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Last year Brand X shoes were sold by dealers in 403 different regions

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gmatt1476
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Last year Brand X shoes were sold by dealers in 403 different regions [#permalink] New post  20 Apr 2020, 12:58
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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



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BrentGMATPrepNow
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Last year Brand X shoes were sold by dealers in 403 different regions [#permalink] New post  Updated on: 17 May 2021, 07:21
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gmatt1476 wrote:
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


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

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Originally posted by BrentGMATPrepNow on 28 Apr 2020, 13:10.
Last edited by BrentGMATPrepNow on 17 May 2021, 07:21, edited 1 time in total.
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Re: Last year Brand X shoes were sold by dealers in 403 different regions [#permalink] New post  20 Apr 2020, 13:14
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Answer: E

Total shoes sold last year= 403*98*2488
Taking approximate values= 400*100*2500
=10^8

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lacktutor
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Last year Brand X shoes were sold by dealers in 403 different regions [#permalink] New post  20 Apr 2020, 13:17
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gmatt1476 wrote:
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



PS94421.02


403 regions
98 dealers per region
2488 pairs of shoes per dealer
----------------------------
In total, 2488*98*403 pairs of shoes were sold last year.

\(2488 ≈ 2.5*10^{3}\),
\(98 ≈10^{2}\),
\(403 ≈ 4*10^{2}\)

---> \(2.5*10^{3}*10^{2}*4*10^{2}= (4*2.5)*10^{7}= 10^{8}\)

Answer (E).
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Re: Last year Brand X shoes were sold by dealers in 403 different regions [#permalink] New post  20 Apr 2020, 14:24
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gmatt1476 wrote:
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



PS94421.02


Obviously, the total number of pairs

= 403 x 98 x 2488
~= 400 x 100 x 2500
= 4 x 10000 x 2500
= 10000 x 10000
= 10^8

Answer E
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Re: Last year Brand X shoes were sold by dealers in 403 different regions [#permalink] New post  13 May 2020, 07:23
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gmatt1476 wrote:
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




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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Re: Last year Brand X shoes were sold by dealers in 403 different regions [#permalink] New post  30 May 2020, 21:43
There are total of 403 regions with an average of 98 dealers per region.

Therefore the total dealer = 403 x 98

And each dealer sold an average of 2,488 pairs of Brand X shoes.

Therefore the total pairs of Brand X sold = 403 x 98 x 2488

Approximately

≈ 400 x 100 x 2500

≈ (4 x 100) x 100 x (25 x 100)

≈ (4 x 25) x 100 x 100 x 100

≈ 100 x 100 x 100 x 100

≈ \(100^{8}\)
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Cambly2020
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Re: Last year Brand X shoes were sold by dealers in 403 different regions [#permalink] New post  09 Sep 2020, 16:02
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I think the proximate equation 403*98*2488 ~ 400*100*2500 is too vage
Beacause 400*100*2500 = (403-3)*(98+2)*(2488+12)
Those reduction and increases (-3, +2 and +12) are not so similar
So we're not sure whether it is closer to 10^7 than 10^8

My solution is that: 403*98*2488 > 400*90*2000 = 72,000,000 > 7*10^7 => it is closer to 10^8 than 10^7

Hope it helps!
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Re: Last year Brand X shoes were sold by dealers in 403 different regions [#permalink] New post  09 Sep 2020, 18:30
[quote="gmatt1476"]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

total no of shoes sold last year = 403 * 98 * 2488 , approx = 400 * 100 * 2500= 1,000,000 * 100 = 10^8
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CrackverbalGMAT
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Re: Last year Brand X shoes were sold by dealers in 403 different regions [#permalink] New post  17 Mar 2021, 05:25
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Solution:

Total number of regions -= 403 = 400 (rounded)

= 4 x 10^2

Total number of dealers per region = 98 (rounded)= 100

=10^2

Total number of pairs of Brand X shoes sold per dealer = 2488

=2500(rounded)

=25 x 10^2

Total number of shoes sold last year = Regions x dealers x sale/dealer

= 4 x 10^2 X 10^2 X 25 x 10^2

= 4 X 25 X 10^6

=10^8 (option e)

Hope this helps :thumbsup:

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Re: Last year Brand X shoes were sold by dealers in 403 different regions [#permalink] New post  27 May 2021, 08:26
Expert Reply
gmatt1476 wrote:
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



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