Mr. Odusote owns two kinds of stock shares: r shares of stock X and

Question

Mr. Odusote owns two kinds of stock shares: r shares of stock X and r shares of stock Y. Stock X yields an annual dividend of 2%, while stock Y yields an annual dividend of 6%. If Mr. Odusote were to sell all or his shares of stock X and use that money to purchase shares of stock Y, by what percent would his annual dividend increase?

(1) Each share of stock X costs twice as much as each share of stock Y.
(2) Each share of stock Y costs $45.

(1) Each share of stock X costs twice as much as each share of stock Y.
(2) Each share of stock Y costs $45.

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hr1212 · Answer

Holding of stock X = r*Cx
Dividend of stock X = r*Cx*0.02

Holding of stock Y = r*Cy
Dividend of stock Y = r*Cy*0.06

Total initial dividend = r*Cx*0.02 + r*Cy*0.06

After switching holding of X to Y, new annual dividend = 0.06*(r*Cx + r*Cy)

Percentage increase =  \frac{ 100*(0.06*(r*Cx + r*Cy) - (r*Cx*0.02 + r*Cy*0.06))}{r*Cx*0.02 + r*Cy*0.06} = \frac{200Cx}{Cx + 3Cy}

Statement 1 - Cx = 2Cy

Percentage increase = 400/5 = 80%

Hence, sufficient.

Statement 2 - Cy = $45

We don't know the value of Cx to calculate percentage increase. Hence, insufficient.

IMO: A

sujoykrdatta · Answer

Dividend = Investment * rate of dividend / 100
Since the % divided is given for both shares, we just need to have some idea about the investment made in each stock. 
Since the Question asks about the "Percent increase" in divided, it would be sufficient to know the ratio of investments made.

S1: Since the price of X is twice of that of Y, while the no. of shares are the same, the investment under X was twice of that of Y. 
So, let the investments under X and Y be $2m and $m respectively

Since Mr O. sells his investment in X and purchases Y, his new investment in Y would be the same as the old investment under X

Note: Investment = Price per share * number of shares

Thus, initial dividend = 2% of 2m + 6% of m = 4% of m + 6% of m = 10% of m
Final dividend = 6% of 2m + 6% of m = 12% of m + 6% of m = 18% of m
=> Percent increase = (8% of m)/(10% of m) * 100 = 80% - Sufficient

S2: The share price is neither necessary nor sufficient

Ans A

Whoisdmx15 · Answer

Statement I: As X costs twice as Y, and as original qunatities are same, hence we cane buy twicce as many Y stocks i.e 2r.

Now Original Dividend: (Let cost of each Y share be "k"): = r*2*k*.02 + r*k*.06
New Dividend: (As we now have 2r+r= 3r Y stocks)= 3*r*k*.06
Solving we get (cancelling out all common variables) 
Original Dividend= .1* variables
New Dividend= .18* variables
Hence % increase= .08/.1*100 = 80%

Satement II: Only gives cost of Y, no info on X, hence can't compute how many new Y shares we get to buy.

Hence IMO Ans A

Shin0099 · Answer

"Mr. Odusote owns two kinds of stock shares: r shares of stock X and r shares of stock Y. Stock X yields an annual dividend of 2%, while stock Y yields an annual dividend of 6%. If Mr. Odusote were to sell all or his shares of stock X and use that money to purchase shares of stock Y, by what percent would his annual dividend increase?"

According to the question, we are given the number of shares and the dividend.

Whats missing to get to the returns (in percent), is a hint about the share of two stocks in the portfolio. 
(From now on, we just assume, that r = 1)

What we need is any hint about both prices.

(1) Each share of stock X costs twice as much as each share of stock Y.

What we can get from that is, that X = 2Y

With this information we are able to calculate: 
2Y*0.02 + Y*0.06 = 0.1Y

In the case of a reallocation we get:

3Y*0.06 = 0.18Y

That leads us to a percentage change of: 0.08Y/0.1Y = 80%

In general, every relationship between the prices should be enough to assume, that in case the same amount is hold and the returns are clear, possible percentage changes could be calculated.

(2) Each share of stock Y costs $45.

That information alone is not enough to lead to any conclusion, as we price of X is missing.

(1) + (2) is solvable, but as 2 is not necessary and the relevant variable is the percentage change, (1) is the solution. 
If the question would ask about an absolute number, the world would seem different.

Mr. Odusote owns two kinds of stock shares: r shares of stock X and

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GMAT Data Sufficiency (DS) Questions

Mr. Odusote owns two kinds of stock shares: r shares of stock X and

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