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Over a certain time period, did the number of shares of

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

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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.
[Reveal] Spoiler: OA
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Re: Data Sufficiency [#permalink]

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New post 17 Jul 2010, 10:27
I chose A...but it isnt the correct answer.
Logic :
(#of shares of stocks/Tot shares+bonds)-->increases
Hence number of shares of stocks would have a direct dependency, hence it increase as well.
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Over a certain time period, did the number of shares of [#permalink]

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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 did \(s\) 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. \(\frac{s}{s+b}\) 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.

Answer: C.

Hope it's clear.
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Re: Over a certain time period, did the number of shares of [#permalink]

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

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

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

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1) The ratio of shares:total could increase by adding more shares or by reducing the number of bonds. Insufficient.

2) The total number could increase by adding shares, adding bonds, or both. Insufficient.

Combined, we know the total number of shares and bonds went up, and we know the ratio of shares:total went up. The only way both statements can be true is if the number of shares increased. Thus, we need both statements.
Hence C.
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Re: Over a certain time period, did the number of shares of   [#permalink] 08 Feb 2017, 19:36
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