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# A new cell phone plan is offering pricing based on average monthly use

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A new cell phone plan is offering pricing based on average monthly use  [#permalink]

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08 Oct 2014, 14:27
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Difficulty:

95% (hard)

Question Stats:

45% (02:19) correct 55% (02:27) wrong based on 218 sessions

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Tough and Tricky questions: Statistics

A new cell phone plan is offering pricing based on average monthly use. Brandon and Jodie are comparing their average use to determine the best plan for them. Brandon's average monthly usage in 2001 was q minutes. Was this less than, greater than, or equal to Jodie's 2001 average monthly usage, in minutes?

(1) From January to August 2001, Jodie's average monthly usage was 1.5q minutes.
(2) From April to December 2001, Jodie's average monthly usage was 1.5q minutes.

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Re: A new cell phone plan is offering pricing based on average monthly use  [#permalink]

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10 Oct 2014, 13:51
A little confused as to how to clearly think this through?

From A, we have a total of 12q for the first 8 months. It could be 00003333.

From B, we have a total of 13.5q for the last 9 months. It could be 033331.5000.

Is it B because that determines how the first 8 months are laid out in terms of minutes?
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Re: A new cell phone plan is offering pricing based on average monthly use  [#permalink]

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11 Oct 2014, 11:18
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Bunuel wrote:

Tough and Tricky questions: Statistics

A new cell phone plan is offering pricing based on average monthly use. Brandon and Jodie are comparing their average use to determine the best plan for them. Brandon's average monthly usage in 2001 was q minutes. Was this less than, greater than, or equal to Jodie's 2001 average monthly usage, in minutes?

(1) From January to August 2001, Jodie's average monthly usage was 1.5q minutes.
(2) From April to December 2001, Jodie's average monthly usage was 1.5q minutes.

1) from jan to august we have 8 months, and average of these 8 months = 1.5q, thus total usage for these 8 months = 12q { (total usage/ 8)=1.5)}

now lets assume she didn't call at the remember 4 months. i.e. total usage for the last 4 months=0. then total average usage of jodi will be 12q/12 = q. now, if she continue to have the same average of 1.5q minutes, then her total cell phone usage for the last 4 months will be 1.5*4= 6. and the average for the whole year will be 12q (for the first eight months) + 6q ( last 4 months) /12 = 1.5q, which is more than q. Thus final usage could be either equal or greater than q.
thus statement 1 alone is not sufficient.

2)

from April to December we have 9 months, and average of these 9 months =1.5q, thus total usage for these 9 months = 1.5q*9 =13.5q

now even if we assume. she didn't use her phone for the initial 3 months. then also her average phone usage for the whole year becomes more than q. (13.5q/12 >q) thus statement 2 alone is sufficient to answer.

hence B
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Re: A new cell phone plan is offering pricing based on average monthly use  [#permalink]

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28 Sep 2016, 09:41
Easy to solve if we plug in numbers.

(1) Q = Brandon's avg, J=Jordie's average
1-8 months J=1.5Q

If Q=2, J=3. Then for the first 8 months , Q=16 and J=24. If J= x*Q (with x={0,01-infinite number}) J>Q overall.
But, if J=0, then Q=J=24 at the end of the year.

So (1) is not sufficient..

(2) For the months April-December, J=1.5Q, which means that if Q=2, J=3 for 9 months, therefore Q=18 and J=27 for these 9 months. Whatever happens to J, on the first 3 months, it will still be J>Q at the end of the year.

So statement (2) is sufficient, and Answer is B.
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Re: A new cell phone plan is offering pricing based on average monthly use  [#permalink]

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23 Feb 2017, 05:41
PROMPT ANALYSIS

Brandon usage is 12q for an year.

SUPER SET

The answer could be <,=,> than 12q.
Translation.
To find the value of usage of Jodie, we need:
1# eact value in terms of q per year.
2# any equation that can help us to determine the answer.

STATEMENT ANALYSIS

St 1: the total usage of Jodie for 8 month will be 1.5q *8 = 12q. For the rest of the 4 months if the usage is zero, then it will be equal. If she uses in any of the other 4 months, it will be greater than 12q. INSUFFICIENT. Option a and d eliminated.

St 2: The total usage for given 9 months is 13.5q. Even if she does not use for rest 3 months, the number will be always greater than 12q. Hence the usage of Jodie will always be greater. SUFFICIENT.

Option B
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Re: A new cell phone plan is offering pricing based on average monthly use  [#permalink]

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23 Mar 2017, 10:52
manpreetsingh86 wrote:
Bunuel wrote:

Tough and Tricky questions: Statistics

A new cell phone plan is offering pricing based on average monthly use. Brandon and Jodie are comparing their average use to determine the best plan for them. Brandon's average monthly usage in 2001 was q minutes. Was this less than, greater than, or equal to Jodie's 2001 average monthly usage, in minutes?

(1) From January to August 2001, Jodie's average monthly usage was 1.5q minutes.
(2) From April to December 2001, Jodie's average monthly usage was 1.5q minutes.

1) from jan to august we have 8 months, and average of these 8 months = 1.5q, thus total usage for these 8 months = 12q { (total usage/ 8)=1.5)}

now lets assume she didn't call at the remember 4 months. i.e. total usage for the last 4 months=0. then total average usage of jodi will be 12q/12 = q. now, if she continue to have the same average of 1.5q minutes, then her total cell phone usage for the last 4 months will be 1.5*4= 6. and the average for the whole year will be 12q (for the first eight months) + 6q ( last 4 months) /12 = 1.5q, which is more than q. Thus final usage could be either equal or greater than q.
thus statement 1 alone is not sufficient.

2)

from April to December we have 9 months, and average of these 9 months =1.5q, thus total usage for these 9 months = 1.5q*9 =13.5q

now even if we assume. she didn't use her phone for the initial 3 months. then also her average phone usage for the whole year becomes more than q. (13.5q/12 >q) thus statement 2 alone is sufficient to answer.

hence B

Hi Bunuel,

Can q be 0 (i.e., if Brandon's usage is zero minutes) minutes? And must we always assume positive values in handling such cases?
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A new cell phone plan is offering pricing based on average monthly use  [#permalink]

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10 Jun 2018, 13:38
Bunuel wrote:

Tough and Tricky questions: Statistics

A new cell phone plan is offering pricing based on average monthly use. Brandon and Jodie are comparing their average use to determine the best plan for them. Brandon's average monthly usage in 2001 was q minutes. Was this less than, greater than, or equal to Jodie's 2001 average monthly usage, in minutes?

(1) From January to August 2001, Jodie's average monthly usage was 1.5q minutes.
(2) From April to December 2001, Jodie's average monthly usage was 1.5q minutes.

Given how the question is worded, I think the answer should be E.

We need to compare Jodie's average usage for the entire year to Brandon's average usage for the entire year. Or, if we know each person's total usage for the entire year, we'll also be able to find the answer. We're given that Brandon's average usage in 2001 was q minutes. So he used 12q minutes in total. Question becomes: Did Jodie use more than, less than, or equal to 12q minutes in 2001?

(1) From Jan to Aug means from Jan 1 to Aug 1, i.e. 7 months. So in 7 months, Jodie used a total of 1.5q*7=10.5q minutes. We don't know if Jodie used any minutes in the following months, so can't say if her total usage was over/under/equal to 12q. Not sufficient

(2) From Apr to Dec means from Apr 1 to Dec 1, i.e. 8 months. So in 8 months, Jodie used a total of 1.5q*8=12q minutes. So her total usage could be greater than or equal to 12q. We don't know. Not sufficient

(1)+(2)
From (2), we know that Jodie used just as many minutes during part of the year as Brandon used during the whole year. So if she used even 1 more minute during another part of the year, we have a definite answer. It's tempting now to pick Answer C since (1) tells us her average during another part of the year. But consider this: What if in (1), she used 0 mins in Jan, Feb, and Mar, and 10.5q mins total in Apr, May, Jun, and Jul. Her average usage for Jan-Aug would still be the same. In this scenario, the time period Apr thru Jul is a subset of the time period in (2), so we can't say for sure if Jodie used any more mins than 12q in 2001.

Not sufficient

Note: If statements said from April to December inclusive, the answer would be B.

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Re: A new cell phone plan is offering pricing based on average monthly use  [#permalink]

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14 Jun 2018, 10:46
Bunuel wrote:

Tough and Tricky questions: Statistics

A new cell phone plan is offering pricing based on average monthly use. Brandon and Jodie are comparing their average use to determine the best plan for them. Brandon's average monthly usage in 2001 was q minutes. Was this less than, greater than, or equal to Jodie's 2001 average monthly usage, in minutes?

(1) From January to August 2001, Jodie's average monthly usage was 1.5q minutes.
(2) From April to December 2001, Jodie's average monthly usage was 1.5q minutes.

From January to August 2001, Jodie's average monthly usage was 1.5q minutes.

The total usage from January to August is 1.5q x 8 = 12q minutes, which means her average monthly average is at least 12q/12 = q minutes. If she used at least 1 minute on her cell phone from September to December, then her average monthly usage would be greater than that of Brandon. However, if she didn’t use any minutes from September to December, then her average monthly usage would equal that of Brandon. Statement one alone is not sufficient.

Statement Two Alone:

From April to December 2001, Jodie's average monthly usage was 1.5q minutes.

The total usage from April to December is 1.5q x 9 = 13.5q minutes, which means her average monthly average is at least 13.5q/12 = 1.125q minutes. Even if she didn’t use any minutes from January to March, her average monthly usage would still be greater than that of Brandon. Statement two alone is sufficient.

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Re: A new cell phone plan is offering pricing based on average monthly use  [#permalink]

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14 Jun 2018, 15:58
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The prompt should require that q>0, and the question stem should provide a crystal clear referent for this.
Also -- if we assume that this refers to Brandon's 2001 average monthly usage -- the question stem can be answered even without the two statements:
Was Brandon's 2001 average monthly usage, in minutes, less than, greater than, or equal to Jodie's 2001 average monthly usage, in minutes?
Since Brandon's average monthly usage must be less than, greater than or equal to Jodie's, the answer to this question stem is YES -- even without any additional information from the two statements.
I believe that the following rewrite reflects the intent of the problem:

Quote:
A new cell phone plan is offering pricing based on average monthly use. Brandon and Jodie are comparing their average use to determine the best plan for them. Brandon's average monthly usage in 2001 was q minutes, where q>0. In 2001, was Jodie's average monthly usage, in minutes, greater than Brandon's average monthly usage, in minutes?

(1) From January to August 2001, Jodie's average monthly usage was 1.5q minutes.

(2) From April to December 2001, Jodie's average monthly usage was 1.5q minutes.

Brandon's total usage in 2001 = (12 months)(average monthly usage) = 12q.
For Jodie's average monthly usage to be greater than Brandon's, Jodie's total usage in 2001 must be greater than Brandon's total usage in 2001.
Questions stem, rephrased:
Was Jodie's total usage in 2001 > 12q?

Statement 1:
Jodie's total usage for the 8 months January though August = (8 months)(average monthly usage) = (8)(1.5)q = 12q.
If Jodie has no usage during the remaining 4 months, then her total usage = 12q, so answer to the question stem is NO.
If Jodie has some usage during the remaining 4 months, then her total usage > 12q, so the answer to the question stem is YES.
Since the answer is NO in the first case but YES in the second case, INSUFFICIENT.

Statement 2:
Jodie's total usage for the 9 months April though December = (9 months)(average monthly usage) = (9)(1.5)q = 13.5q.
Thus, the answer to the question stem is YES.
SUFFICIENT.

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Re: A new cell phone plan is offering pricing based on average monthly use  [#permalink]

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15 Jun 2018, 09:00
Given: Brandon's average monthly usage in 2001 was q minutes.
To find: Was this less than, greater than, or equal to Jodie's 2001 average monthly usage, in minutes?

Statement 1:
From January to August 2001, Jodie's average monthly usage was 1.5q minutes.
This statement gives a total of usage for 8 months which is equal to = 12q.
So, if we consider that the Jodie didn't use for the remaining months. Then, the average = $$\frac{12q}{12}$$ = q.
But, if she at least used anything > 0. Then the average comes down to something > q.
So, Statement1 is insufficient.

Statement 2:
From April to December 2001, Jodie's average monthly usage was 1.5q minutes.
This statement gives a total of usage for 9 months which is equal to = 13.5q.
So, if we consider that the Jodie didn't use for the remaining months. Then, the average = $$\frac{13.5q}{12}$$ > q.
So, Statement 2 is sufficient.

Correct choice is B.
Re: A new cell phone plan is offering pricing based on average monthly use &nbs [#permalink] 15 Jun 2018, 09:00
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