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DS Question

by MI3 » Sun Jul 17, 2011 3:01 am
Q. 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.

IMO - [spoiler]C , with the reasoning that since there is an overlap between the months, we can argue that at no given point Jodie's usage was < Brandon's [/spoiler]..Yay / Nay?
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by blackjack » Sun Jul 17, 2011 4:42 am
If q is Brandon's average monthly usage, then his yearly usage is 12q. Let Jodie's average monthly usage be j, then her yearly usage is 12j. We need to prove 12j is equal to or greater than 12q.

#1. Jodie's average monthly usage for 8 months was 1.5q. So total for 8 months was 12q. If her usage was zero for the remaining 4 months then her total usage is equal to 12q, but then it might be more than 12q, if she used more minutes in the remaining 4 months.--->insufficient.

#2 Jodie's average monthly for 9 months was 1.5q. So total for 9 months was 13.5q. Tjis is greater than 12q and will remain so irrespective of the usage in remaining months.--->sufficient.

Answer is B. Hope this helps!
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