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The area of field A is 30% greater than that of field B

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The area of field A is 30% greater than that of field B  [#permalink]

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New post 16 Apr 2018, 13:15
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The area of field A is 30% greater than that of field B, and 35% less than that of field C. The area of C is what percent greater than the area of field B?

A. 25%
B. 50%
C. 53,8%
D. 100%
E. 200%

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Re: The area of field A is 30% greater than that of field B  [#permalink]

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New post 16 Apr 2018, 19:07
1
Let B =100
Then A = 30% greater than B = 130
A is 35% less than C
That means A is 65 % of C
Hence C =A*100/65 =130*100/65=200

C -B =200-100=100
(C-B)/B *100 = (200-100)/100 *100 =100%
Hence C is greater than B by 100%

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The area of field A is 30% greater than that of field B  [#permalink]

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New post 16 Apr 2018, 21:44
benejo wrote:
The area of field A is 30% greater than that of field B, and 35% less than that of field C. The area of C is what percent greater than the area of field B?

A. 25%
B. 50%
C. 53,8%
D. 100%
E. 200%

Source: ExpertsGlobal

Find C in terms of B; use A=A
Area of B = B
Area of A = 1.3B
Area of A = .65 C

\(A = A\)
\(1.3 B = .65C\)

\(\frac{C}{B}=\frac{1.3}{.65}\)

\(\frac{C}{B}=\frac{2}{1}\)


C = 2B

C's area is twice the area of B, and "Twice" = 100% greater than.

That is, C is what percent greater than B?

\(C = 2B\)
Percent greater than: \(\frac{New-Old}{Old}*100\)

\((\frac{C-B}{B}*100)=(\frac{2B-B}{B}*100)=\)

\((\frac{B}{B}*100)=(1*100)=100\)
% greater than

Answer D

Choose values
Let area of B = 100
Area of A = 30% greater than B's = 130
Area of C? Work from the other direction

A, 130, is 35 percent less than C
130 = .65C
C = \(\frac{130}{.65} = 200\)

200 is what percent greater than 100?

Percent greater than: \(\frac{New-Old}{Old}*100\)

\((\frac{200-100}{100}*100)=(\frac{100}{100}*100)\)

\(=(1*100)=100\)
% greater than

Answer D
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Re: The area of field A is 30% greater than that of field B  [#permalink]

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New post 19 Apr 2018, 17:00
benejo wrote:
The area of field A is 30% greater than that of field B, and 35% less than that of field C. The area of C is what percent greater than the area of field B?

A. 25%
B. 50%
C. 53,8%
D. 100%
E. 200%


We can let the area of field B = n and thus the area of field A = 1.3n.

Since 1.3n is 35% less than the area of field C, we can create the equation:

1.3n = 0.65C

1.3n/0.65 = C

130n/65 = C

2n = C

We now can determine the area of C is what percent greater than the area of field B:

(2n - n)/n x 100 = 1 x 100 = 100 percent

Alternate Solution:

Let’s let the area of field B to be 100. Since area of field A is 30% greater than the area of field B, area of field A is 1.3 x 100 = 130. Let c denote the area of field C. Since area of field A is 35% less than field C, we must have

0.65c = 130

c - 130/0.65 = 200

Thus, the area of field C is [(200 - 100)/100] x 100 = 100% greater than the area of field A.

Answer: D
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Re: The area of field A is 30% greater than that of field B &nbs [#permalink] 19 Apr 2018, 17:00
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