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Over a certain time period, did the number of shares of [#permalink]

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09 Jun 2009, 06:11

3

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00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

60% (01:29) correct
40% (00:26) wrong based on 65 sessions

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Over a certain time period, did the number of shares of stock in Ruth's portfolio increase?

(1) Over the time period, the ratio of number of shares of stock to the total number of shares of stocks and bonds in Ruth's portfolio increased. (2) Over the time period, the total number of shares of stocks and bonds in Ruth's portfolio increased.

I would go for 'A'. The first statement is sufficient. Let say, S- Stocks and B- Bonds 1) S/S+B has increased which can only happen if the numerator increases, therefore, S increases. 2) S+B increase. Can be in S or B or both.
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Re: Over a certain time period, did the number of shares of [#permalink]

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26 Jul 2012, 23:40

venmic wrote:

i vvonder vvhat is really the concept being tested here ..

I think maybe "How to compare two fractions"?

(1) For example, \(S/(S+B)\) can increase if S increases and B stays the same, but also if S stays the same and B decreases (she can sell some bonds). Therefore, (1) is not sufficient.

(2) Obviously, not sufficient. S+B can also increase by increasing B, while S stays the same.

(1) and (2) together: We have to compare \(\frac{S_1}{S_1+B_1}\) to \(\frac{S_2}{S_2+B_2}\). If \(S_2+B_2 > S_1+B_1\) (the total number increased), then to have the second fraction larger than the first we need a larger \(S_2\), or increase in S. Otherwise, the second fraction is going to be smaller, because it has a larger denominator.

Answer, definitely C.
_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Over a certain time period, did the number of shares of stock in Ruth's portfolio increase?

Let the # of stock be \(s\) and the # of bonds be \(b\). The question is does \(s\) increased?

(1) Over the time period, the ratio of number of shares of stock to the total number of shares of stocks and bonds in Ruth's portfolio increased. \(\frac{s}{s+b}\) increased. Not sufficient, as for example it's possible that \(s\) increased \(b\) remained the same or \(s\) remained the same and \(b\) decreased.

(2) Over the time period, the total number of shares of stocks and bonds in Ruth's portfolio increased. \(s+b\) increased. Clearly insufficient.

(1)+(2) \(\frac{s}{s+b}\) increased and \(s+b\) (denominator) also increased, so it must be true that \(s\) (nominator) increased too. Sufficient.

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