annual dividend

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mehrasa: Master | Next Rank: 500 Posts; Posts: 279; Joined: Fri Nov 05, 2010 5:43 pmFollowed by: 1 member; Thanked: 15 times

by mehrasa » Fri Sep 30, 2011 12:06 am

Mr. Smith have two kinds of stock share, r from stock x and r from stock y..stock x yield annual dividend of %2 and stock y yield %6 annual dividends. if he decide to sell all stock x and buy stock y. by what percent his annual yield increase?

1)each shares of x cost twice as much as stock y
2) each share of stock Y is $45

[spoiler]OA: A[/spoiler]I would like to know how we can solve the statement A mathematically.

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Source: Beat The GMAT — Data Sufficiency | Fri Sep 30, 2011 12:06 am

amit2k9: Master | Next Rank: 500 Posts; Posts: 461; Joined: Tue May 10, 2011 9:09 amFollowed by: 3 members; Location: pune; Thanked: 36 times

by amit2k9 » Fri Sep 30, 2011 1:26 am

a. considering r=1
x costing 200 units and y costing 100 units

seling x gives 200 units there by purchasing 2 more Y shares.
thus total 3 Y shares will give annual return of 6% = 1.06*300 = 318
original annual return of Y share = 1.06 * 100 = 106
thus increase % = (318-106)/106 * 100.

OA has to be A indeed.

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Fri Sep 30, 2011 1:30 am

Assume I have 100 stocks of each type (=r)

Cost of X = X
Cost of Y = Y

Hence,

100X + 100 Y = Total Invested

102X+106Y = Total after annual dividends

(1) Given, X = 2Y.

Therefore,

200Y + 100 Y = 300Y (Total Invested)

318 Y = Total after dividends.

From, this we can find % increase. Hence, SUFFICIENT

(2) Given, Y = 45

We dont know X and hence we cannot find how many stocks of X he sold to buy equivalent Y stocks. Not Sufficient.

A IMO

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Fri Sep 30, 2011 1:34 am

I think original annual yield for both X and Y needs to be considered.
X would have got him 204 and Y 106, so Total = 310.

Now he gets 318, so it shld be 318-310/310 IMO

amit2k9 wrote:a. considering r=1
x costing 200 units and y costing 100 units

seling x gives 200 units there by purchasing 2 more Y shares.
thus total 3 Y shares will give annual return of 6% = 1.06*300 = 318
original annual return of Y share = 1.06 * 100 = 106
thus increase % = (318-106)/106 * 100.

OA has to be A indeed.

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