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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:
85%
(hard)
Question Stats:
49% (02:47) correct
51%
(02:26)
wrong
based on 37
sessions
History
Date
Time
Result
Not Attempted Yet
Taj’s Taxis has a flat fare of $20, which includes up to 4 passengers, 6 suitcases and 5 kilometers . For each additional passenger , suitcase and kilometer or fraction thereof, Taj’s charges an additional p dollars, s dollars and k dollars respectively.
Today, the Smith, Jones, and Baker families each took a taxi with Taj’s Taxis. The Smith family had 14 passengers and 11 suitcases, and traveled 20 kilometers.
What was the total fare for the Smith family?
(1) The Jones family had 10 passengers and 9 suitcases, and traveled 6 kilometers: their total fare was $38.
(2) The Baker family traveled 11 kilometers, and had 8 passengers and 8 suitcases: their total fare was $40.
Today, the Smith, Jones, and Baker families each took a taxi with Taj’s Taxis. The Smith family had 14 passengers and 11 suitcases, and traveled 20 kilometers.
What was the total fare for the Smith family?
(1) The Jones family had 10 passengers and 9 suitcases, and traveled 6 kilometers: their total fare was $38.
(2) The Baker family traveled 11 kilometers, and had 8 passengers and 8 suitcases: their total fare was $40.
09 Mar 2026, 23:01
Kudos
Bookmarks
kevincan
Flat fare = $20
Fixed charge of x , for each pax exceeding 4 = (pax - 4) *x
Fixed charge of s, for each suitcase exceeding 6 = (Suitcase - 6) * s
Fixed charge of k, for each kilometre exceeding 5 km = (Km -5) * k
Total charge = 20 + (pax - 4) *x + (Suitcase - 6) * s + (Km -5) * k
Smith family Total charge = 20 + (14 - 4) *x + (11 - 6) * s + (20 -5) * k = 20 + 10x + 5s + 15k = ?
Statement 1:
The Jones family had 10 passengers, 9 suitcases, and traveled 6 kilometers, and their total fare was $38.
Total charge for Jones = 20 + (10 - 4) *x + (9 - 6) * s + (6 -5) * k
20 + 6x + 3s +k = $38
6x + 3s + k = $18.
Hence, Insufficient
Statement 2:
The Baker family traveled 11 kilometers, had 8 passengers, and 8 suitcases, and their total fare was $40.
Total charge for Baker = 20 + (8 - 4) *x + (8 - 6) * s + (11 -5) * k = $40
20 + 4*x + 2 * s + 6 * k = $40
4x + 2s + 6k = $20
2x + s + 3k = $10
Multiply by 5, we get 10x + 5s + 15k = $50
Smith total family charge = 20 + 10x + 5s + 15k = $ 20 + $50 = $ 70.
Hence, Sufficient
Option B
10 Mar 2026, 00:34
Kudos
Bookmarks
Nice systems-of-equations DS question. Let me walk through the structure.
Key concept being tested: Systems of linear equations in Data Sufficiency — specifically, when do you have enough equations to solve for the unknowns you need?
Setup: Total fare = 20 + (passengers − 4)x + (suitcases − 6)s + (km − 5)k, where charges x, s, k only apply when the threshold is exceeded.
Smith family: 14 passengers, 11 suitcases, 20 km
Smith fare = 20 + (14−4)x + (11−6)s + (20−5)k = 20 + 10x + 5s + 15k
Evaluating Statement (1): Jones family — 10 passengers, 9 suitcases, 6 km, fare = $38.
Jones fare = 20 + 6x + 3s + 1k = 38 → 6x + 3s + k = 18
One equation, three unknowns. Insufficient.
Evaluating Statement (2): Baker family — 8 passengers, 8 suitcases, 11 km, fare = $40.
Baker fare = 20 + 4x + 2s + 6k = 40 → 4x + 2s + 6k = 20 → 2x + s + 3k = 10
One equation, three unknowns. Insufficient.
Both together:
From Statement (2): 2x + s + 3k = 10 → multiply by 5: 10x + 5s + 15k = 50
Smith fare = 20 + 50 = $70
The beautiful thing here: you never need to find x, s, and k individually. The combined statement gives you exactly 10x + 5s + 15k — the precise expression in Smith's fare formula — in one step.
Common trap: Students set up three equations hoping to solve for x, s, k separately and panic when they can't (you only have 2 equations from both statements combined). The trick is to check whether Statements 1 and 2 together produce the exact linear combination you need for Smith, even without isolating each variable.
Answer: C (Both statements together are sufficient.)
Takeaway: In DS with multiple unknowns, always check if the combined statements produce the exact expression the question needs — individual variable values aren't always required.
Key concept being tested: Systems of linear equations in Data Sufficiency — specifically, when do you have enough equations to solve for the unknowns you need?
Setup: Total fare = 20 + (passengers − 4)x + (suitcases − 6)s + (km − 5)k, where charges x, s, k only apply when the threshold is exceeded.
Smith family: 14 passengers, 11 suitcases, 20 km
Smith fare = 20 + (14−4)x + (11−6)s + (20−5)k = 20 + 10x + 5s + 15k
Evaluating Statement (1): Jones family — 10 passengers, 9 suitcases, 6 km, fare = $38.
Jones fare = 20 + 6x + 3s + 1k = 38 → 6x + 3s + k = 18
One equation, three unknowns. Insufficient.
Evaluating Statement (2): Baker family — 8 passengers, 8 suitcases, 11 km, fare = $40.
Baker fare = 20 + 4x + 2s + 6k = 40 → 4x + 2s + 6k = 20 → 2x + s + 3k = 10
One equation, three unknowns. Insufficient.
Both together:
From Statement (2): 2x + s + 3k = 10 → multiply by 5: 10x + 5s + 15k = 50
Smith fare = 20 + 50 = $70
The beautiful thing here: you never need to find x, s, and k individually. The combined statement gives you exactly 10x + 5s + 15k — the precise expression in Smith's fare formula — in one step.
Common trap: Students set up three equations hoping to solve for x, s, k separately and panic when they can't (you only have 2 equations from both statements combined). The trick is to check whether Statements 1 and 2 together produce the exact linear combination you need for Smith, even without isolating each variable.
Answer: C (Both statements together are sufficient.)
Takeaway: In DS with multiple unknowns, always check if the combined statements produce the exact expression the question needs — individual variable values aren't always required.
