A certain salesperson earns a total sales commission of d dollars for

Question

A certain salesperson earns a total sales commission of d dollars for the first  12  items she sells in a given month, plus a commission of  0.05d  dollars for each additional item, where  d > 500 . Last month, did the salesperson sell at least  28  items?

(1) Last month, the salesperson earned a total of  1.9d  dollars in commissions
(2) Last month, the salesperson earned a total of  $1159  in commissions

GMATNinja · Answer

Check out question 4 in the video below for the solution:

https://www.youtube.com/watch?v=JjsHjL7X-vo&t=1954s

adityakaregamba · Answer

Hey can you please tell me where I am going wrong  GMATNinja 
commission >= d+0.05d(16) (for at least 28 orders)
its given that d >500

so if I put d = 500
then for 28 orders min. commission has to be greater than 900 (500 + 400) 
1) First statement
1.9d = 1.9*500 = 950
since 950 > 900

therefore the number orders will be greater than 28
Sufficient

2) Second statement
total commission = 1159 $

which again is greater than 900
therefore the number of orders will be greater than 28
Sufficient

where am I going wrong ?

GMATNinja · Answer

At the very beginning of your solution, you're on the right track. Here's the original question: 
 
 Q: Are items sold ≥ 28 ?  
And you translated it into a completely equivalent question, as shown in the video:
 
 Q: Is total commission ≥ 1.8d ?  
So far, so good. The trouble started when you replaced d with 500, which gave you this (incorrect) version of the question:
 
 Q: Is total commission ≥ $900 ?   
You're suggesting that if the commission was greater than $900, then the salesperson MUST have sold more than 28 items, and that simply isn't the case, since d could be MUCH greater than $500. For example, imagine what happens if d = $1000. In that scenario, the salesperson could have sold just 12 items, and still earned a commission greater than $900, right?

In other words, by replacing d with $500, you end up with a version of the question that isn't logically equivalent to the original. Yes, if at least 28 items were sold, the total commission had to be greater than $900. But the converse isn't true: if the commission is greater than $900, we still don't know whether the salesperson sold at least 28 items, since we don't know much about the value of d.

For more on why (B) isn't sufficient, check out the video explanation above.

I hope that helps a bit!

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A certain salesperson earns a total sales commission of d dollars for

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A certain salesperson earns a total sales commission of d dollars for

Prep Toolkit

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

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