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

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If the length of Wanda's telephone call was rounded up to [#permalink]

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If the length of Wanda's telephone call was rounded up to the nearest whole minute by her telephone company, then Wanda was charged for how many minutes for her telephone call?

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

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

Diagnostic Test
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Page: 25
Difficulty: 650

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Re: If the length of Wanda's telephone call was rounded up to [#permalink]

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SOLUTION

If the length of Wanda's telephone call was rounded up to the nearest whole minute by her telephone company, then Wanda was charged for how many minutes for her telephone call?

(1) The total charge for Wanda's telephone call was $6.50. Clearly insufficient since we don't know the cost per minute of call.

(2) Wanda was charged $0.50 more for the first minute of the telephone call than for each minute after the first. So, if the first minute costs \($(x+0.5)\) then each succeeding minute costs \($x\). Still not sufficient.

(1)+(2) We have that \((x+0.5)+x(n-1)=6.5\) --> \(xn=6\), where \(n\) is the number of minutes. We have one equation and two unknowns, hence we cannot solve for \(n\). Not sufficient.

Answer: E.
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Re: If the length of Wanda's telephone call was rounded up to [#permalink]

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Hi,

Difficulty level: 600

To find the time duration of Wanda's call,

Using (1),
Total charge for the call = $6.5, we neither know the number of minutes nor call charges. Insufficient.

Using (2),
Wanda was charged $0.50 more for the first minute of the telephone call than for each minute after the first.
x+0.5 for first minute,
for second minute x, & so on,
for the whole call total charges would be nx+0.5 (n = number of minutes)
or nx+0.5 = 6.5
or nx = 6 (1*6 or 6*1 or 2*3 or 3*2)
thus, (n,x) = (1,6) or (6,1) or ....
which means, for 1 min $6 can be charged.
or for 6 mins $1 can be charged. Insufficient.

Answer is (E),

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Re: If the length of Wanda's telephone call was rounded up to [#permalink]

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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
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Re: If the length of Wanda's telephone call was rounded up to [#permalink]

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New post 23 Jul 2012, 07:29
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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Re: If the length of Wanda's telephone call was rounded up to [#permalink]

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If the length of Wanda's telephone call was rounded up to [#permalink]

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New post 29 Apr 2017, 02:26
Bunuel wrote:
SOLUTION

If the length of Wanda's telephone call was rounded up to the nearest whole minute by her telephone company, then Wanda was charged for how many minutes for her telephone call?

(1) The total charge for Wanda's telephone call was $6.50. Clearly insufficient since we don't know the cost per minute of call.

(2) Wanda was charged $0.50 more for the first minute of the telephone call than for each minute after the first. So, if the first minute costs \($(x+0.5)\) then each succeeding minute costs \($x\). Still not sufficient.

(1)+(2) We have that \((x+0.5)+x(n-1)=6.5\) --> \(xn=6\), where \(n\) is the number of minutes. We have one equation and two unknowns, hence we cannot solve for \(n\). Not sufficient.

Answer: E.


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 !
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Re: If the length of Wanda's telephone call was rounded up to [#permalink]

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New post 22 Aug 2017, 06:31
Bunuel wrote:
If the length of Wanda's telephone call was rounded up to the nearest whole minute by her telephone company, then Wanda was charged for how many minutes for her telephone call?

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

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

Diagnostic Test
Question: 27
Page: 25
Difficulty: 650


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?
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Re: If the length of Wanda's telephone call was rounded up to [#permalink]

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New post 22 Aug 2017, 07:44
shrutiwali wrote:
Bunuel wrote:
If the length of Wanda's telephone call was rounded up to the nearest whole minute by her telephone company, then Wanda was charged for how many minutes for her telephone call?

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

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

Diagnostic Test
Question: 27
Page: 25
Difficulty: 650


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
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Re: If the length of Wanda's telephone call was rounded up to [#permalink]

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New post 12 Dec 2017, 11:51
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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Re: If the length of Wanda's telephone call was rounded up to   [#permalink] 12 Dec 2017, 11:51
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