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John and Mary own shares of stock in a certain company. Does [#permalink]
25 Dec 2006, 05:40

4

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

69% (01:42) correct
31% (00:47) wrong based on 109 sessions

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

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.

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

John and Mary own shares of stock in a certain company. Does [#permalink]
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

Re: John and Mary own shares of stock in a certain company. Does [#permalink]
23 Feb 2012, 08:08

Expert's post

2

This post was BOOKMARKED

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.

Re: John and Mary own shares of stock in a certain company. Does [#permalink]
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.

Re: John and Mary own shares of stock in a certain company. Does [#permalink]
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. _________________

Re: John and Mary own shares of stock in a certain company. Does [#permalink]
20 Jun 2015, 23:01

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