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If the total price of n equally priced stock shares is p,

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If the total price of n equally priced stock shares is p, [#permalink]

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New post 25 Nov 2010, 09:30
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If the total price of n equally priced stock shares is p, what is p?

(1) If the price of each share were to increase by $1, p would increase by $40.
(2) If the price of half of the shares increased by 25 percent each, p would increase by $10.
(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.


I am not sure about the OA can some one explain this answer to me
[Reveal] Spoiler: OA

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Re: Tough Algebra DS [#permalink]

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New post 25 Nov 2010, 14:01
I hope I read the question right, I got a bit confused with statement #2.

From the question, let n be the number of stocks, x be the price of each stock, and p is…what p is.

So our equation is nx = p, and we want n and x

1) x increase by $1, then p increase by $40, and simply implies n = 40. Not sufficient since we don’t know x

2) 25% price increase for only half of the shares and p increased by 10. So…

(1/2 n * x) + (1/2 n * 5/4 x) = p + 10
9/8 nx = p + 10

Since: nx = p, substitute nx with p in the above equation

p = 80. Sufficient.
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Re: Tough Algebra DS [#permalink]

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New post 25 Nov 2010, 16:04
rxs0005 wrote:
If the total price of n equally priced stock shares is p, what is p?

(1) If the price of each share were to increase by $1, p would increase by $40.
(2) If the price of half of the shares increased by 25 percent each, p would increase by $10.

(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.


I am not sure about the OA can some one explain this answer to me


Let us assume the price of each stock to be x, then we are told that nx = p.

Statement 1:\(n (x+1) = p + 40. nx + n = p + 40\) But we know that nx = p, which means that n = 40. Insufficient.

Statement 2: \(\frac{nx}{2} + \frac{5nx}{4*2} = p + 10\)
\(\frac{4nx}{8} + \frac{5nx}{8} = p + 10\)

\(\frac{9nx}{8} = p + 10.\) But we know that nx = p. Thus we have \(\frac{9p}{8} - p = 10.\) Hence p = 80. This is sufficient and hence the answer is B.
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Re: Tough Algebra DS [#permalink]

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New post 27 Nov 2010, 22:05
rxs0005 wrote:
If the total price of n equally priced stock shares is p, what is p?

(1) If the price of each share were to increase by $1, p would increase by $40.
(2) If the price of half of the shares increased by 25 percent each, p would increase by $10.
(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.


I am not sure about the OA can some one explain this answer to me


the total price of n equally priced stock shares is p

This statement tells us that the price of each share is p/n.

Stmnt 1: If the price of each share were to increase by $1, total price would increase by $40. This means 40 shares must have contributed an extra dollar each so n = 40. But no information about p. Not Sufficient.
Stmnt 2: If the price of half of the shares increased by 25 percent each, p would increase by $10
'Price of half the shares' is p/2. 25% of this is equal to $10. So (p/2)*(25/100) = 10.
p = 80. Sufficient.

Answer (B).
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Re: Tough Algebra DS   [#permalink] 27 Nov 2010, 22:05
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