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# An investor purchased a bond for p dollars on Monday. For a certain nu

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An investor purchased a bond for p dollars on Monday. For a certain nu  [#permalink]

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Updated on: 25 May 2018, 18:37
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Difficulty:

95% (hard)

Question Stats:

44% (02:36) correct 56% (02:51) wrong based on 234 sessions

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An investor purchased a bond for p dollars on Monday. For a certain number of days, the value of the bond increased by r percent per day. After this period of constant increase, the bond decreased the next day by q dollars and the investor decided to sell the bond that day for v dollars. When did the investor sell the bond if

$$r = 100*[\sqrt{\frac{(v+q)}{p}} - 1]$$?

A. Two working days later.

B. Three working days later.

C. Four working days later.

D. Five working days later.

E. Six working days later.

Originally posted by 101mba101 on 25 May 2018, 03:03.
Last edited by niks18 on 25 May 2018, 18:37, edited 2 times in total.
Renamed the topic and edited the question.
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An investor purchased a bond for p dollars on Monday. For a certain nu  [#permalink]

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25 May 2018, 09:07
8
101mba101 wrote:
An investor purchased a bond for p dollars on Monday. For a certain number of days, the value of the bond increased by r percent per day. After this period of constant increase, the bond decreased the next day by q dollars and the investor decided to sell the bond that day for v dollars. When did the investor sell the bond if

$$r = 100*[\sqrt{\frac{(v+q)}{p}} - 1]$$?

A. Two working days later.

B. Three working days later.

C. Four working days later.

D. Five working days later.

E. Six working days later.

$$r = 100*[\sqrt{\frac{(v+q)}{p}} - 1]$$

$$=>\frac{r}{100} =\sqrt{\frac{(v+q)}{p}} - 1$$

$$=>\frac{r}{100} +1=\sqrt{\frac{(v+q)}{p}}$$, Now square both sides to get

$$=>(\frac{r}{100}+1)^2 =\frac{(v+q)}{p}$$

$$=>p*(\frac{r}{100}+1)^2 =v+q$$

$$=>p*(\frac{r}{100}+1)^2-q=v$$

Now as he sells at price $$v$$, hence he sells the bond after $$2$$ days of increase and the third day of decrease

Option B
##### General Discussion
VP
Joined: 11 Feb 2015
Posts: 1146
Re: An investor purchased a bond for p dollars on Monday. For a certain nu  [#permalink]

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25 May 2018, 18:15
2
If the brackets are not there then how did you take the 100 on left hand side in step number two in your solution?

niks18 wrote:
CAMANISHPARMAR wrote:
Did you mean $$r = 100*[\sqrt{[fraction](v+q)/p[/fraction]} - 1]$$?

101mba101 wrote:
An investor purchased a bond for p dollars on Monday. For a certain number of days, the value of the bond increased by r percent per day. After this period of constant increase, the bond decreased the next day by q dollars and the investor decided to sell the bond that day for v dollars. When did the investor sell the bond if

$$r = 100*\sqrt{\frac{(v+q)}{p}} - 1$$?

A. Two working days later.

B. Three working days later.

C. Four working days later.

D. Five working days later.

E. Six working days later.

Hi CAMANISHPARMAR

the brackets are not there. bracket before 100 would imply that -1 will have to be multiplied by 100.

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Re: An investor purchased a bond for p dollars on Monday. For a certain nu  [#permalink]

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25 May 2018, 18:40
1
CAMANISHPARMAR wrote:
If the brackets are not there then how did you take the 100 on left hand side in step number two in your solution?

niks18 wrote:
CAMANISHPARMAR wrote:
Did you mean $$r = 100*[\sqrt{[fraction](v+q)/p[/fraction]} - 1]$$?

Hi CAMANISHPARMAR

yes you are correct. i thought of something otherwise. I have edited the question and my solution. Thanks for pointing it out.
VP
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Re: An investor purchased a bond for p dollars on Monday. For a certain nu  [#permalink]

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25 May 2018, 10:19
Did you mean $$r = 100*[\sqrt{\frac{(v+q)}{p}} - 1]$$?

101mba101 wrote:
An investor purchased a bond for p dollars on Monday. For a certain number of days, the value of the bond increased by r percent per day. After this period of constant increase, the bond decreased the next day by q dollars and the investor decided to sell the bond that day for v dollars. When did the investor sell the bond if

$$r = 100*\sqrt{\frac{(v+q)}{p}} - 1$$?

A. Two working days later.

B. Three working days later.

C. Four working days later.

D. Five working days later.

E. Six working days later.

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Joined: 25 Feb 2013
Posts: 1124
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Re: An investor purchased a bond for p dollars on Monday. For a certain nu  [#permalink]

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25 May 2018, 11:07
CAMANISHPARMAR wrote:
Did you mean $$r = 100*[\sqrt{[fraction](v+q)/p[/fraction]} - 1]$$?

101mba101 wrote:
An investor purchased a bond for p dollars on Monday. For a certain number of days, the value of the bond increased by r percent per day. After this period of constant increase, the bond decreased the next day by q dollars and the investor decided to sell the bond that day for v dollars. When did the investor sell the bond if

$$r = 100*\sqrt{\frac{(v+q)}{p}} - 1$$?

A. Two working days later.

B. Three working days later.

C. Four working days later.

D. Five working days later.

E. Six working days later.

Hi CAMANISHPARMAR

the brackets are not there. bracket before 100 would imply that -1 will have to be multiplied by 100.
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Re: An investor purchased a bond for p dollars on Monday. For a certain nu  [#permalink]

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25 May 2018, 19:26
101mba101 wrote:
An investor purchased a bond for p dollars on Monday. For a certain number of days, the value of the bond increased by r percent per day. After this period of constant increase, the bond decreased the next day by q dollars and the investor decided to sell the bond that day for v dollars. When did the investor sell the bond if

$$r = 100*[\sqrt{\frac{(v+q)}{p}} - 1]$$?

A. Two working days later.

B. Three working days later.

C. Four working days later.

D. Five working days later.

E. Six working days later.

Can you please provide the OE?
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Posts: 3
Re: An investor purchased a bond for p dollars on Monday. For a certain nu  [#permalink]

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01 Aug 2019, 00:37
Bunuel Can you please explain here?
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Re: An investor purchased a bond for p dollars on Monday. For a certain nu  [#permalink]

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04 Aug 2019, 14:30
Anyone think taking derivatives for this problem is a good idea?

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Re: An investor purchased a bond for p dollars on Monday. For a certain nu  [#permalink]

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04 Aug 2019, 14:32
101mba101 wrote:
An investor purchased a bond for p dollars on Monday. For a certain number of days, the value of the bond increased by r percent per day. After this period of constant increase, the bond decreased the next day by q dollars and the investor decided to sell the bond that day for v dollars. When did the investor sell the bond if

$$r = 100*[\sqrt{\frac{(v+q)}{p}} - 1]$$?

A. Two working days later.

B. Three working days later.

C. Four working days later.

D. Five working days later.

E. Six working days later.

Could we instead use derivatives?

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Re: An investor purchased a bond for p dollars on Monday. For a certain nu  [#permalink]

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08 Sep 2019, 00:32
101mba101 wrote:
An investor purchased a bond for p dollars on Monday. For a certain number of days, the value of the bond increased by r percent per day. After this period of constant increase, the bond decreased the next day by q dollars and the investor decided to sell the bond that day for v dollars. When did the investor sell the bond if

$$r = 100*[\sqrt{\frac{(v+q)}{p}} - 1]$$?

A. Two working days later.

B. Three working days later.

C. Four working days later.

D. Five working days later.

E. Six working days later.

Okay I think I got a shortcut method here and I am not sure whether anyone else has suggested this.

In the question the value of r has a square root in it, meaning that in the compound interest formula, the value n = 2. This means that if the bond was purchased on Monday, then value of n on Monday would be 0, on Tuesday, it would be 1, and on Wednesday, it would the 2. On Thursday, the price falls and the bond is sold that very day.

Tuesday is one working day later
Wednesday is two working days later
Thursday is three working days later

Hence, answer is B.
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Re: An investor purchased a bond for p dollars on Monday. For a certain nu  [#permalink]

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25 Sep 2019, 04:17
101mba101 wrote:
An investor purchased a bond for p dollars on Monday. For a certain number of days, the value of the bond increased by r percent per day. After this period of constant increase, the bond decreased the next day by q dollars and the investor decided to sell the bond that day for v dollars. When did the investor sell the bond if

$$r = 100*[\sqrt{\frac{(v+q)}{p}} - 1]$$?

A. Two working days later.

B. Three working days later.

C. Four working days later.

D. Five working days later.

E. Six working days later.

I did by using simple numbers
$$r = 100*[\sqrt{\frac{(v+q)}{p}} - 1]$$

If p=1
q=1 and v=3

Putting values in the formula will give
r= 100%

1st day 100% increase p=1+1=2
2nd day 100% increase 2+2=4

But v=3
that means one more day when q dollars decrease(we have taken q=1), so 3rd day =4-1=3=V

hence 3 working days later.

Please let me know if you find something wrong in this method.

thank you!
Re: An investor purchased a bond for p dollars on Monday. For a certain nu   [#permalink] 25 Sep 2019, 04:17

# An investor purchased a bond for p dollars on Monday. For a certain nu

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