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John and Mary own shares of stock in a certain company. Does

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John and Mary own shares of stock in a certain company. Does [#permalink] New post 25 Dec 2006, 05:40
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John and Mary own shares of stock in a certain company. Does John own more shares of the company's stock than Mary?

(1) Mary owns more than 500 shares of the company's stock.
(2) The number of shares of the company's stock that John owns is 400 less than twice the number of shares of the company's stock that Mary owns
[Reveal] Spoiler: OA

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 [#permalink] New post 25 Dec 2006, 06:18
I am not sure about your second statement, but if it says that The number of shares of the company's stock that John owns is 400 less than twice the number of shares of the company's stock that Mary owns, then here goes.

I get C.
Let J -- number of stocks owned by John
M -- number of stocks owned by Mary
Question asks J >M?
or J-M >0?


1) A - INSUFF
2) J = 2M - 400

=> J-M = M- 400



=> J-M > 0 when M-400>0 or M>400. Since we dont know M, we cant say if J-M >0.

Together, however, since M>500 means M> 400, we can conclude John has more shares.
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 [#permalink] New post 25 Dec 2006, 08:46
My answer is C

asking: is J > M ?
J : number of stocks that John owns
M : number of stocks that Mary owns


(1) M > 500
---------------
this tells us nothing about how J is compared to M

statement 1 is insufficient


(2) J < 2M - 400
---------------------
Although this statement provide an inequality comparing J and M, yet the appearance of the constant 400 proves nothing about whether J > M.
You can try plugging numbers in the inequality
[ case A: J = 500 , M = 1000 --> J < 1600 true ]
[ Case B: J = 500, M = 470 --> J < 540 true ]

statement 2 is insufficient

(1) + (2) together
------------------------
As long as M > 500, the only case for J < 2M - 400 is when M > J
The cutoff point for this relation is when M = 400 or when J = M = 400, then
J < 800 - 400 = 400
In other words,
J = 2M - 400 --> M = 2M - 400 --> M = 400
For M > 400 --> M > J

Thus, statements 1 and 2 together are sufficient to answer the question

Answer is C
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John and Mary own shares of stock in a certain company. Does [#permalink] New post 23 Feb 2012, 07:14
John and Mary own shares of stock in a certain company. Does John own more shares of the company's stock than Mary?

(1) Mary owns more than 500 shares of the company's stock.
(2) The number of shares of the company's stock that John owns is 400 less than twice the number of shares of the company's stock that Mary owns
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Re: John and Mary own shares of stock in a certain company. Does [#permalink] New post 23 Feb 2012, 08:08
Expert's post
John and Mary own shares of stock in a certain company. Does John own more shares of the company's stock than Mary?

Question: is J>M?

(1) Mary owns more than 500 shares of the company's stock --> M>500. Clearly insufficient, since no info about J.

(2) The number of shares of the company's stock that John owns is 400 less than twice the number of shares of the company's stock that Mary owns --> J=2M-400 --> substitute J in the question --> question becomes: "is 2M-400>M?" --> "is M>400?" We don't know that. Not sufficient.

(1)+(2) From (2) the question became "is M>400?" and (1) says that M>500, thus the answer to the question is YES. Sufficient.

Answer: C.

Hope it's clear.
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Re: John and Mary own shares of stock in a certain company. Does [#permalink] New post 06 Jan 2014, 12:58
but, the question says that john and mary own shares, i.e. both have to own 1 share each, atleast .
Therefore, if mary has even 2 shares, that means john owns 201 shares (2J-400=M).
So if M rises, J will always rise.
So, it answers the quest. stem, John will always have more shares that Mary.

Ans. is B.

Am i Right?
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Re: John and Mary own shares of stock in a certain company. Does [#permalink] New post 06 Jan 2014, 21:52
Expert's post
piug wrote:
but, the question says that john and mary own shares, i.e. both have to own 1 share each, atleast .
Therefore, if mary has even 2 shares, that means john owns 201 shares (2J-400=M).
So if M rises, J will always rise.
So, it answers the quest. stem, John will always have more shares that Mary.

Ans. is B.

Am i Right?


The equation you have come up with is not correct.

"stock that John owns is 400 less than twice the number of shares of the company's stock that Mary owns"
This gives us that J=2M-400
Now if M = 500, J= 600
If M = 300, J = 200
So (B) is not enough alone.
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Re: John and Mary own shares of stock in a certain company. Does [#permalink] New post 07 Jan 2014, 01:40
Such a stupid mistake..

Thanks Karishma for pointing and clearing out my doubt!
Re: John and Mary own shares of stock in a certain company. Does   [#permalink] 07 Jan 2014, 01:40
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