Last year Brand X shoes were sold by dealers in 403

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pmFollowed by: 1 member

by BTGModeratorVI » Thu May 07, 2020 6:00 am

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Last year Brand X shoes were sold by dealers in 403 different regions worldwide, with an average (arithmetic mean) of 98 dealers per region. If last year these dealers sold an average of 2,488 pairs of Brand X shoes per dealer, which of the following is closest to the total number of pairs of Brand X shoes sold last year by the dealers worldwide?

A. 10^4
B. 10^5
C. 10^6
D. 10^7
E. 10^8

Answer: E
Source: Official guide 2021

Source: Beat The GMAT — Problem Solving | Thu May 07, 2020 6:00 am

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Re: Last year Brand X shoes were sold by dealers in 403

by Brent@GMATPrepNow » Fri May 08, 2020 6:00 am

BTGModeratorVI wrote: ↑
Thu May 07, 2020 6:00 am
Last year Brand X shoes were sold by dealers in 403 different regions worldwide, with an average (arithmetic mean) of 98 dealers per region. If last year these dealers sold an average of 2,488 pairs of Brand X shoes per dealer, which of the following is closest to the total number of pairs of Brand X shoes sold last year by the dealers worldwide?

A. 10^4
B. 10^5
C. 10^6
D. 10^7
E. 10^8

Answer: E
Source: Official guide 2021

Tip: ALWAYS scan the answer choices before deciding on an approach to take. For more on this, see the video below.
Since the answer choices are very spread apart (each answer choice is 10 TIMES the previous answer choice), we can be very aggressive with our estimations

Last year Brand X shoes were sold by dealers in 403 different regions worldwide, with an average (arithmetic mean) of 98 dealers per region.
So, total number of dealers = (403)(98) ≈ (400)(100)

Dealers sold an average of 2,488 pairs of Brand X shoes per dealer
Total number of pairs of shoes sold ≈ (400)(100)(2488)
≈ (400)(100)(2500)
≈ (4)(100)(100)(25)(100)
≈ (100)(100)(100)(100)
≈ 100,000,000
≈ 10^8

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Re: Last year Brand X shoes were sold by dealers in 403

by Scott@TargetTestPrep » Sun May 10, 2020 11:33 am

BTGModeratorVI wrote: ↑
Thu May 07, 2020 6:00 am
Last year Brand X shoes were sold by dealers in 403 different regions worldwide, with an average (arithmetic mean) of 98 dealers per region. If last year these dealers sold an average of 2,488 pairs of Brand X shoes per dealer, which of the following is closest to the total number of pairs of Brand X shoes sold last year by the dealers worldwide?

A. 10^4
B. 10^5
C. 10^6
D. 10^7
E. 10^8

Answer: E
Source: Official guide 2021

The number of pairs of Brand X shoes sold last year was:

403 x 98 x 2,488,

which is approximately:

400 x 100 x 2,500 = 4 x 25 x 1,000,000 = 100 x 10^6 = 10^8

Answer: E

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