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Attachment:
triangle.jpg
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\(d > c\)

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.
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B
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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:

This question is part of GREPrepClub - The Questions Vault Project




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
3
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] New post   11 Jan 2019, 18:07
1
Carcass wrote:
\(d > c\)

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.
Attachment:
triangle.jpg
triangle.jpg [ 25.59 KiB | Viewed 11107 times ]

Now I get it,

a+b=c (Triangle property)
=>a=c-b.............(i)

now,
Quantity A:a
Quantity B:d-b

Quantity A:c-b (replacing value from i)r
Quantity B:d-b

Quantity A:c-b+b (add b)
Quantity B:d-b+b (add b)

Quantity A:c
Quantity B:d

Given,
d>c

Hence
Quantity B is greater.
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Re: d > c [#permalink] New post   05 Mar 2019, 06:41
I got the math correct, though after toiling (!) for ten minutes . I used few equation based on the angles of the triangles. However, 180-a-b+c=180 ( straight angle) . So, c=a+b. as d>c, so d>a+b and d-b>a. Answer B.
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Re: d > c [#permalink] New post   20 Aug 2019, 18:45
2
The easiest approach is ,

According to triangle theory, an Exterior angle is always the sum of opposite interior angles of any triangle.

So we can write (from the figure provided) c=a+b and provided is d>c

therefore , we can write substituting the value of c ,

d>a+b
=> d-b > a

hence , the answer is option B
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Re: d > c [#permalink] New post   25 Aug 2019, 06:31
1
simple approach
consider angle just below angle (a) to be (x)
now by exterior angle property d=x+c ...............[1]
and similarly a+b=c =>b=c-a..........................[2]
subtract eq. [2] from [1] to evaluate (d-b) by substituting the values of b and d
d-b=a+x
Quantity A= a and Quantity B=a+x
clearly choice b is the answer
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Re: d > c [#permalink] New post   27 Aug 2019, 08:09
1
Building on what others have said.

a + b = c {External Angle Theorem}

d > c {given}

therefore if we combine the two we get:

d > c = a + b

therefore (by transitive properties)

d > a + b

d - b > a

therefore answer is B
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Re: d > c [#permalink] New post   31 Aug 2019, 19:39
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Very easy c=a+b (triangle property) as d>c hence d> a+b or rearranging d-b>a
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Re: d > c [#permalink] New post   31 May 2021, 04:05
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C is exterior angle for triangle on top
c=a+b
d>c given
d>a+b
d-b>a hence QtyB is greater
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Re: d > c [#permalink] New post   22 Jun 2021, 08:22
1
Because an exterior angle of a triangle is equal to the sum of the two
opposite interior angles of the triangle (in this case, the top small triangle), c =
a + b.
Therefore, d > c and a + b = c taken together imply that d > a + b.
Subtract b from both sides: d – b > a.
Quantity B is greater.
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Re: d > c [#permalink] New post   26 Jun 2021, 04:08
Solution:

Angle supplementary to d will be 180-d; angle supplementary to c will be 180-c

Thus, the top most triangle will be: a+b+(180-c)=180
a+b+180-c=180
a+b-c=0
Therefore, a=c-b

Now, we can substitute the above in Qty A
Qty A: c-b
Qty B: d-b

Adding b will leave us with c & d
And as we know c<d

Qty A<Qty B

IMO B

Hope this helps!
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Re: d > c [#permalink] New post   17 Nov 2024, 06:02
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Re: d > c [#permalink]
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