Did Jeff record more sales revenue this month than Dan did?

Question

(1) Jeff earned 20% more in sales commission this month than Dan did.

(2) Dan earns 6% commission on his sales, and Jeff earns 8% commission on his.

KarishmaB · Accepted Answer

Based on revenue, salespeople earn commission. We need to know whether Jeff recorded more revenue than Dan.

(1) Jeff earned 20% more in sales commission this month than Dan did.
Jeff's more commission doesn't imply more revenue, Their rate of commission could be different (as given in stmnt 2) due to their different profile, the products they sell could offer varying commissions etc

(2) Dan earns 6% commission on his sales, and Jeff earns 8% commission on his.
This alone is not sufficient since we don't know who got more commission in absolute terms.

Using both, we know that Dan earns 6% and Jeff earns 8%. This means for every $100 of revenue, Dan gets $6 and Jeff gets $8 so Jeff gets (2/6)*100 = 33.33% more than Dan for same revenue. 
Had their revenue been same, Jeff would have earned 33.33% more than Dan in commission. Since Jeff earned only 20% more in commission, his revenue must have been less than that of Dan. Both statements together are sufficient.

Answer (C)

dav90 · Answer

I am not able to understand the reasoning, Why are we assuming that both of them are getting percentage on same amount,
It's commission so one's sale could be 10000$ while other's sale could be 10$ so how can the percentage give me the correct answer?

KarishmaB · Answer

We are not assuming that their revenue is the same. What we are saying is that if the revenue were the same, Jeff would have earned 33.33% more than Dan in commission. If Jeff's revenue were higher than Dan's, then Jeff would have earned more than 33.33% more than Dan, say 40% more commission than Dan or 50% more than Dan etc. 
If Jeff's revenue were lower than Dan's, then Jeff would have earned less than 33.33% more than Dan, that is Jeff would have earned 30% more commission than Dan, or 20% more commission than Dan etc.

Try some numbers to understand this better.

Since we are given that Jeff's commission is only 20% more than Dan's commission, it means Jeff's revenue must be lower than Dan's revenue.

KarishmaB · Answer

Responding to a pm:

On $100, Dan earns $6 and Jeff earns $8. So for every $100, Jeff earns $2 more than Dan.

So for every $100, Jeff earns (2/6)*100 = 33.33% more than Dan.
2 is Jeff's extra earning and 6 is Dan's earning.

ajdse22 · Answer

statement #1 -- says Jeff's sales comission is more than Dan's. But it is possible that this could be due to comission rate. Even if Dan's sales commission is higher he could still make less comission. Another case is when their sales comission rate is same in that case Jeff's sales will have to be higher. NS

statement #2 -- sales commission rate of Dan is higher. But we dont know what is Dan's total comission relative to Jeff's.

combining the statements. If Dan's commission rate is higher but he still makes less total commission, this implies his sales has to be lower to make this happen.
I have solved it via intuition and reasoning, but we can apply algebra inequality as well

Sj - sales of Jeff
Sd- sales of Dan
Rj - Jeff's commission rate
Rd- Dan's commission rate

combine statements
statement #1 --Sj*Rj> Sd*Rd --cross multiply ..since we know everything is positive so
Sj/Sd> Rd/Rj.
statement #2--.now since Rd > Rj this implies Sj/Sd >1 => Sj>Sd--sufficient
Note that
If instead it was given that commission rate of Dan is less than commission rate of Jeff, that would still have been insufficient and answer would have been E. Why?
Rd<Rj=> Rd/Rj <1. If Sj/Sd> Rd/Rj -- this does not imply Sj/Sd is either greater or less than or equal to 1. Anything can happen.

manishtank1988 · Answer

My 2 cents:
NOTE: Commission = (x%)*Revenues; 
 Sales Commission = (x%)*(Sales Revenues). Therefore, C = (x%)*R
Question: Jr > Dr?
1) Jc = 1.2*Dc 
2) Jc = 0.08*Jr & Dc = 0.06Dr
1+2) Jc = 1.2*Dc 
=> 0.08*Jr = 1.2*0.06*Dr 
=> 8*Jr = 1.2*6*Dr
=> Jr = (7.2/8)*Dr | 72/80 = 9/10 = 0.9
=> Jr = 0.9*Dr
=> Jr < Dr | Answer C

bumpbot · Answer

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Did Jeff record more sales revenue this month than Dan did?

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Did Jeff record more sales revenue this month than Dan did?

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