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11 Mar 2026, 23:34
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
56% (03:18) correct
44%
(03:13)
wrong
based on 25
sessions
History
Date
Time
Result
Not Attempted Yet
Vane earns a fixed monthly salary plus a commission for each sale she closes. In January, she closed 90 sales and earned $2,610. In February, she closed 45 sales and earned $2,205. If Vane averaged 165 sales per month over January, February, and March, how much more did she earn in March than she earned in January and February combined?
A. $180
B. $225
C. $270
D. $405
E. $600
A. $180
B. $225
C. $270
D. $405
E. $600
12 Mar 2026, 03:01
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This is a classic System of Two Linear Equations question — one of the most reliable question types on the GMAT Focus Problem Solving section.
The big trap here: students try to find Vane's March earnings by guessing or making assumptions about her commission rate, instead of actually solving the system. The two-equation setup completely determines both unknowns.
Let S = fixed monthly salary, c = commission per sale.
Step 1 — Set up the two equations from January and February:
January: S + 90c = 2,610
February: S + 45c = 2,205
Step 2 — Subtract the February equation from the January equation to eliminate S:
(S + 90c) − (S + 45c) = 2,610 − 2,205
45c = 405
c = 9
So each sale earns Vane $9 in commission.
Step 3 — Substitute back to find S:
S + 45(9) = 2,205
S + 405 = 2,205
S = 1,800
Step 4 — Find March sales using the average:
Average over Jan, Feb, March = 165 sales
Total sales = 165 × 3 = 495
March sales = 495 − 90 − 45 = 360
Step 5 — Calculate March earnings:
March = 1,800 + 360(9) = 1,800 + 3,240 = $5,040
Step 6 — Calculate the difference:
Jan + Feb combined = 2,610 + 2,205 = $4,815
March − (Jan + Feb) = 5,040 − 4,815 = $225
The answer is B.
Common trap: Students often compute Jan earnings and Feb earnings separately, find the difference between March and each month, and end up picking $405 (answer D). The question asks how much MORE March earnings are compared to Jan AND Feb COMBINED.
Takeaway: Any time a problem gives you two data points with the same fixed component, subtract the equations immediately — it cancels the fixed salary and isolates the commission rate cleanly.
The big trap here: students try to find Vane's March earnings by guessing or making assumptions about her commission rate, instead of actually solving the system. The two-equation setup completely determines both unknowns.
Let S = fixed monthly salary, c = commission per sale.
Step 1 — Set up the two equations from January and February:
January: S + 90c = 2,610
February: S + 45c = 2,205
Step 2 — Subtract the February equation from the January equation to eliminate S:
(S + 90c) − (S + 45c) = 2,610 − 2,205
45c = 405
c = 9
So each sale earns Vane $9 in commission.
Step 3 — Substitute back to find S:
S + 45(9) = 2,205
S + 405 = 2,205
S = 1,800
Step 4 — Find March sales using the average:
Average over Jan, Feb, March = 165 sales
Total sales = 165 × 3 = 495
March sales = 495 − 90 − 45 = 360
Step 5 — Calculate March earnings:
March = 1,800 + 360(9) = 1,800 + 3,240 = $5,040
Step 6 — Calculate the difference:
Jan + Feb combined = 2,610 + 2,205 = $4,815
March − (Jan + Feb) = 5,040 − 4,815 = $225
The answer is B.
Common trap: Students often compute Jan earnings and Feb earnings separately, find the difference between March and each month, and end up picking $405 (answer D). The question asks how much MORE March earnings are compared to Jan AND Feb COMBINED.
Takeaway: Any time a problem gives you two data points with the same fixed component, subtract the equations immediately — it cancels the fixed salary and isolates the commission rate cleanly.
12 Mar 2026, 07:50
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kevincan
Earning = Fixed cost + Commission per sale
= a + x
For 90 sales, earnings = a + 90x = $2610
For 45 sales , earnings = a + 45x = $2205
Difference = $405 = 45x , thus x =9
Substitute x=9 , in the second equation we get
a + $405 = $2205
a = $1800
Sales average for three months = 165.
Total sales = 165*3 = 495
Sum of Jan + Feb + Mar = 495
90 + 45 + March = 495
March = 495 - (135)
= 360
Earnings march = $1800 + 360*9 = 1800+3240 = $5040.
March earnings - combined ( Jan and Feb earnings)
= $5040 - ( $2610 + $2205)
= $225
Option B
