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

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

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09 Jun 2009, 07:11
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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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: over-a-certain-time-period-did-the-number-of-shares-of-97397.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 Jul 2012, 00:55, edited 1 time in total.
Edited the question and added the OA.
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09 Jun 2009, 08:36
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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09 Jun 2009, 22:30
I would go for 'E'.
Let say, S- Stocks and B- Bonds
1) S/S+B has increased .B might decrease which can increase the ratio and we have no clue of B

2) S+B increase. Can be in S or B or both.

Combining does not tell anything abt. B
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09 Jun 2009, 23:00
I agree with above explanation. Answer should be E. The ratio can even increase when S actually decreased.

E.g let S = 500 and B = 500. Ration of S:total = 1:2

Suppose S decreased by 100 and B decreased by 400,
new ratio of S:total = 400:500 = 4:5
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10 Jun 2009, 02:43
s/s+b

combingin 1 & 2, S+b is increased.. and to keep the ratio more, S has to be increased.

hence C.
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10 Jun 2009, 02:44
bigoyal wrote:
I agree with above explanation. Answer should be E. The ratio can even increase when S actually decreased.

E.g let S = 500 and B = 500. Ration of S:total = 1:2

Suppose S decreased by 100 and B decreased by 400,
new ratio of S:total = 400:500 = 4:5

you are missing out the option B which says that total is also increased.
in this case the total comes to 500 which is less than 1000.
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10 Jun 2009, 02:46
mdfrahim wrote:
I would go for 'E'.
Let say, S- Stocks and B- Bonds
1) S/S+B has increased .B might decrease which can increase the ratio and we have no clue of B

2) S+B increase. Can be in S or B or both.

Combining does not tell anything abt. B

when comined,

if B is increased, to maintain an increased ration, S has to be increased.
thusoption shud be C
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13 Jun 2009, 03:09
Neochronic wrote:
mdfrahim wrote:
I would go for 'E'.
Let say, S- Stocks and B- Bonds
1) S/S+B has increased .B might decrease which can increase the ratio and we have no clue of B

2) S+B increase. Can be in S or B or both.

Combining does not tell anything abt. B

when comined,

if B is increased, to maintain an increased ration, S has to be increased.
thusoption shud be C

Well explained!! OA is C.
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Re: Over a certain time period, did the number of shares of [#permalink]

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27 Jul 2012, 00:15
i vvonder vvhat is really the concept being tested here ..
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Re: Over a certain time period, did the number of shares of [#permalink]

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27 Jul 2012, 00:40
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.

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27 Jul 2012, 00:43
bigoyal wrote:
I agree with above explanation. Answer should be E. The ratio can even increase when S actually decreased.

E.g let S = 500 and B = 500. Ration of S:total = 1:2

Suppose S decreased by 100 and B decreased by 400,
new ratio of S:total = 400:500 = 4:5

By decreasing both S and B your total decreased, not increased, so (2) is not fulfilled.
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Re: Over a certain time period, did the number of shares of [#permalink]

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27 Jul 2012, 00:55
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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 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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: over-a-certain-time-period-did-the-number-of-shares-of-97397.html
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Re: Over a certain time period, did the number of shares of   [#permalink] 27 Jul 2012, 00:55
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# Over a certain time period, did the number of shares of

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