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emmak
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The value of investment Q increased by q percent from t 15 Apr 2013, 03:11
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95% (hard)

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56% (03:21) correct 44% (03:08) wrong based on 484 sessions

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The value of investment Q increased by q percent from the beginning of a particular year through June 30 of that year, and then experienced no net change from June 30 to the end of the year. The value of investment P increased by p percent from the beginning of that year to June 30, and the new value increased again by p percent from June 30 to the end of the year. If the percent increase in value from the beginning to the end of the year was the same for both investments, which of the following expressions gives the value of p in terms of q ?

(A) \(\sqrt{100q + 10,000}-100\)
(B) \(\frac{q}{2}\)
(C) \(\sqrt{100q}\)
(D) \(2q + \frac{q^2}{100}\)
(E) \(\sqrt{100+q}-100\)
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Bunuel
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The value of investment Q increased by q percent from t 15 Apr 2013, 04:12
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emmak
The value of investment Q increased by q percent from the beginning of a particular year through June 30 of that year, and then experienced no net change from June 30 to the end of the year. The value of investment P increased by p percent from the beginning of that year to June 30, and the new value increased again by p percent from June 30 to the end of the year. If the percent increase in value from the beginning to the end of the year was the same for both investments, which of the following expressions gives the value of p in terms of q ?

(A) \(\sqrt{100q + 10,000}-100\)

(B) \(\frac{q}{2}\)

(C) \(\sqrt{100q}\)

(D) \(2q + \frac{q^2}{100}\)

(E) \(\sqrt{100+q}-100\)

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Say, at the beginning of the year the value of investment Q was Q and the value of investment P was P.

At the end of the year the value of investment \(Q = Q*(1+\frac{q}{100}) = \frac{Q*(100+q)}{100}\);

At the end of the year the value of investment \(P = P*(1+\frac{p}{100})*(1+\frac{p}{100}) = P*(\frac{(100+p)}{100})^2\).

We re told that:

    \(\frac{100+q}{100}=(\frac{100+p}{100})^2\);

    \(100(100+q)=(100+p)^2\);

    \(100+p=\sqrt{10,000+100q}\);

    \(p=\sqrt{10,000+100q}-100\).

Answer: A.

Hope it's clear.
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The value of investment Q increased by q percent from t 15 Apr 2013, 05:04
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emmak
The value of investment Q increased by q percent from the beginning of a particular year through June 30 of that year, and then experienced no net change from June 30 to the end of the year. The value of investment P increased by p percent from the beginning of that year to June 30, and the new value increased again by p percent from June 30 to the end of the year. If the percent increase in value from the beginning to the end of the year was the same for both investments, which of the following expressions gives the value of p in terms of q ?

(A) \(\sqrt{100q + 10,000}-100\)
(B) \(\frac{q}{2}\)
(C) \(\sqrt{100q}\)
(D) \(2q + \frac{q^2}{100}\)
(E) \(\sqrt{100+q}-100\)

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You can also use number plugging.

Say p=100%, so by the end of the year the value of investment P must double twice so increase 4 times.

4 times increase is increase by 300%, so q=300%.

Now, plug q=300 and see which answer yields 100. Only answer choice A works.

Answer: A.

Hope it's clear.
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The value of investment Q increased by q percent from t 16 Mar 2016, 18:32
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ok..now after reading the bunuel's explanation..I see where I made the mistake..I picked E...because I did not multiply by 100 when it was needed...
(100+q)/100 = [(100+p)/100]^2

multiply by 100
100+q = (100+p)^2 / 100
multiply again by 100
10,000 + 100q = (100+p)^2
square root both sides:
sqrt(10,000+100q) = 100+p
p= sqrt(10,000+100q)-100

A
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The value of investment Q increased by q percent from t 07 Apr 2016, 19:46
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Bunuel
emmak
The value of investment Q increased by q percent from the beginning of a particular year through June 30 of that year, and then experienced no net change from June 30 to the end of the year. The value of investment P increased by p percent from the beginning of that year to June 30, and the new value increased again by p percent from June 30 to the end of the year. If the percent increase in value from the beginning to the end of the year was the same for both investments, which of the following expressions gives the value of p in terms of q ?
(A) \(\sqrt{100q + 10,000}-100\)
(B) \(\frac{q}{2}\)
(C) \(\sqrt{100q}\)
(D) \(2q + \frac{q^2}{100}\)
(E) \(\sqrt{100+q}-100\)

Show Spoiler
Would like to see a active participation before i post the answer

Say, at the beginning of the year the value of investment Q was Q and the value of investment P was P.

At the end of the year the value of investment Q = Q*(1+q/100) = Q*(100+q)/100;
At the end of the year the value of investment P = P*(1+p/100)*(1+p/100) = P*((100+p)/100)^2.

We re told that \(\frac{100+q}{100}=(\frac{100+p}{100})^2\) --> \(100(100+q)=(100+p)^2\) --> \(100+p=\sqrt{10,000+100q}\) --> \(p=\sqrt{10,000+100q}-100\).

Answer: A.

Hope it's clear.
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Where the P & Q part gone (highligted part)
it should be Q*(100+q)/100= P*((100+p)/100)^2.
??
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The value of investment Q increased by q percent from t 19 Sep 2022, 11:10
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q% increase means
100-->100+q if increases once------A
Similarly for p% increase twice
100-->100+p---Once
(100)^2-->(100+p)^2--Twice----B
Multiplying eqn A by 100, we get
(100+p)^2=(100+q)100
P=sqrt[(100+q)100]-100
Therefore option A
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The value of investment Q increased by q percent from t 23 Sep 2022, 11:32
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Hi Everyone,

Assume Numbers here as question says difference from start of both numbers will be equal so Interest capitalized will be same so assume : P=Q=100 , p=10%, q=21%

P increases by p% twice = 100*(1.1) = 110 , Again 110(1.1) = 121.
Q increases by q% once a year which is equal to interest above so, = 100%(1.21) = 121.

Put Numbers in Option A : ( 100*21 + 10000 )^1/2 -100 ( substituted q=21 )
p = ( 2100 + 10000 )^1/2 -100
= (121000)^1/2 -100
= 110 - 100
=10 = p

so, this satisfies Ans is A
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The value of investment Q increased by q percent from t 03 Sep 2025, 08:14
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Hi KarishmaB , can we solve it using the formula for overall percent change = (a + b + ab/100)%

we will have q = p + p + p^2/100
q = (200p + p^2)/ 100

I wasn't able to get p in terms of q, but i see that when i put this value of q in ans options, i get the right ans.

Why are we not able to get the value of p directly from this, am i missing on something?
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The value of investment Q increased by q percent from t 04 Sep 2025, 02:38
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Natansha
Hi KarishmaB , can we solve it using the formula for overall percent change = (a + b + ab/100)%

we will have q = p + p + p^2/100
q = (200p + p^2)/ 100

I wasn't able to get p in terms of q, but i see that when i put this value of q in ans options, i get the right ans.

Why are we not able to get the value of p directly from this, am i missing on something?
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This is correct: q = p + p + p^2/100

It is far easier to plug in p = 10 here to find that q = 21.
In the options, put q = 21 and see which option gives you 10.

Answer (A)

Though we can get p in terms of q algebraically like this:

\(q = 2p + (\frac{p^2}{100})\)
\(q + 100 = 100 + 2p + (\frac{p}{10})^2\)
\(q + 100 = (\frac{p}{10} + 10)^2\)

\(\sqrt{q + 100} = \frac{p}{10} + 10\\
\)

\(p = 10(\sqrt{q + 100} - 10)\)

\(p = \sqrt{100q + 10,000} - 100\)

Answer (A)
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