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Given:

Cost = p (first 5 miles) + 0.1p per extra mile

Total miles = d

Total cost = p × (1 + 0.1(d − 5))

Is d > 30?

Statement (1): The moving service charged a total of 3.3p dollars.
So,
Total cost = 3.3p
==>3.3p = p(1+ 0.1(d-5))
3.3 = (1+0.1(d-5))
d = 28

Since d = 28 < 30, the answer to the question "Was the trip more than 30 miles?" is NO.
So Statement (1) alone is sufficient.

Statement (2): The total charge was $132
Total cost = $132
132 = p(1+0.1(d-5))
Above equation has 2 variables...couldn't be solved with one equation..
So statement (2) alone is not sufficient

Final answer A
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A. (1) is sufficient

(1)
p + (Miles-5)*0.1p = 3.3p
Miles = (3.3-1)/0.1 + 5 = 28
Answer NO -> SUFFICIENT

(2)
p + (Miles-5)*0.1p = 132
You can't get amount of miles out of 1 equation with 2 variables.
Alternatively try with values 30 (non-included border) and 100. You get 34 miles and 3.2 miles, hence, you can't answer the question.
-> NOT SUFFICIENT
Bunuel
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?

(1) The moving service charged a total of 3.3p dollars for the trip.
(2) The moving service charged a total of $132 for the trip.


 


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Bunuel
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?

(1) The moving service charged a total of 3.3p dollars for the trip.
(2) The moving service charged a total of $132 for the trip.


 


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As per the question given statements we can form the equation:

p + 0.1 p (k-5) = Total Charges ............ (Where k is the total distance covered)

S-1 Referring this we form the equation:

p + 0.1 p (k-5) = 3.3p

Solving k= 28 ( So Trip was not more that 30 miles)

S-2 Referring this we form the equation:

p + 0.1 p (k-5) = 132

The above equation has 2 variables not solvable.

Despite that lets assume if :

If p= 40 then k =28 ; If p= 30 then k =39

Hence it can be either < 30 or >30 in both cases which is not deducable.

Hence S-2 is not enough to answer.

Thus Final Answer is A — Statement (1) alone is sufficient, but (2) is not.
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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?

Suppose trip is of 31 miles
p+2.6p= 3.6p

Statement 1
The moving service charged a total of 3.3p dollars for the trip.
As trip has 3.3 p which is less than 3.6 p thus trip is less than 30 miles.
Sufficient to answer.
(2) The moving service charged a total of $132 for the trip.
P can be anything above 30
Suppose p is 31, Distance will 31+3.1*(x-5)=132
x= 37.5
Suppose p=40
Distance will be
40+4*(x-5)=132
x=28
Thus for different value of p>30 distance will be different and therefore the statement is not sufficient

Answer is B
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Bunuel
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?

(1) The moving service charged a total of 3.3p dollars for the trip.
(2) The moving service charged a total of $132 for the trip.


 


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As per the question we have
Let Total distance = D,
Is D>30?

First 5 miles = p
Next rate = 0.1p * (D - 5)

Total price of a trip of D miles = p + 0.1p * (D - 5)

(1) The moving service charged a total of 3.3p dollars for the trip.
=> p + 0.1p * (D - 5) = 3.3p
=> 1 + 0.1(D - 5) = 3.3
=> 0.1(D - 5) = 2.3
=> (D - 5) = 23
=> D = 23 + 5 = 28
Hence D < 30

Sufficient

(2) The moving service charged a total of $132 for the trip.
=> p + 0.1p * (D - 5) = 132
=> 0.1p * (D - 5) = 132 - p
=> p * (D - 5) = 1320 - 10p
=> D = (1320 - 10p)/p + 5

Since p> 30 let's test p = 31 to figure this out
=> D = (1320 - 310)/31 + 5
=> D = 37.5

Let's test p = 40 to figure this out
=> D = (1320 - 400)/40 + 5
=> D = 28

Hence D can be greater or lesser than 30 as p increases beyond 30

Insufficient


IMHO Option A
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miles travelled during the trip \(- m\)

Total cost of trip \(- T\)

\(p+0.1p(m-5)=p+0.1pm-0.5p =T\)

\(0.5p+0.1pm=T\)

when \(p>30\) is \(m>30?\)

Statement 1: The moving service charged a total of 3.3p dollars for the trip.

\(T=3.3p\)

\(0.5p+0.1pm=3.3p\)

\(m=28\)

\(m<30\)

Sufficient

Statement 2: The moving service charged a total of \($132\) for the trip.


\(T=$132\)

\(0.5p+0.1pm=$132\)

when \(p=30\), \(m=39\)

when \(p=40\), \(m=28\)

when \(p=33\), \(m=35\)

when \(p>30\), both \(m>30\) & \(m<40\) are possible

Not Sufficient

Answer: A
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From the question we know that the sum would be p+0.1*p*distance after 5 miles. Now assuming it was more than 30 miles we get equation as p+2.5p=3.5p at 30 miles. Now 1st statement says that total charge was 3.3p dollars ie the distance is less than 30 miles. So 1st is enough.
2nd says that total amount is 132 dollars. But the problem is we have 2 unknowns, distance and value of p So This is not enough. 1st is enough to answer.
Bunuel
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?

(1) The moving service charged a total of 3.3p dollars for the trip.
(2) The moving service charged a total of $132 for the trip.


 


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Bunuel
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?

(1) The moving service charged a total of 3.3p dollars for the trip.
(2) The moving service charged a total of $132 for the trip.


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Let's consider total cost of trip of x miles:
cost=p+0.1p(x-5)
We are asked if x>30?

Statement 1:
given cost=3.3p

p+0.1p(x-5)=3.3p
Solving, x=28 (which is less than 30)
Sufficient.

Statement 2:
given cost= 132
p+0.1p(x-5)=132
without p, we can't solve for x.
Insufficient.

Hence, A) Statement 1 alone is sufficient.
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(1)
p + 0.1p.n = 3.3p
p + 0.1p.n = p + 2.3p
p + 0.1p.n = p + 0.1p(23)
n = 23
total miles = 28 < 30
So sufficient

(2)
132 = p + 0.1pn
if p = 30
1020 = 30.n
n ~ 33
if p = 100
320 = 100.n
n ~= 3

So (2) is insufficient as we can and cannot have miles more than 30
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Using the information provided in statement 1 we can find the value of x in the formula (p + 0.1p * (x-5)) which would tell us the length of the trip in miles, but we are not able to determine the value of p which will be essential to answer the question, thus statement 1 alone is insufficient. Statement 2 provides us with the total service charged to be 132, this value alone is clearly insufficient because we have only one equation with two variables p and x which can't be solved with this information. Using the two statements together we can determine x using statement 1 and afterwards p using the determined value of x as well as the total service charged to be 132. Thus in this question IMO there is no need to do the jacky math out because we know that we could solve it at this point, Answer C.

Regards,
Lucas
Bunuel
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?

(1) The moving service charged a total of 3.3p dollars for the trip.
(2) The moving service charged a total of $132 for the trip.


 


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P is greater than 30, so lets take P=35.

First 5 miles = 35 Dollars
Additional mile =0.1*35=3.5 for x ( lets take additional mile as x)

1.) 3.3p dollars for the trip-
3.3*35=35+(0.1*35)x
23=x
Total 28 miles (23+5).

2.) 132 dollars for the trip-
132=35+3.5x
27.7=x
Total= 32.7 miles(27.7+5)
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(1) total of 3.3p dollars for the trip: 3.3p-p = 2.3p. It charged 2.3p for each additional mile and a fraction of a mile. So there were atleast 2.2p/0.1p = 22 miles + a fraction of a mile. So 5+22= 27, the trip could have been 27 miles and a fraction of a mile or 28 miles. The trip was less than 30 miles long. Sufficient.
(2) total of $132 for the trip. 132= p+0.1px, 132 = p(1+0.1x)
p> 30
If p = 33, 1+0.1x = 4 and x= 30. In this case 30+5= 35
If p = 66, 1+0.1x = 2 and x= 10. In this case 10+5= 15
Not sufficient.

Answer is A.
Bunuel
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?

(1) The moving service charged a total of 3.3p dollars for the trip.
(2) The moving service charged a total of $132 for the trip.


 


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First 5 miles: p dollars
Each additional mile or fraction of a mile: 0.1*p dollars
If p>30, was a particular trip >30 miles long?
Let total mile (excluding first 5 miles) = x
If total dollar = p+ (0.1*x)p >30, total mile = 5 + x >30?

(1) Total trip = 3.3p = (1+ 2.3)p = p + 2.3p
=> x = 2.3/0.1 = 23 => Total miles of the trip is 23 + 5 = 28
=> Total miles of the trip is smaller than 30 miles no matter what value of p
=> Sufficient.

(2) p+ (0.1*x)p = 132

If p = 33 >30 => x = 30 => Total mile = 35 >30 => Yes
If p = 40 >30 => x = 23 => Total mile = 28 <0 => No
=> With with p values >30, two answers yes and no => Insufficient.

Answer: A
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Statement (1) Analysis
The first statement provides that the total charge for the trip was 3.3p dollars.

Set up the cost formula: Let x be the number of additional miles (or fractions of a mile) after the first 5 miles. The total cost is p + (0.1p * x).

Cost = p * (1 + 0.1x)

Solve for x: We can set the cost formula equal to the given charge.

3.3p = p * (1 + 0.1x)

Since p > 30, we can divide both sides by p.

3.3 = 1 + 0.1x

2.3 = 0.1x

x = 23

Find the total distance: The variable x represents the number of additional miles charged after the first 5. The total distance, m, is defined by x = ceiling(m - 5).

23 = ceiling(m - 5)

This means that m - 5 must be greater than 22 and less than or equal to 23.

22 < m - 5 ≤ 23

27 < m ≤ 28

The total distance of the trip was between 27 and 28 miles. Therefore, the trip was not more than 30 miles long. This provides a definitive "No" to the question.

This statement is sufficient.

Statement (2) Analysis
The second statement provides that the total charge for the trip was $132.

Set up the equation:

132 = p * (1 + 0.1x)

Test scenarios: This equation has two unknown variables, p and x. We only know that p > 30. We must check if different valid scenarios lead to different answers.

Scenario A (Trip is NOT > 30 miles): Let's assume the trip was 28 miles. As calculated above, this means x = 23.

132 = p * (1 + 0.1 * 23)

132 = p * (3.3)

p = 132 / 3.3 = 40

This is a valid scenario because p = 40 satisfies the condition p > 30. So, it's possible the trip was not more than 30 miles.

Scenario B (Trip IS > 30 miles): Let's assume the trip was 35 miles. This would mean x = ceil(35 - 5) = 30.

132 = p * (1 + 0.1 * 30)

132 = p * (4)

p = 33

This is also a valid scenario because p = 33 satisfies the condition p > 30. So, it's possible the trip was more than 30 miles.

Since this statement allows for both a "Yes" and a "No" answer to the question, it is not sufficient to determine the answer.

This statement is not sufficient. Hence the answer is A
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Pricing formula:
  • First 5 miles: p dollars
  • Each additional mile: 0.1p dollars
  • For n miles (where n > 5): Total = p + 0.1p(n-5)
Statement (1): Total charge = 3.3p
equation:
3.3p = p + 0.1p(n-5)
3.3p = p + 0.1pn - 0.5p
3.3p = 0.5p + 0.1pn
2.8p = 0.1pn
n = 28 miles

Since 28 < 30, the trip was NOT more than 30 miles.

Statement (1) is sufficient - answers "No"

Statement (2): Total charge = $132
132 = p + 0.1p(n-5)
132 = 0.5p + 0.1pn
n = (132 - 0.5p)/(0.1p)
= 1320/p - 5
Since p > 30:
  • If p = 40: n = 1320/40 - 5 = 33 - 5 = 28 miles
  • If p = 33: n = 1320/33 - 5 = 40 - 5 = 35 miles
We get different answers depending on p's value.
Statement (2) is insufficient

Answer: A - Statement (1) alone is sufficient
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Bunuel
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?

(1) The moving service charged a total of 3.3p dollars for the trip.
(2) The moving service charged a total of $132 for the trip.


 


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Let the trip be of m miles we need to prove m>30. We have p>30.

Stmt 1 : The moving service charged a total of 3.3p dollars for the trip.
Charge = p + m-5(0.1p)

So (m-5)0.1p = 2.3p => m=28.

Hence, stmt 1 is sufficient.

Stmt 2 : The moving service charged a total of $132 for the trip.
m Charge p + (m-5) 0.1p => 132.

Let m be 28, Then p = 40.
If m be 31 then p = 36.66.

So for both m >30, m<30 all conditions are satisfied, Hence Stmt 2 is insufficient.


Hence IMO A


We have only p>30, Let p bee 28. So then m =
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