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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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Updated on: 21 Oct 2017, 04:53
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82% (02:26) correct 18% (01:57) wrong based on 119 sessions

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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. $$\frac{2a}{1+2a}$$

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Originally posted by sanjoo on 07 Jan 2014, 09:29.
Last edited by Bunuel on 21 Oct 2017, 04:53, 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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07 Jan 2014, 10:04
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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 = $$p(1+\frac{a}{100})(1-\frac{b}{100})$$.

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

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

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

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

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07 Jan 2014, 10:07
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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07 Jan 2014, 22:13
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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07 Sep 2016, 20:30
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.

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

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14 Oct 2017, 09:11
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