If the length of Wanda's telephone call was rounded up to the nearest

Difficulty level: 650

We have to find the duration of the call say N minutes.

1. Statement 1: It gives information about the cost of total call however we do not know per minute cost hence can not calculate the minutes.

2. Statement 2: We know that the cost of first minute was higher by 0.50 cents however we do not know the cost of subsequent minutes. Secondly, we cant calculate the duration of the call with this information.

Put together, we know the total cost and also know that cost of first minute was higher by 0.50. If for example cost of subsequent minutes were 50 cents, the total duration would have been 12 minutes. Reduce the cost of call made after first minute, the duration will change.

Hence answer is E

Total call minutes=Total call cost/Cost per min
(i) m=6.5/c insufficient
(ii)m={(c+0.5)+c*(m-1)}/c insufficient
combining;
m can't be calculated
so, (E)

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I've just an important question (at least imo). I solved the problem correctly but it took me a too much time. I also ended up with an equation with two unknowns. But since they said "telephone call was rounded up to the nearest whole minute" i was a bit suspicious and tried out numbers in order to make sure that there is more than one solution. Often in DF we make the argument that we can't solve an equation with two unknown, but in fact sometimes we can infer that theres only one plausible solutions (For Instance in the following problem)

A certain fruit stand sold apples for $0.70 each and bananas for $0.50 each. If a customer purchased both apples and bananas from the stand for a total of $6.30, what total number of apples and bananas did the customer purchase ?


So my question is just, when we can make the argument that we are dealing with an equation with two unknowns and when we can't make this argument.

hope its clear

Thank you !

Hi Brunel,
I have one question.
Since xn = 6 and to get 6 (x,n) can be (1,6) or (6,1) or (3,2) or (2,3).
Because if the length of the call was less than a minute, then I think the total charge for the call would be $6.50.
And out of all the possibilities listed above, only (2,3) satisfies the equation 1(x+0.50)+(x-1)n = 6.50.
So Answer C.
Tell me where did I go wrong?

There are other cases possible:
n = 6 minutes and x = 1 --> the cost of the first minute = $1.5 and the cost each of the remaining 5 minutes = $1 --> total = $6.50
n = 3 minutes and x = 2 --> the cost of the first minute = $2.5 and the cost each of the remaining 2 minutes = $2 --> total = $6.50
n = 2 minutes and x = 3 --> the cost of the first minute = $3.5 and the cost of the remaining 1 minute = $3 --> total = $6.50

Hi All,

We're told that Wanda's telephone call was rounded up to the nearest whole minute by her telephone company. We're asked for the number of minutes that she was charged for her telephone call. We can answer this question with a bit of logic and TESTing VALUES.

1) The total charge for Wanda's telephone call was $6.50.

With Fact 1, we know the total cost of the call, but we don't know what rate Wanda was charged per minute.
Fact 1 is INSUFFICIENT

2) Wanda was charged $0.50 more for the first minute of the telephone call than for each minute after the first.

Fact 2 tells us the DIFFERENCE in the rates, but does not tells us the rates themselves nor the length of the call
Fact 2 is INSUFFICIENT

Combined, we know
-The total cost of the call was $6.50
-The first minute cost $0.50 more than each of the additional minutes

IF....
1st minute = $1.00 and each addl. minute = $0.50, then the call would have been 12 minutes
1st minute = $1.50 and each addl. minute = $1.00, then the call would have been 6 minutes
Combined, INSUFFICIENT

Final Answer:

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Rich

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