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05 Jul 2025, 03:30
Kudos
Bookmarks
Given,
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.
Distance = d
Charges, c = p + (d-5)* 0.1p
Question:
If p > 30, was a particular trip more than 30 miles long?
Statement 1:
The moving service charged a total of 3.3p dollars for the trip.
i.e. c = 3.3 p
Check:
3.3 p = p + (d-5)*0.1 p
2.3 p = 0.1 pd - 0.5 p
Cancelling “p” from both sides,
2.3 + 0.5 = 0.1 d
d = 28 miles
So, it can be answered if the trip is more than 30 miles long i.e. No
Sufficient
Statement 2:
The moving service charged a total of $132 for the trip..
i.e. c = $132
Check:
132 = p + (d-5)*0.1 p
132 = p + 0.1 pd – 0.5 p
132 = 0.5 p + 0.1 pd
Assuming value of p = 30 ,
We get value of d = 39 i.e more than 30 miles.
As we increase the value of p , we will see the value of d are decreasing
If value of p = 40, we get value of d = approx. 25 i.e less than 30 miles.
So, it cannot be answered if the trip is 30 miles long
Not Sufficient
Answer : A
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.
Distance = d
Charges, c = p + (d-5)* 0.1p
Question:
If p > 30, was a particular trip more than 30 miles long?
Statement 1:
The moving service charged a total of 3.3p dollars for the trip.
i.e. c = 3.3 p
Check:
3.3 p = p + (d-5)*0.1 p
2.3 p = 0.1 pd - 0.5 p
Cancelling “p” from both sides,
2.3 + 0.5 = 0.1 d
d = 28 miles
So, it can be answered if the trip is more than 30 miles long i.e. No
Sufficient
Statement 2:
The moving service charged a total of $132 for the trip..
i.e. c = $132
Check:
132 = p + (d-5)*0.1 p
132 = p + 0.1 pd – 0.5 p
132 = 0.5 p + 0.1 pd
Assuming value of p = 30 ,
We get value of d = 39 i.e more than 30 miles.
As we increase the value of p , we will see the value of d are decreasing
If value of p = 40, we get value of d = approx. 25 i.e less than 30 miles.
So, it cannot be answered if the trip is 30 miles long
Not Sufficient
Answer : A
Bunuel
05 Jul 2025, 03:43
Kudos
Bookmarks
cost with d rounded to the greatest integer:
c=p+(d-5)*0.1*p=(1+0.1d-0.5)*p=(0.5+0.1d)*p=(5+d)*p/10
(1)
cost for a trip whose distance is between (30, 31] miles:
c=(5+d)*p/10=3.6p
3.3p is less than 3.6p, so the miles are 30 or less but no more than 30. The answer is no.
SUFFICIENT
(2)
d must be an integer (greater than or equal to 5):
132=(5+d)*p/10
1320=(5+d)*p
As p>30, then 5+d<44 -> d<39
5<=d<39 -> d can be greater than, equal to or less than 30
INSUFFICIENT
IMO A
c=p+(d-5)*0.1*p=(1+0.1d-0.5)*p=(0.5+0.1d)*p=(5+d)*p/10
(1)
cost for a trip whose distance is between (30, 31] miles:
c=(5+d)*p/10=3.6p
3.3p is less than 3.6p, so the miles are 30 or less but no more than 30. The answer is no.
SUFFICIENT
(2)
d must be an integer (greater than or equal to 5):
132=(5+d)*p/10
1320=(5+d)*p
As p>30, then 5+d<44 -> d<39
5<=d<39 -> d can be greater than, equal to or less than 30
INSUFFICIENT
IMO A
05 Jul 2025, 03:51
Kudos
Bookmarks
Bunuel
Given:
p dollars for 1st 5 miles
0.1p dollars for each additional mile or a fraction of a mile.
If p>30, trip >30 miles long?
Statement 1
Total: 3.3p dollars for the trip
Let p=31
Total = 3.3*31= 102.3
Cost for the rest apart from first 5 miles: 102.3-31=71.3
Number of miles apart from the first 5: 71.3/3.1
= 23 miles.
Total trip length= 23+5=28miles
Let p=35
Total= 3.3*35= 115.5
Cost for the rest apart from first 5 miles : 115.5-35=80.5
Number of miles apart from the first 5: 80.5/3.5= 23 miles
Total trip length = 23+5= 28 miles
This means that for any value of p>30, this statement will hold true as the values will stay in proportion and the total length will remain the same.
The length of the trip <30 miles. A definite answer : NO
Sufficient.
Statement 2:
Total: $132
Let p=32
Remaining= 132-32= 100
Number of miles apart from the first 5 = 31.25 miles.
Let p=42
Remaining = 132-42 =90
Number of miles apart from the first five = 90/4.2= 21.42 miles
We aren't getting a definite YES/NO Answer.
Not Sufficient.
Answer: A
