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04 Jul 2025, 14:41
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Correct answer should be D.
Statement I:
3.3p can also be written as p + 2p +0.1p + 0.1p + 0.1p
p is charged for first 5 miles
2p can be charged for maximum of 20 miles
0.1p can be charged for a maximum of 1 mile
Maximum miles for a particular trip can be = 5 + 20 + 1 + 1 + 1 = 28. Sufficient.
Statement II:
Let total distance be x miles
132 = p + [x-5] * 0.1p, [x-5] is the nearest integer greater than or equal to x-5.
[x-5] = (132 - p) / 0.1p
Let's test values of p > 30
If p = 40
[x-5] = 23
which implies,
22 < x-5 <= 23
27 < x <= 28
If p = 60
[x-5] = 12
16 < x <=17
Similarly, other values of p greater than 30 can also be checked. Therefore sufficient.
Statement I:
3.3p can also be written as p + 2p +0.1p + 0.1p + 0.1p
p is charged for first 5 miles
2p can be charged for maximum of 20 miles
0.1p can be charged for a maximum of 1 mile
Maximum miles for a particular trip can be = 5 + 20 + 1 + 1 + 1 = 28. Sufficient.
Statement II:
Let total distance be x miles
132 = p + [x-5] * 0.1p, [x-5] is the nearest integer greater than or equal to x-5.
[x-5] = (132 - p) / 0.1p
Let's test values of p > 30
If p = 40
[x-5] = 23
which implies,
22 < x-5 <= 23
27 < x <= 28
If p = 60
[x-5] = 12
16 < x <=17
Similarly, other values of p greater than 30 can also be checked. Therefore sufficient.
Bunuel
04 Jul 2025, 17:23
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Topic(s)- Revenue, Max/Min
Strategy: Algebra, Max/Min Testing
Variable(s)- Miles = "x"; Revenue = "R(x)"
0. Pre-Work
R(x) = (p) + (p/10)*(x - 5)
Rephrase the Question: Is x > 30 miles?
(1) R(x) = 3.3p
i. Is x affected by the value of p?
3.3p = p + (p/10)*(x-5) -> Who cares what p is??
Multiply both sides by (10/p)
[3.3*(p) = (p) + (p/10)*(x-5)] * (10/p)
33 = 10 + (x - 5)
x = 28, regardless of p [Eliminate B,C,E]
(2) R(x) = $132
i. 132 = p + (p/10)*(x-5)
ii. Isolate x
1320 = 10p + (px) - 5p
1320 - 5p = px
x = (1320 - 5p)/p
iii. Max/Min Testing
for p(min) = 30.00000001 = 30
x = (1320 - 5*(30)) / (30) > 30 miles [Question is a YES]
for p("max") = 300
x = (1320 - 5*(300) / (300) < 30 miles [Question is a NO]
-> Conflicting Results [Eliminate B, D]
Answer: A
Strategy: Algebra, Max/Min Testing
Variable(s)- Miles = "x"; Revenue = "R(x)"
0. Pre-Work
R(x) = (p) + (p/10)*(x - 5)
Rephrase the Question: Is x > 30 miles?
(1) R(x) = 3.3p
i. Is x affected by the value of p?
3.3p = p + (p/10)*(x-5) -> Who cares what p is??
Multiply both sides by (10/p)
[3.3*(p) = (p) + (p/10)*(x-5)] * (10/p)
33 = 10 + (x - 5)
x = 28, regardless of p [Eliminate B,C,E]
(2) R(x) = $132
i. 132 = p + (p/10)*(x-5)
ii. Isolate x
1320 = 10p + (px) - 5p
1320 - 5p = px
x = (1320 - 5p)/p
iii. Max/Min Testing
for p(min) = 30.00000001 = 30
x = (1320 - 5*(30)) / (30) > 30 miles [Question is a YES]
for p("max") = 300
x = (1320 - 5*(300) / (300) < 30 miles [Question is a NO]
-> Conflicting Results [Eliminate B, D]
Answer: A
04 Jul 2025, 17:53
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A moving service charges p dollars for the first 5 miles of any trip, plus 0.1*p dollars for each additional mile or fraction of a mile.
If p > 30, was a particular trip more than 30 miles long?
Consider boundary condition P = 30; Then total cost would be P + 0.1P * 25 = 3.5 P;
(1) The moving service charged a total of 3.3p dollars for the trip.
From this, we can say that the total charges were less than 3.5 p, hence the trip length was less than 30 miles.
(2) The moving service charged a total of $132 for the trip.
We don't know the exact distance, hence we can't say what was total cost is in terms of p, and hence can't calculate the distance. Not Sufficient.
If p > 30, was a particular trip more than 30 miles long?
Consider boundary condition P = 30; Then total cost would be P + 0.1P * 25 = 3.5 P;
(1) The moving service charged a total of 3.3p dollars for the trip.
From this, we can say that the total charges were less than 3.5 p, hence the trip length was less than 30 miles.
(2) The moving service charged a total of $132 for the trip.
We don't know the exact distance, hence we can't say what was total cost is in terms of p, and hence can't calculate the distance. Not Sufficient.
