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In a specific market, only three competitors, X, Y and Z operate. Last

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Bunuel
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In a specific market, only three competitors, X, Y and Z operate. Last [#permalink] New post   27 Jan 2021, 09:15
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In a specific market, only three competitors, X, Y and Z operate. Last year, the market share of the firm Y was 10% more than that of X. In a year’s time, both the firms X and Y increased their respective market share by 20%. This year, the market share of the firm Y is five times that of Z. How much was the market share of the firm Z last year, if the total sales remained constant over these two years?

(A) 40%
(B) 28%
(C) 25%
(D) 23%
(E) 20%
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C
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Vivor
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Re: In a specific market, only three competitors, X, Y and Z operate. Last [#permalink] New post   27 Jan 2021, 11:33
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Let last year's market shares of X, Y, Z be \(x_1\)%, \(y_1\)%, \(z_1\)%
And, this year's market shares of X, Y, Z be \(x_2\)%, \(y_2\)%, \(z_2\)%

Last year, Share(Y) = 10% more than Share(X)
or, \(y_1\) = 1.1\(x_1\)

In a year's time, shares of both X & Y increased by 20%
or, \(x_2\) = \(1.2x_1\)
and, \(y_2\) = \(1.2y_1\)

This year, Share(Y) = 5 times Share(Z)
or, \(y_2\) = \(5z_2\)

\(x_2+y_2+z_2=100 => 1.2x_1+1.2y_1+\frac{y_2}{5} = 100 => 1.2x_1+1.2*1.1x_1+\frac{1.2*1.1x_1}{5} = 100\)
\(x_1=\frac{500}{13.92}\)

\(x_1+y_1+z_1=100\)
or, \(z_1 = 100-x_1-y_1 = 100-x_1-1.1x_1 = 100-2.1x_1 = 100-2.1*\frac{500}{13.92} \approx{25%}\)

Ans is C IMO
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Re: In a specific market, only three competitors, X, Y and Z operate. Last [#permalink] New post   09 Feb 2021, 04:12
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x, y and z for year 1 -> 100, 110, z
x, y and z for year 2 -> 120, 130, 26 , Total = 276.

Total sales remains same thus -> 100 + 110 + z = 276 => z = 66

% share = 66/276*100 => approximately 25%.
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Re: In a specific market, only three competitors, X, Y and Z operate. Last [#permalink] New post   25 Feb 2021, 02:02
HOW you got 130 for y in 2nd year ? should not it be 132 for y in 2nd year after increase of 20% FROM 110?
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Re: In a specific market, only three competitors, X, Y and Z operate. Last [#permalink] New post   07 Nov 2023, 03:03
Hello from the GMAT Club BumpBot!

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Re: In a specific market, only three competitors, X, Y and Z operate. Last [#permalink]
07 Nov 2023, 03:03
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