The cost of a certain phone call...

[joshhowatt]

I am beating my head on this one from GMAT Prep. Someone please help.

The cost of a certain phone call was $.75 for the first 3 minutes and $.20 for each additional minute after the first 3 minutes. Did the phone call last longer than 15 minutes?

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

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

Looks easy enough, right?

The OA is: C

Although upon working through it I came up with E




My logic:

subtract .75 from 4.16 you get 3.41. Then I can divide 3.41 by .20 to give me the number of LESS THAN minutes. m<17 INSUF

Same for 2. subtract .75 from 3.35 gives 2.6$, divide by .20 gives must be GREATER THAN 13 m>13 INSUF

Combining the two gives us options for 14, 15, 16. Which would be insufficient.

However, the explanation that GMAT Prep gives is that we're to use a formula .75 + (.2)(t-3) subbing in minutes for t starting with 15 and working our way up determining a price structure. I'm having a hard time figuring out how my logic doesn't pan out. Can someone please help?


Same for

[eagleeye]

Hi joshhowatt:

This is how I did it. It should be easy to follow:

We are told that for the first 3 minutes, 75 cents are charged, for each additional minute it is 20 cents. We need to find out whether the call was longer than 15 minutes. Let's find the threshold value at 15 minutes so that we can solve the problem the fastest. For talk time of 15 minutes, we are charged 75cents for the first 3, and 20 cents for each of the remaining 12.

Total cost for 15 minutes = 75 + 20 * 12 = 75 + 240 = 315

1) The cost of the call was less than 416.
Since the cost was less than 416, it could either be greater than 315 or less than it, so we can't be sure, INSUFFICIENT.

2) The cost of the call was greater than 335. Clearly this means that money spent was greater than 315 (for the 15 minute case). Hence the call is definitely longer than 15 minutes. SUFFICIENT.

Hence the correct answer is B

I know you said that the OA says C, but it must be incorrect. Clearly, B is the correct answer.

Let me know if this helps

[joshhowatt]

Hey Eagleeye,
You're right! I actually went back and checked and it is B! I've been looking at this screen for WAAAAY too long apparently.

And now looking at it again, I realize my method would have work as well, had I remembered to INCLUDE the 3 minutes attributed to the .75 cents. That would have given me

1. m<20
2. m>16

Which is clearly B

Some times this test makes me feel so stupid. I need a night off. LOLOL.

Thank you for helping to sort things out.