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Company A owns 40 percent of the stock in the XYZ Corporation. Company

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Company A owns 40 percent of the stock in the XYZ Corporation. Company [#permalink]

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New post 02 Nov 2017, 22:07
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Company A owns 40 percent of the stock in the XYZ Corporation. Company B owns 15,000 shares. Company C owns all the shares not owned by company A or B. How many shares of stock does company A own if company C has 25 percent more shares than company A?

(A) 45,000
(B) 50,000
(C) 60,000
(D) 75,000
(E) 90,000
[Reveal] Spoiler: OA

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Re: Company A owns 40 percent of the stock in the XYZ Corporation. Company [#permalink]

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New post 02 Nov 2017, 22:56
Bunuel wrote:
Company A owns 40 percent of the stock in the XYZ Corporation. Company B owns 15,000 shares. Company C owns all the shares not owned by company A or B. How many shares of stock does company A own if company C has 25 percent more shares than company A?

(A) 45,000
(B) 50,000
(C) 60,000
(D) 75,000
(E) 90,000


Let the total shares of XYZ corporation be x.

Since Company A owns 40% of the stock, it must own 0.4x of the share
It has been given that the Company B has 15000 shares
Company C owns the remaining shares, which is \(x - (0.4x + 15000) = 0.6x - 15000\)

Now, we know that the Company C owns 25% more shares than company A

\(0.6x - 15000 = \frac{5}{4}(0.4x)\) => \(4(0.6x - 15000) = 2x\) => \(2.4x - 60000 = 2x\) => \(0.4x = 60000\)

Therefore, \(x = \frac{60000}{0.4} = 150000\)

The company A owns 0.4x or 60000 shares(Option C)
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Company A owns 40 percent of the stock in the XYZ Corporation. Company [#permalink]

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New post 04 Nov 2017, 18:05
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Bunuel wrote:
Company A owns 40 percent of the stock in the XYZ Corporation. Company B owns 15,000 shares. Company C owns all the shares not owned by company A or B. How many shares of stock does company A own if company C has 25 percent more shares than company A?

(A) 45,000
(B) 50,000
(C) 60,000
(D) 75,000
(E) 90,000

A owns 40 percent of shares, S
B owns 15,000 shares

C owns 25 percent more than A
C = 1.25(40) = 50 percent of the shares

C and A together own 40 + 50 = 90 percent of the shares

B owns 10 percent, B owns 15,000 S
15,000 = .10S
S = \(\frac{15,000}{.10}\) = 150,000

A = 40 percent of 150,000 = 60,000 shares

Answer C

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Re: Company A owns 40 percent of the stock in the XYZ Corporation. Company [#permalink]

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New post 06 Nov 2017, 17:04
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Expert's post
Bunuel wrote:
Company A owns 40 percent of the stock in the XYZ Corporation. Company B owns 15,000 shares. Company C owns all the shares not owned by company A or B. How many shares of stock does company A own if company C has 25 percent more shares than company A?

(A) 45,000
(B) 50,000
(C) 60,000
(D) 75,000
(E) 90,000


We can let the total number of shares = n. Thus, A = 0.4n, B = 15,000, and C = 1.25(0.4n) = 0.5n. Now we can create the following equation:

0.4n + 15,000 + 0.5n = n

15,000 = 0.1n

150,000 = n

Thus, A owns 0.4 x 150,000 = 60,000 shares.

Answer: C
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Re: Company A owns 40 percent of the stock in the XYZ Corporation. Company   [#permalink] 06 Nov 2017, 17:04
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