Tariq works as a salesperson for a telephone retailer. For each of the

Question

Tariq works as a salesperson for a telephone retailer. For each Model X telephone he sells in a given month, he earns a bonus of $15 per telephone. In addition, if he sells at least 60 telephones in a month, he receives an extra $90 bonus for that month.

Last year, Tariq sold between 350 and 500 Model X telephones, inclusive, and he sold at least 200 telephones in December.

If Tariq received a total of d dollars in bonuses from selling Model X telephones last year, what is the difference between the greatest possible value of d and the smallest possible value of d?

A) 2490
B) 2550
C) 2700
D) 2850
E) 2940

BadalDewani · Answer

this is GMAT FE type problem??

HarshG7 · Answer

can we get the solution to this ?

kevincan · Answer

Clue : The difference between the greatest possible value of D and the smallest possible value D comes from two quantities : the difference between the greatest and the smallest possible number of phones that he sold in the year , and the difference between the greatest and smallest number of times he got the 90 dollar bonus

Cgoebel · Answer

Lowest value for d = only 350 telephones sold and all in December = 30 x $15 + $90 bonus = $540

Highest value for d = 500 telephones sold with 200 in December and 300 spread over 10 months, 30 per month = $540 + (30 x 10 x $15) = $540 + $4,500 = $5,040

Difference between the highest and lowest values for d = $5,040 - $540 = $4,500

Why is $4,500 not an answer here? It looks like you arrive at $2,700 if you maximize d by selling 60 for 5 months instead of 30 over 10 months, the former computing to only $540 x 5, versus the latter computing to $450 x 10.

Am I missing something here?

kevincan · Answer

I have corrected the question, thank you for noticing and sorry

Cgoebel · Answer

Lowest value for d = only 350 telephones sold and all in December = 350 x $15 + $90 = $5,340

Highest value for d = 500 telephones sold with 200 in December and 300 spread over 5 months, 60 per month, in order to get the bonus = (200 x $15 + $90) + (300 x $15) + ($90 x 5) = $3,090 + $4,500 + $450 = $8,040 (or simply (500 x $15) + (6 x $90) = $8,040)

Difference between the highest and lowest values for d = $8,040 - $5,340 =   $2,700

kevincan · Answer

We minimize d in the case that he sold 350, 200 in December and the other 150 throughout the 11 remaining months in such a way that he sold no more than 59 in any other month

Total Bonus would be 350(150) + 90

egmat · Answer

What Tariq earns: 
•  $15  for each phone sold
•  $90 extra bonus  if he sells  60 or more  phones in any month

What we know: 
• Total phones last year: between  350  and  500 
• December: at least  200  phones sold

---

FINDING THE MAXIMUM BONUS:

To maximize bonuses, we want: 
1. Maximum phones sold =  500 
2. As many months as possible hitting the  60-phone threshold  for the $90 bonus

December already has  200+  phones, so that's 1 month with the bonus.

Remaining phones:  500 - 200 = 300  phones for other 11 months.

If we spread  300  phones across  5 months  at  60 each , that's 5 more months qualifying for the $90 bonus.

Total months with $90 bonus:  1 + 5 = 6 months

Maximum bonus = (500 × $15) + (6 × $90) = $7,500 + $540 =  $8,040

---

FINDING THE MINIMUM BONUS:

To minimize bonuses, we want: 
1. Minimum phones sold =  350 
2. As FEW months as possible hitting the 60-phone threshold

Key insight:  December  must  have at least 200 phones, so December ALWAYS gets the $90 bonus.

Trick: Put ALL 350 phones in December alone!

This means only  1 month  gets the $90 bonus.

Minimum bonus = (350 × $15) + (1 × $90) = $5,250 + $90 =  $5,340

---

THE DIFFERENCE:

$8,040 - $5,340 = $2,700

Answer: C

Tariq works as a salesperson for a telephone retailer. For each of the

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