Jimmy had 7.2 million followers on December 31 of a given year and set

Question

Jimmy had 7.2 million followers on December 31 of a given year and set a goal of increasing followership by \(83\frac{1}{3}%\) the following year. During the second, third, and fourth quarters of the following year, Jimmy gained 1,200,000, 2,000,000, and 1,900,000 new followers and lost no existing followers. What annual rate of increase would Jimmy have needed in the first quarter to ensure that he reached his goal?

(A) \(12\frac{1}{2}%\)

(B) \(16\frac{2}{3}%\)

(C) 20%

(D) 50%

(E) 70.8%

(A)  12\frac{1}{2}\%

(B)  16\frac{2}{3}\%

(C) 20%

(D) 50%

(E) 70.8%

Bunuel · Accepted Answer

GMATNinja Video Solution:

https://www.youtube.com/watch?v=3ikJ9r6j1uI&t=2908s

AdarshSambare · Answer

Jimmy starts with 7.2 million followers.
His goal is to increase followers by 831⁄3%, which is 5/6 of 7.2 million.
Required increase = 7.2 × 5/6 = 6.0 million followers.
During Q2, Q3, and Q4, he gains:
1.2 + 2.0 + 1.9 = 5.1 million followers.
So the gain needed in Q1 is:
6.0 − 5.1 = 0.9 million followers.
Q1 increase as a percent of the starting 7.2 million followers:
0.9 / 7.2 = 0.125 = 12.5%.
But the question asks for the  annual rate of increase  needed in the first quarter.
A quarterly rate of 12.5% corresponds to an annual rate of:
12.5% × 4 = 50%.
Answer:  (D) 50% .

Kinshook · Answer

Jimmy had 7.2 million followers on December 31 of a given year and set a goal of increasing followership by  83\frac{1}{3}\%  the following year. During the second, third, and fourth quarters of the following year, Jimmy gained 1,200,000, 2,000,000, and 1,900,000 new followers and lost no existing followers.

What annual rate of increase would Jimmy have needed in the first quarter to ensure that he reached his goal?

83\frac{1}{3}\% * 7200000 = 6000000

New followers needed in first quarter = 6000000 - 1200000 - 2000000 - 1900000 = 900000

Annual rate of increase needed = 900000*4/7200000 * 100% = 50%

IMO D

architkap · Answer

is it only me that finds the wording of "What annual rate of increase would Jimmy have needed in the first quarter to ensure that he reached his goal?" a bit confusing?

I got till 12.5% but then I don't understand why its asking us to annualise that?

I understood it as the other 3 quarters are already fixed so what percent of 7.2 mil would he need to increase by in Q1 to reach the goal of 13.2 million followers totally. Couldn't this have been worded better?

SlyWave · Answer

i agree. i interpreted the question exactly the same as you. ive watched the gmat ninja video about the same question but i still dont see why the question was taken differently.

egmat · Answer

Hi SlyWave,

You and architkap did everything right up to  12.5% . That number is real and correct: it's the actual growth Jimmy needs  within Q1  (a  0.9M  gain on a  7.2M  base). The only thing tripping you up is what the phrase " annual rate " is asking for.

Two different quantities

There's a difference between:

-  The percent he grows during Q1  - that's the  12.5%  you found.
-  The annual  rate  that growth represents  - that's what the question wants.

A "rate" is a  pace , quoted per a stated time unit. When a rate is stated  per year  but the growth actually happens  in a quarter , you scale the quarterly figure up to a full year. Four quarters make a year, so:

12.5%  per quarter ×  4  =  50%  per year.

So the question isn't saying Jimmy grew  50%  in Q1. It's saying: the Q1 pace, if expressed as a yearly rate, is  50%  - that's answer  D .

The everyday version of this

Think of a bank. Suppose an account pays  5%  in one quarter. How does the bank advertise that? Not as " 5% " - it quotes the  annual rate :  5%  ×  4  =  20%  per year. Same money, same quarter; the  rate  is just stated on a yearly basis.

That's exactly what's happening here. The wording is admittedly clunky, but "annual rate ... needed in the first quarter" = "take the Q1 growth pace and state it as a yearly rate."

Quick check to lock it in: if Jimmy had needed a  7%  increase in Q1, what annual rate is that? (Answer:  7%  ×  4  =  28% .) Once you separate "amount grown this quarter" from "rate stated per year," the  50%  clicks.

Answer: D

Jimmy had 7.2 million followers on December 31 of a given year and set

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Jimmy had 7.2 million followers on December 31 of a given year and set

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