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04 Mar 2026, 20:00
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Difficulty:
15%
(low)
Question Stats:
88% (01:43) correct
12%
(02:44)
wrong
based on 82
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The per-head cost for a group of students for renting a van was $40. At the last moment, five students backed out and thus, the remaining students paid extra $5 each to rent the van. How many students initially rented the van ?
A. 30
B. 35
C. 40
D. 45
E. 50
A. 30
B. 35
C. 40
D. 45
E. 50
05 Mar 2026, 03:12
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This is a classic inverse variation word problem — total cost is fixed, and as the number of payers drops, the per-person cost rises. The trick the GMAT loves here is that students set up two equations but forget to connect them through the fixed total.
The common trap: setting up (x − 5)(40 + 5) = x × 40 without thinking carefully about what x represents. Let's be precise.
Step 1: Define the variable clearly.
Let n = number of students originally in the group.
Step 2: Express the total cost of renting the van.
Total cost = 40 × n = 40n (original group pays $40 each)
Step 3: After 5 students back out, (n − 5) students remain.
These students now share the same total cost, paying $45 each.
So: 45(n − 5) = 40n
Step 4: Solve.
45n − 225 = 40n
5n = 225
n = 45
Answer: D (45)
Quick sanity check: 45 students × $40 = $1,800 total. After 5 leave, 40 students × $45 = $1,800. ✓
The trap most people fall into is letting x represent the wrong quantity (mixing up "original" vs "remaining" students) and then losing track mid-algebra. Defining n clearly at the start prevents that entirely.
Takeaway: For any "some people back out and the rest pay more" word problem, anchor on the fixed total — that single equation is all you need.
The common trap: setting up (x − 5)(40 + 5) = x × 40 without thinking carefully about what x represents. Let's be precise.
Step 1: Define the variable clearly.
Let n = number of students originally in the group.
Step 2: Express the total cost of renting the van.
Total cost = 40 × n = 40n (original group pays $40 each)
Step 3: After 5 students back out, (n − 5) students remain.
These students now share the same total cost, paying $45 each.
So: 45(n − 5) = 40n
Step 4: Solve.
45n − 225 = 40n
5n = 225
n = 45
Answer: D (45)
Quick sanity check: 45 students × $40 = $1,800 total. After 5 leave, 40 students × $45 = $1,800. ✓
The trap most people fall into is letting x represent the wrong quantity (mixing up "original" vs "remaining" students) and then losing track mid-algebra. Defining n clearly at the start prevents that entirely.
Takeaway: For any "some people back out and the rest pay more" word problem, anchor on the fixed total — that single equation is all you need.
