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The value of land increases by a% during June and decreases by b%

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The value of land increases by a% during June and decreases by b% [#permalink]

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The value of land increases by a% during June and decreases by b% during July. If the value of the land is the same at the end of July as at the beginning of June, what is b in terms of a?


A. \(\frac{200a}{(100+2a)}\)

B. \(\frac{100a}{(100+a)}\)

C. \(\frac{a(2+a)}{(1+a)^2}\)

D. \(\frac{a(200+a)}{10000}\)

E. \(\frac{2a}{1+2a}\)
[Reveal] Spoiler: OA

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Last edited by Bunuel on 21 Oct 2017, 03:53, edited 1 time in total.
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Re: The value of land increases by a% during June and decreases by b% [#permalink]

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sanjoo wrote:
The value of land increases by a% during June and decreases by b% during July. If the value of the land is the same at the end of July as at the beginning of June, what is b in terms of a?

1) 200a/100+2a
2) 100a/100+a
3) A(2+a)/(1+a)2
4) A(200+a)/10000
5) 2a/a+2a


The price in June = \(p\).
The price in July = \(p(1+\frac{a}{100})(1-\frac{b}{100})\).

\(p = p(1+\frac{a}{100})(1-\frac{b}{100})\);

\(1 =\frac{100+a}{100}*\frac{100-b}{100}\);

\(b=100 - \frac{10,000}{100+a}=\frac{100a}{100+a}\).

Answer: B.
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Re: The value of land increases by a% during June and decreases by b% [#permalink]

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New post 07 Jan 2014, 09:07
sanjoo wrote:
The value of land increases by a% during June and decreases by b% during July. If the value of the land is the same at the end of July as at the beginning of June, what is b in terms of a?

1) 200a/100+2a
2) 100a/100+a
3) A(2+a)/(1+a)2
4) A(200+a)/10000
5) 2a/a+2a




let the value of land be : x
it is increased by a%, new value= (x)+(ax/100)
now, it is decreased by b%, such that it equals the initial value
hence final value of land= x(1+a/100) - x(1+a/100)(b/100)= x(1+a/100)(1-b/100)=x
solving for b you get b=100a/(100+a)

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Re: The value of land increases by a% during June and decreases by b% [#permalink]

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New post 07 Jan 2014, 21:13
sanjoo wrote:
The value of land increases by a% during June and decreases by b% during July. If the value of the land is the same at the end of July as at the beginning of June, what is b in terms of a?

A. 200a/(100+2a)
B. 100a/(100+a)
C. a(2+a)/(1+a)2
D. a(200+a)/10000
E. 2a/a+2a


You can also use the formula of total % change in case of two successive % changes

Total % change = a + b + ab/100 where a and b are the successive % changes.

0 = a - b - ab/100 (because b is a decrease so we write it as -b)
Separating the variables, we get
b(1 + a/100) = a
b = 100a/(100 + a)

For more on this formula, check: http://www.veritasprep.com/blog/2011/02 ... e-changes/
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Re: The value of land increases by a% during June and decreases by b% [#permalink]

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New post 07 Sep 2016, 19:30
Hi All,

This is a relatively rare concept on the GMAT, but there are certain percentages that will "offset" one another in the way that this question describes. The simplest pairing is a 25% increase will be offset by a 20% decrease.

Here's the proof:

Starting value = 100
25% increase = 100 + (.25)(100) = 125
20% decrease = 125 - (.2)(125) = 100
Ending value = 100

So we would be looking for an answer that equals 20 when A=25. While the answers might appear 'complex', you can actually avoid much of the 'math' if you just fill in the parts and take a good look at what you have...

Answer A: (200)(25)/(150) ... since 200>150, this answer will be greater than 25. ELIMINATE A.

Answer B: (100)(25)/125) = (100)(1/5) = 20 This is a MATCH.

Answer C: (25)(27)/(26)2 ... nothing 'cancels out', so this cannot = 20. ELIMINATE C.

Answer D: (25)(225)/10000... the 'units' digit of the numerator is a 5; when dividing by 10,000, this won't end in a 0. ELIMINATE D.

Answer E: (50/25) + 50 = 52. ELIMINATE E.

Final Answer:
[Reveal] Spoiler:
B


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Re: The value of land increases by a% during June and decreases by b% [#permalink]

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Re: The value of land increases by a% during June and decreases by b%   [#permalink] 14 Oct 2017, 08:11
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