The revenue of a small company increased from x dollars in 2000 to z

Question

The revenue of a small company increased from x dollars in 2000 to z dollars in 2002. If the percent increase in the company's revenue from 2000 to 2001 was equal to the percent increase in the company's revenue from 2001 to 2002, what was the company's revenue in 2001 in terms of x and z?

Percent Change From 2000 to 2002 $= \frac{z - x}{x} × 100$

So, $z = x(1 + \frac{z - x}{x})$.

Thus, 2001 revenue $= x\sqrt{1 + \frac{z - x}{x}}$.

$= \sqrt{x^2 + xz - x^2}$

$= \sqrt{xz}$

(A) $\frac{x+z}{2}$

(B) $\frac{xz}{2}$

(C) $\frac{z-x}{2x}$

(D) $\sqrt{xz}$

(E) $\sqrt{\frac{z-x}{x}}$

Correct answer: D

Bunuel · Accepted Answer

The company's revenue from 2000 to 2002 increased  \frac{z}{x}  times (for example, if the revenue increased from 100 to 400, it increased 400/100 = 4 times).

Assuming the increase from 2000 to 2001, and from 2001 to 2002, was k times, then  k^2=\frac{z}{x} , yielding  k=\sqrt{\frac{z}{x}}  (for example, if the revenue from 2000 to 2002 increased 4 times, and the increase from 2000 to 2001, and from 2001 to 2002, was the same, then each year the revenue increases twice, (from  k^2=4 , we get ( k=2 )).

Hence, the revenue in 2001 was  x*\sqrt{\frac{z}{x}}=\sqrt{\frac{x^2z}{x}}=\sqrt{xz} .

Answer: D.

isanyamm · Answer

Step 1: Define variables
Let x be the revenue in 2000
Let y be the revenue in 2001
Let z be the revenue in 2002

Step 2: Set up the equation for percent increase
r = (y - x) / x * 100

Step 3: Set up the equation for equal percent increase
r = (z - y) / y * 100

Step 4: Set the two equations equal to each other
(y - x) / x * 100 = (z - y) / y * 100

Step 5: Simplify the equation
(y^2) = xz

Step 6: Solve for y
y = sqrt(xz)

Kinshook · Answer

ekwok

Given:  The revenue of a small company increased from x dollars in 2000 to z dollars in 2002.

Asked:  If the percent increase in the company's revenue from 2000 to 2001 was equal to the percent increase in the company's revenue from 2001 to 2002, what was the company's revenue in 2001 in terms of x and z?

Let the company's revenue in 2001 be y

y/x = z/y
y^2 = xz
 y = \sqrt{xz}

IMO D

nyota.benson · Answer

Let's denote the company's revenue in 2000 as $x$ dollars, the revenue in 2001 as $y$ dollars, and the revenue in 2002 as $z$ dollars.

The percent increase from 2000 to 2001 is given by:

\

The percent increase from 2001 to 2002 is given by:

\

According to the given information, these two percent increases are equal:

\

Now, let's simplify this equation:

\

Cross-multiply to eliminate the fractions:

\

Add $xy$ to both sides:

\

Now, solve for $y$:

\

So, the company's revenue in 2001 in terms of $x$ and $z$ is $y = \sqrt{xz}$ dollars.

TylerFerreira1 · Answer

Hey Bunuel, could you please link some other questions similar to this ?

Bunuel · Answer

Check the links below: https://gmatclub.com/forum/m20-184230.html https://gmatclub.com/forum/m28-184507.html https://gmatclub.com/forum/m24-184400.html https://gmatclub.com/forum/m25-184408.html https://gmatclub.com/forum/m08-183772.html https://gmatclub.com/forum/m20-184243.html https://gmatclub.com/forum/m15-184049.html Hope this helps.

oneinabillion · Answer

hi, why are we equating it as y/x? and how do we get the percent increase from it?

ronnnie · Answer

let , x = 100 (2000) , 10% increase : y=110 (2001) , 10% increase : z = 121 (2002)

now place the value in the answers and see which gives y = 110 (that's our answer)

MartyMurray · Answer

The revenue of a small company increased from x dollars in 2000 to z dollars in 2002. If the percent increase in the company's revenue from 2000 to 2001 was equal to the percent increase in the company's revenue from 2001 to 2002, what was the company's revenue in 2001 in terms of x and z? 
 
(A)  \frac{x+z}{2}

(B)  \frac{xz}{2}

(C)  \frac{z-x}{2x}

(D)  \sqrt{xz}

(E)  \sqrt{\frac{z-x}{x}}

Let the percent increase from each year to the next equal p.

In that case, we have the following:

x(1 + \frac{p}{100})^2 = z

Thus, the following is true:

(1 + \frac{p}{100})^2 = \frac{z}{x}

Also, in that case, the value for 2001 is the following:

ext{2001 Revenue} = x(1 + \frac{p}{100})

(1 + \frac{p}{100}) = \sqrt{(1 + \frac{p}{100})^2}

So, we can say the following:

ext{2001 Revenue} = x\sqrt{\frac{z}{x}}

ext{2001 Revenue} = \sqrt{\frac{x^2z}{x}}

ext{2001 Revenue} = \sqrt{xz}

Correct answer:  D

HarshavardhanR · Answer

We are given that the % increase from 2000 to 2001 and from 2001 to 2002 is the same.

Let p be the multiplication factor associated with this % increase.

For example, if the % increase is 10%, then p = 1.1. If the % increase is 30%, then p = 1.3.

Harsha

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MartyMurray · Answer

The revenue of a small company increased from x dollars in 2000 to z dollars in 2002. If the percent increase in the company's revenue from 2000 to 2001 was equal to the percent increase in the company's revenue from 2001 to 2002, what was the company's revenue in 2001 in terms of x and z?

(A) $\frac{(x+z)}{2}$

(B) $\frac{xz}{2}$

(C) $\frac{(z-x)}{2x}$

(D) $\sqrt{xz}$

(E) $\sqrt{\frac{(z-x)}{x}}$

Percent Change From 2000 to 2002  = \frac{z - x}{x} × 100

So,  z = x(1 + \frac{z - x}{x}) .

Thus, 2001 revenue  = x\sqrt{1 + \frac{z - x}{x}} .

= \sqrt{x^2 + xz - x^2}

= \sqrt{xz}

(A)  \frac{x+z}{2}

(B)  \frac{xz}{2}

(C)  \frac{z-x}{2x}

(D)  \sqrt{xz}

(E)  \sqrt{\frac{z-x}{x}}

Correct answer:  D

rajatyadav1994 · Answer

Given information:
Revenue for Year 2000 = x dollars
Revenue for year 2002 = z dollars

Let revenue for year 2001 = y dollars

Given:
 \frac{y}{x} -1 = \frac{z}{y} - 1     
Solve: 
 \frac{y}{x} = \frac{z}{y}  
 y^2 = xz 
 y = \sqrt{xz }

Option D

Rohanx9 · Answer

Easy to plugin values and check.

Let x = 100 and % increase = 50%

x =100
y = 150
z = 200

Clearly only option D provides us an answer of 150.

triptiim · Answer

Let's assume that the revenue of 2000, ie. x = 1000$. Therefore, y = 1100$ and z = 1210$. Now we see each option, A/. 2210/2 = 1105, so no. We can already see B is not possible. C. 210/2, again no. D. sqrt 1210000 = 1100. Therefore D is our answer.

I took barely 1.5 mins to solve this question this way, so decided to share it here.

The revenue of a small company increased from x dollars in 2000 to z

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The revenue of a small company increased from x dollars in 2000 to z

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