On December 31, 2018, a company had 9.6 million regular users of its

Question

On December 31, 2018, a company had 9.6 million regular users of its product and set a goal to increase this number by \(16 \frac{2}{3}\)% the next year. In the second, third, and fourth quarters of the following year, the company gained 400,000, 425,000, and 475,000 users, respectively. Approximately what annual rate of increase would the company have needed in the first quarter to ensure they reached the goal ?

A. \(6 \frac{1}{4}\)%
B. \(8\)%
C. \(10\)%
D. \(12 \frac{1}{2}\)%
E. \(20\)%

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Official Answer

D

A.  6 \frac{1}{4} %
B.  8 %
C.  10 %
D.  12 \frac{1}{2} %
E.  20 %

NehaKalani · Accepted Answer

The company had 9.6M = 9,600,000 (96lacs) users in 2018, but wanted a 16\frac{2}{3}% increase by the end of next year.
This increase would mean 9,600,000 * (\frac{50}{300}) = 1,600,000 (16lacs) more users.

In the second, third and fourth quarters, the company already did 400k + 425k + 475k = 1,300,000 (13lacs) users.

To attain their goal, they'd have to do 300,000 in the first quarter.

We need to find x in 9,600,000*(\frac{x}{100}) = 300,000
But this 300,000 increase is for the quarter, and we are asked to find the annual increase.

So, we will have to make sure to multiply \frac{x}{100} with \frac{3}{12. }

Therefore, now finding x in the equation: 9,600,000*(\frac{x}{100}*\frac{3}{12}) = 300,000
x = 12.5%

RiyaJain69 · Answer

I'm getting >3%. Wondering where I'm going wrong. 🤔

reeyab · Answer

Can you explain why you multiply by 3/12 for an annual increase please? Thank you

PietroMeltzer · Answer

He is adjusting a quarter of the year (3/12) = time for the equation.
This adjustment allows the use of the formula for simple interest or proportional growth

So you can formulate the equation: value * rate * time = increase (simple interest) 
9.6*10^6 * x/100 * 3/12 = 300.000

Kinshook · Answer

On December 31, 2018, a company had 9.6 million regular users of its product and set a goal to increase this number by  16 \frac{2}{3} % the next year. In the second, third, and fourth quarters of the following year, the company gained 400,000, 425,000, and 475,000 users, respectively.

Approximately what annual rate of increase would the company have needed in the first quarter to ensure they reached the goal ?

16 2/3 % = 50%/3 = 1/6

9.6 million = 9600 thousands

9600*1/6 = 1600 thousands

Users to be added in first quater = 1600 - 400 - 425 - 475 = 300 thousands

Quarterly rate of increase needed in the first quarter = 300/9600 = 100%/32

Annual rate of increase needed in the first quarter = 100%*32*12/3 = 100%/8 = 12.5%

IMO D

lavanya.18 · Answer

Why did we divide it by 12/3 in the end?

Andrew89 · Answer

You're doing right .. 3% quarterly or 12% annually so the answer is 12%

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