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

Question

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

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

PS94421.02

BrentGMATPrepNow · Accepted Answer

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

RELATED VIDEO
 https://www.youtube.com/watch?v=8GqcJGUVIk4

abannore · Answer

Answer: E

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

Posted from my mobile device

lacktutor · Answer

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).

sujoykrdatta · Answer

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

ScottTargetTestPrep · Answer

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

perfectreview · Answer

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}

Cambly2020 · Answer

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!

minustark · Answer

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

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

CrackverbalGMAT · Answer

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

Devmitra Sen (GMAT Quant Expert)

GMATinsight · Answer

Answer: Option E

Video solution by  GMATinsight

https://www.youtube.com/watch?v=rpALIvnBQww

atquereiciendis · Answer

98=DEALER/403

DEALEAR/REIGON=403/98 (This gives you no of dealers)

Then they give us Mean of shoes/dealer =2488

Therefore, No of shoes = 2488*403*98=10^8

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards