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RaghavKhanna
Total amount invested = $100,000
Stocks = S
Bonds = 100,000 - S

Statement 1:
Amount of stocks diverted to bonds = 0.75S
Amount of bonds diverted to stocks = (100,000 - S)*0.75 = 75000 - 0.75S

Amount of stocks = 0.25S + 75000 - 0.75S
And,
Amount of bonds = 25000 + 0.25S + 0.75S

You have a sign error in your analysis of Statement 1 (it should be a minus, not a plus), when computing the bond value, and there's a similar error in Statement 2 (you divided 100,000 by 4 instead of 2 and also flipped a sign). Conceptually speaking, using either Statement, it must be possible that S = B, because we're doing identical things to both investments and ending up with equal amounts, so any solution that proves S has a unique value different from $50,000 cannot be right. The only question we need to answer is whether it's also possible that S and B are unequal, i.e. whether it's possible S can take on other values besides $50,000.

From Statement 1, if he plans to invest $S in stock and $B in bonds, then when he transfers 3/4 of his stock investment to bonds, he'll be investing only $S/4 in stock. But then he adds to that 3/4 of his bond investment, so he adds to that $3B/4. So if he changes his plans as per Statement 1, he'll be investing S/4 + 3B/4 in stock, and similarly will be investing B/4 + 3S/4 in bonds. If these are equal we get this equation:

S/4 + 3B/4 = B/4 + 3S/4
B = S

from which we know S = $50,000.

From Statement 2, transfering half of each investment to the other, the new investment in stock becomes S/2 + B/2, and the new investment in bonds becomes B/2 + S/2. Those are obviously equal no matter what, so S and B can be anything, and Statement 2 gives us no information. So the answer is A.

I object to the wording of Statement 1 though. Solving, we find that he plans to invest $50,000 in stocks and $50,000 in bonds. We then learn that if he "changes his plans" he will be investing $50,000 in stocks and $50,000 in bonds. That is not a change from his previous plans.
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IanStewart
RaghavKhanna
Total amount invested = $100,000
Stocks = S
Bonds = 100,000 - S

Statement 1:
Amount of stocks diverted to bonds = 0.75S
Amount of bonds diverted to stocks = (100,000 - S)*0.75 = 75000 - 0.75S

Amount of stocks = 0.25S + 75000 - 0.75S
And,
Amount of bonds = 25000 + 0.25S + 0.75S

You have a sign error in your analysis of Statement 1 (it should be a minus, not a plus), when computing the bond value, and there's a similar error in Statement 2 (you divided 100,000 by 4 instead of 2 and also flipped a sign). Conceptually speaking, using either Statement, it must be possible that S = B, because we're doing identical things to both investments and ending up with equal amounts, so any solution that proves S has a unique value different from $50,000 cannot be right. The only question we need to answer is whether it's also possible that S and B are unequal, i.e. whether it's possible S can take on other values besides $50,000.

From Statement 1, if he plans to invest $S in stock and $B in bonds, then when he transfers 3/4 of his stock investment to bonds, he'll be investing only $S/4 in stock. But then he adds to that 3/4 of his bond investment, so he adds to that $3B/4. So if he changes his plans as per Statement 1, he'll be investing S/4 + 3B/4 in stock, and similarly will be investing B/4 + 3S/4 in bonds. If these are equal we get this equation:

S/4 + 3B/4 = B/4 + 3S/4
B = S

from which we know S = $50,000.

From Statement 2, transfering half of each investment to the other, the new investment in stock becomes S/2 + B/2, and the new investment in bonds becomes B/2 + S/2. Those are obviously equal no matter what, so S and B can be anything, and Statement 2 gives us no information. So the answer is A.

I object to the wording of Statement 1 though. Solving, we find that he plans to invest $50,000 in stocks and $50,000 in bonds. We then learn that if he "changes his plans" he will be investing $50,000 in stocks and $50,000 in bonds. That is not a change from his previous plans.

IanStewart

That is a change in plan since he didn't invest an equal amount of money before. He invested a certain amount of money. Just a subtle change in language.

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Bunuel
Manfred plans to invest a certain amount of money in stocks and a certain amount in bonds. If he plans to invest a total of $100,000 in stocks and bonds, how much money does he plan to invest on stocks?


(1) If Manfred were to change his plans such that 75% of the planned investment in stocks is diverted to bonds and 75% of the planned investment in bonds is diverted to stocks, then his investment in stocks would be equal to his investment in bonds.

(2) If Manfred were to change his plans such that 50% of the planned investment in stocks is diverted to bonds and 50% of the planned investment in bonds is diverted to stocks, then his investment in stocks would be equal to his investment in bonds.

 
IMO A is the correct answer.

Let's say investment in stocks = S, investment in bonds = B

Since the total amount of investment is $100,000 then S + B = $100,000

(1) If he do it this way then:
The NEW investment in stocks = 25% S + 75% B
The NEW investment in bonds = 25% B + 75% S
Since these NEW investments are equal, we have 25% S + 75% B = 25% B + 75% S
Therefore 50% B = 50% S, which means B = S = $100,000 / 2 = $50,000
--> (1) is SUFFICIENT

(2) If he do it this way then:
The NEW investment in stocks = 50% S + 50% B
The NEW investment in bonds = 50% B + 50% S
Since these NEW investments are always equal, this new information do not provide any clue to solve S and B
--> (2) is INSUFFICIENT­
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Kindly see the attachment. The question is long due to the length but the best way is to create equations.
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Method 1.png
Method 1.png [ 361.62 KiB | Viewed 2396 times ]

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Nice question - classic pitfall, as post solving first statement, one can quickly move ahead thinking similar equation will work for second statement also - thus marking option C.
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