GMAT Forum
2 postsPage 1 of 1
- Guest
- RonPurewal
- Students
- Posts: 19744
- Joined: Tue Aug 14, 2007 8:23 am
For pete's sake, don't post image files for questions like this (especially not that small - some of us have bad eyes!). Just type out the question, which would probably take less time than capturing the screen and uploading it to an image hosting site anyway...
I'm not going to write thousands, just to save some electronic trees: "$150" = $150,000, and so on.
Using the arithmetic mean, the TOTAL price of all the homes is 15 x $150 = $2250. That's all that tells us.
The median, which is the 8th price in the list if they are arranged in ascending/descending order, is $130.
Since these are AT LEAST statements, it's better to evaluate the statement by substituting NONE. If the statement doesn't work with NONE, then AT LEAST ONE MUST is true. If the statement _does_ work with NONE, then AT LEAST ONE MUST is false.
(I) If NONE of the homes was more than $165, then the most expensive house was $165. But the highest sum total you can get this way is seven $165's and eight $130's (because #8 has to be $130), which adds to $2195. That's too low, so there must have been at least one house for over $1653
(II) It's very possible for NONE of the homes to have sold between $130 and $150. Remember, all you need is one counterexample, so you can pick numbers as absurd as possible: Let the seven cheapest houses be FREE ($0), and the eighth be $130 as required. That gives you $2120 to split up between the seven most expensive houses, so they could all cost 2120/7 = $302 and change apiece. Therefore this is false.
(III) If NONE of the homes sold for less than $130, that means the bottom eight ALL sold for exactly $130 (because $130 still has to be the median). That gives 2250 - (8x130) = $1210 left for the most expensive seven houses. If they all cost 1210/7 = just shy of $173 apiece, that'll do the trick. So this is false.
I'm not going to write thousands, just to save some electronic trees: "$150" = $150,000, and so on.
Using the arithmetic mean, the TOTAL price of all the homes is 15 x $150 = $2250. That's all that tells us.
The median, which is the 8th price in the list if they are arranged in ascending/descending order, is $130.
Since these are AT LEAST statements, it's better to evaluate the statement by substituting NONE. If the statement doesn't work with NONE, then AT LEAST ONE MUST is true. If the statement _does_ work with NONE, then AT LEAST ONE MUST is false.
(I) If NONE of the homes was more than $165, then the most expensive house was $165. But the highest sum total you can get this way is seven $165's and eight $130's (because #8 has to be $130), which adds to $2195. That's too low, so there must have been at least one house for over $1653
(II) It's very possible for NONE of the homes to have sold between $130 and $150. Remember, all you need is one counterexample, so you can pick numbers as absurd as possible: Let the seven cheapest houses be FREE ($0), and the eighth be $130 as required. That gives you $2120 to split up between the seven most expensive houses, so they could all cost 2120/7 = $302 and change apiece. Therefore this is false.
(III) If NONE of the homes sold for less than $130, that means the bottom eight ALL sold for exactly $130 (because $130 still has to be the median). That gives 2250 - (8x130) = $1210 left for the most expensive seven houses. If they all cost 1210/7 = just shy of $173 apiece, that'll do the trick. So this is false.
2 posts Page 1 of 1