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

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

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

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.

Such a stupid mistake..

Thanks Karishma for pointing and clearing out my doubt!

J>M
(1) M > 500, not sufficient
(2) J = 2M - 400, not sufficient
(1)+(2) M > 500 let's say 501, J= 2*501-400=602 --> the larger J the larger will be the difference between M and J. Sufficient
Answer C

Algebra works well here, but you can also think about Statement 2 more conceptually. We're doubling Mary's shares, then subtracting 400. We really just want to know which of those two operations will have the larger effect. When Mary has exactly 400 shares, they will have the same effect, and then Mary and John have the same number of shares. If Mary has more than 400 shares, doubling will add more shares than the 400 we're taking away, so John will have more shares than Mary. If Mary has less than 400 shares, doubling will add less than 400, and John will have fewer shares than Mary. So Statement 2 is not sufficient, but as long as Statement 1 tells us Mary has more than 400 shares, the answer will be C, and Statement 1 tells us even more than that.

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