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Last year Mrs. Long received $160 in dividends on her shares [#permalink]

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20 Jul 2004, 14:58

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Last year Mrs. Long received $160 in dividends on her shares of Company X stock, all of which she had held for the entire year. If she had had 12 more shares of the stock last year, she would have received $15 more in total annual dividends. How many shares of the stock did she have last year?

Re: Last year Mrs. Long received $160 in dividends on her shares [#permalink]

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20 Jul 2004, 15:43

A

1. Realize that if there were 12 more shares and 15 more dollars, the shares are worth more than a dollar a share, so there would have to be less than 160. Cancel out c, d, e.

2. Now there are at least three ways of doing it, all of which depend on who you are and how you think. I'll put as many below as I can think of - I think they're all fine and expediant. Remember - if you're spending time looking for the most sophisticated way, you could be just wasting time, especially if you know how to do it algebraically.

Method 1: Algebra
160/x = 175/(x+12)

That's because each stock is worth the same, so if you divide the 160 by the number of shares, or 175 by the number of shares plus 12, you get the same answer. Solve for x = 128.

Method 2: 12 more shares cost $15, so that means each one cost $1.25. So 160/1.25. To do this quickly, convert 1.25 into 5/4 (I LOVE FRACTIONS!) Now you've got 160/(5/4) = 160x4/5 = 32x4 = 128.

Method 3: Once you've cancelled c,d,e, you can plug in a or b and see what happens. One will work and one won't, but either way, after just one time through, you'll have your answer.

Last year Mrs. Long received $160 in dividends on her shares of Company X stock, all of which she had held for the entire year. If she had had 12 more shares of the stock last year, she would have received $15 more in total annual dividends. How many shares of the stock did she have last year?

(A) 128 (B) 140 (C) 172 (D) 175 (E) 200

A - 128

$15 for 12 shares - thus $1.25 per share - so 160/1.25 = 128

Last year Mrs. Long received $160 in dividends on her shares of Company X stock, all of which she had held for the entire year. If she had had 12 more shares of the stock last year, she would have received $15 more in total annual dividends. How many shares of the stock did she have last year?

lets consider Mrs Long has "n" shares of Company X. dividend is paid on the basis of the number of shares held for a certain duration (here one year) then dividend per share is 160/n.

q says that if she had 12 more shares she would had got 15$ more. so 160/n = (160+15)/(n+12). solving this we get n=128.

12 more shares = $15 more is 15/12 to get the per share cost. That's 1.25, or 5/4 per share

so \(\frac{5}{4}=\frac{160}{n}\) = \(\frac{4*160}{5}\) = 4*32 = 128.

reduce where you can

Adigmat wrote:

Last year Mrs. Long received $160 in dividends on her shares of Company X stock, all of which she had held for the entire year. If she had had 12 more shares of the stock last year, she would have received $15 more in total annual dividends. How many shares of the stock did she have last year? (A) 128 (B) 140 (C) 172 (D) 175 (E) 200

_________________

------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

Re: Last year Mrs. Long received $160 in dividends on her shares [#permalink]

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26 Apr 2015, 04:31

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Re: Last year Mrs. Long received $160 in dividends on her shares [#permalink]

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24 Jun 2016, 08:58

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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