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The cost of a certain phone call was $0.75 for the first 3 minutes and 17 Dec 2013, 17:06
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The cost of a certain phone call was $0.75 for the first 3 minutes and $0.20 for each additional minute after the first 3 minutes. Did the phone call last longer than 15 minutes?

(1) The cost of the phone call was less than $4.16.

(2) The cost of the phone call was greater than $3.35.


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The cost of a certain phone call was $0.75 for the first 3 minutes and 18 Dec 2013, 01:39
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Bunuel
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The cost of a certain phone call was $0.75 for the first 3 minutes and $0.20 for each additional minute after the first 3 minutes. Did the phone call last longer than 15 minutes

(1) The cost of the phone call was less than $4.16
(2) The cost of the phone call was greater than $3.35



While this is a seemingly simple min/max problem, I was wondering if there is a faster way to deal with decimals—as it took me ~4mins to arrive at the solution.

The cost of a certain phone call was $0.75 for the first 3 minutes and $0.20 for each additional minute after the first 3 minutes. Did the phone call last longer than 15 minutes

According to the above the cost for n minutes, where n>3, is \(75 + (n-3)*20=20n+15\) cents. W need to find whether n>15. The cost for 15 minutes is \(20n+15=20*15+15=315\) cents, so we need to find whether the cost is greater than 315 cents.

(1) The cost of the phone call was less than $4.16. Not sufficient.

(2) The cost of the phone call was greater than $3.35. Sufficient.

Answer: B.
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The cost of a certain phone call was $0.75 for the first 3 minutes and 18 Dec 2013, 01:34
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megafan
The cost of a certain phone call was $0.75 for the first 3 minutes and $0.20 for each additional minute after the first 3 minutes. Did the phone call last longer than 15 minutes

(1) The cost of the phone call was less than $4.16
(2) The cost of the phone call was greater than $3.35



While this is a seemingly simple min/max problem, I was wondering if there is a faster way to deal with decimals—as it took me ~4mins to arrive at the solution.
Show more

The cost of a certain phone call was $0.75 for the first 3 minutes and $0.20 for each additional minute after the first 3 minutes. Did the phone call last longer than 15 minutes

According to the above the cost for n minutes, where n>3, is \(75 + (n-3)*20=20n+15\) cents. W need to find whether n>15. The cost for 15 minutes is \(20n+15=20*15+15=315\) cents, so we need to find whether the cost is greater than 315 cents.

(1) The cost of the phone call was less than $4.16. Not sufficient.

(2) The cost of the phone call was greater than $3.35. Sufficient.

Answer: B.
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The cost of a certain phone call was $0.75 for the first 3 minutes and 02 Jul 2014, 08:05
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Hi Bunuel,
I tried solving this question by following method and i feel both the statements are not sufficient to get an answer.

given: The cost of a certain phone call was $0.75 for the first 3 minutes and $0.20 for each additional minute after the first 3 minutes. Did the phone call last longer than 15 minutes

let's assume phone call lasted for x mins
1) The cost of the phone call was less than $4.16
75+x*20< 416
x<17.04.. Not sufficient as x can be > , < or = 15

2) The cost of the phone call was greater than $3.35
75+x*20>335
x>13 again not sufficient

combining both 13<x<17..not sufficient..
Please let me know where i am going wrong.
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The cost of a certain phone call was $0.75 for the first 3 minutes and 02 Jul 2014, 21:26
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varikaur
Hi Bunuel,
I tried solving this question by following method and i feel both the statements are not sufficient to get an answer.

given: The cost of a certain phone call was $0.75 for the first 3 minutes and $0.20 for each additional minute after the first 3 minutes. Did the phone call last longer than 15 minutes

let's assume phone call lasted for x mins
1) The cost of the phone call was less than $4.16
75+x*20< 416
x<17.04.. Not sufficient as x can be > , < or = 15

2) The cost of the phone call was greater than $3.35
75+x*20>335
x>13 again not sufficient

combining both 13<x<17..not sufficient..
Please let me know where i am going wrong.
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I get the fallacy mate. The call of 0.20 is after three minutes. So once you as per you calculation get 13 , you have to add the first 3 minutes. Thus you get the total time as 13 + 3 = 16 minutes
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The cost of a certain phone call was $0.75 for the first 3 minutes and 02 Dec 2014, 21:00
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Lets t = 15 then C = .75 + 12*.20 = 3.15. basically is C > $3.15

1. C < 4.16 not sufficient
2. C > 3.35 so C is definitely greater then 3.15 Sufficient.

Answer: B

megafan
The cost of a certain phone call was $0.75 for the first 3 minutes and $0.20 for each additional minute after the first 3 minutes. Did the phone call last longer than 15 minutes

(1) The cost of the phone call was less than $4.16
(2) The cost of the phone call was greater than $3.35



While this is a seemingly simple min/max problem, I was wondering if there is a faster way to deal with decimals—as it took me ~4mins to arrive at the solution.
Show more
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The cost of a certain phone call was $0.75 for the first 3 minutes and 09 Aug 2016, 18:39
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The cost of a certain phone call was $0.75 for the first 3 minutes and $0.20 for each additional minute after the first 3 minutes. Did the phone call last longer than 15 minutes

(1) The cost of the phone call was less than $4.16
(2) The cost of the phone call was greater than $3.35



While this is a seemingly simple min/max problem, I was wondering if there is a faster way to deal with decimals—as it took me ~4mins to arrive at the solution.

The cost of a certain phone call was $0.75 for the first 3 minutes and $0.20 for each additional minute after the first 3 minutes. Did the phone call last longer than 15 minutes

According to the above the cost for n minutes, where n>3, is \(75 + (n-3)*20=20n+15\) cents. W need to find whether n>15. The cost for 15 minutes is \(20n+15=20*15+15=315\) cents, so we need to find whether the cost is greater than 315 cents.

(1) The cost of the phone call was less than $4.16. Not sufficient.

(2) The cost of the phone call was greater than $3.35. Sufficient.

Answer: B.
Show more

What is the flaw in my reasoning -

0.75X3 + A X 0.2 = Total Cost.

Where A is the # of Minutes after 3 Minutes.

Basically, now we boil down to if A>12

Statement 1 =
0.75X3 + A X 0.2 = 4.16
A = 9.55 Minutes - That means A is not greater than 12. Hence with the calculation we did above we can clearly say that this statement is sufficient to forecast that A is not greater than 12.
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The cost of a certain phone call was $0.75 for the first 3 minutes and 10 Aug 2016, 01:06
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The cost of a certain phone call was $0.75 for the first 3 minutes and $0.20 for each additional minute after the first 3 minutes. Did the phone call last longer than 15 minutes

(1) The cost of the phone call was less than $4.16
(2) The cost of the phone call was greater than $3.35



While this is a seemingly simple min/max problem, I was wondering if there is a faster way to deal with decimals—as it took me ~4mins to arrive at the solution.

The cost of a certain phone call was $0.75 for the first 3 minutes and $0.20 for each additional minute after the first 3 minutes. Did the phone call last longer than 15 minutes

According to the above the cost for n minutes, where n>3, is \(75 + (n-3)*20=20n+15\) cents. W need to find whether n>15. The cost for 15 minutes is \(20n+15=20*15+15=315\) cents, so we need to find whether the cost is greater than 315 cents.

(1) The cost of the phone call was less than $4.16. Not sufficient.

(2) The cost of the phone call was greater than $3.35. Sufficient.

Answer: B.

What is the flaw in my reasoning -

0.75X3 + A X 0.2 = Total Cost.

Where A is the # of Minutes after 3 Minutes.

Basically, now we boil down to if A>12

Statement 1 =
0.75X3 + A X 0.2 = 4.16
A = 9.55 Minutes - That means A is not greater than 12. Hence with the calculation we did above we can clearly say that this statement is sufficient to forecast that A is not greater than 12.
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You should read the stem and the solution more carefully.

1. The cost of a certain phone call was $0.75 for the first 3 minutes, not $0.75 for each of the first 3 minutes;
2. A in your solution must be more than 15, not more than 12;
3. (1) says that the cost of the phone call was less than $4.16, not equal to $4.16.

So, it should be 0.75+ A *0.2 < 4.16 --> A < 17.05.
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The cost of a certain phone call was $0.75 for the first 3 minutes and 05 Sep 2016, 12:03
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The trick here is understanding that the 0,75 was for all three minutes (not 0,75 per minute).
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The cost of a certain phone call was $0.75 for the first 3 minutes and 02 Dec 2017, 10:55
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megafan
The cost of a certain phone call was $0.75 for the first 3 minutes and $0.20 for each additional minute after the first 3 minutes. Did the phone call last longer than 15 minutes

(1) The cost of the phone call was less than $4.16
(2) The cost of the phone call was greater than $3.35
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For First 3 mins, the cost = 0.75$
For each additional minute after the first 3 minutes, the cost = 0.20$

SO, calculate the cost for the 15 minutes -- cost for first 3 mins + cost for each additional minute after the first 3 minutes
= 0.75$ + 12*0.20$ = 0.75$ + 2.40$ = 3.15$

Now, Question becomes whether the cost of phone call > 3.15$?

1. <4.16$
so the cost can OR cannot be > 3.15$ Insufficient

2. >3.35$
Sufficient. As cost > 3.35$ will always be > than 3.15$.

Answer : B
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The cost of a certain phone call was $0.75 for the first 3 minutes and 23 Jan 2019, 23:44
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For a 15 minute call, the call cost will be 3.15 dollars.
A call greater than 15 minutes will have to cost more than 3.15 dollars.

Statement 1 - Not sufficient.
Statement 2 - Sufficient.

Hence B.
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The cost of a certain phone call was $0.75 for the first 3 minutes and 24 Sep 2025, 01:00
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Hey! This is a classic DS question that tests your ability to translate between cost and time - let's break it down step by step.

The Key Insight

First, let's think about what we're really asking here. We need to know if the call lasted longer than 15 minutes. Since cost increases directly with time after the first 3 minutes, this becomes a cost question.

Let's calculate what a 15-minute call would cost:
- First 3 minutes: \($0.75\) (flat fee)
- Additional 12 minutes: \($0.20 × 12 = $2.40\)
- Total for 15 minutes: \($0.75 + $2.40 = $3.15\)

So our question transforms into: Did the call cost more than \($3.15\)?

Analyzing Statement 1

Statement 1 tells us the cost was less than \($4.16\).

Notice how this doesn't help us determine if the cost exceeded \($3.15\). The actual cost could be:
- \($3.00\) (less than \($3.15\)) → Call was shorter than 15 minutes
- \($3.50\) (more than \($3.15\) but still less than \($4.16\)) → Call was longer than 15 minutes

Since we get different answers depending on the actual cost, Statement 1 alone is NOT sufficient.

Analyzing Statement 2

Statement 2 tells us the cost was greater than \($3.35\).

Here's what you need to see: Since \($3.35 > $3.15\) (our 15-minute threshold), we know the call definitely lasted longer than 15 minutes. Any cost above \($3.35\) means the call went beyond 15 minutes.

Statement 2 alone is sufficient.

Answer: B

Statement 2 alone gives us enough information, while Statement 1 alone does not.

---

You can check out the complete framework on Neuron to master the systematic approach for all cost-time relationship problems in DS. You can also explore comprehensive solutions for similar official questions here to build consistent accuracy across different question variations.
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