amanvermagmat wrote:
itisSheldon wrote:
There are five homes. If the median price of a home is $200,000, is the range of all prices greater than $80,000?
1) The average price of the five homes is $240,000.
2) Three of five homes have the same price.
Statement 1:Average price of 5 homes = $240,000. This means total price of 5 homes = 5*240000 = $1,200,000.
To keep our range minimum, we should try to keep smallest and largest values (out of these 5) as close as possible.
Our smallest value can go up to 200,000 (since thats the median), and in that case, first 3 values will be 200,000 only.
So let the price of first 3 homes be $200,000 each. This makes it $600,000. Remaining price of 2 costlier homes = 1,200,000 - 600,000 = $600,000
In this case, costliest room will get the smallest value if we assume price of 4th and 5th homes to be equal, i.e., $300,000 each.
So here we have accomplished the purpose of keeping the smallest and largest value as close as possible. And the range in this case = price of highest - price of lowest = 300,000 - 200,000 = $100,000. So when here only the range is more than $80,000 then in any other case it will definitely be more than $80,000.
Sufficient.
Statement 2:Which three homes have same price we don't know. And also this doesn't help in determining the range. So
not sufficient.
Hence
A answerI think even B is sufficient.... working for option B.
even though we dont know which 2 houses have same price, we have to make either of the choices.. as there are only two choices available if we keep house in ascending order of their value.
choice I : 1, 2 & 3 have same price
Choice II : 2, 3 & 4 have same price
Choice I : 1 2 & 3 have same price, since the median is known to us 200000. price of 1, 2 & 3 totals to 600,000 and rest 3 & 4 have a value of 600,000.
now whatever value we give to 4 & 5 range is going to be more than 80,000.
Choice II : 2 3 & 4 have same price, again as we know median is 200000. price of 2 3 & 4 totals to 600,000 and rest 1 & 5 have a value of 600,000.
now whatever value we give to 1 & 5 range is going to be more than 80,000.
Hence under both choices we get same answer that is range of all prices
IS greater than $80,000. so even B is sufficient statement.
pls help me, if m on the wrong track !!
You are falling into the common trap of GMAT DS questions.
If you exclusively consider Statement 2, You only know that three out of five homes have the same price, but you don't know the average price of five homes.(For instance the average price of five homes can be $200,000. In that case range of the homes will be zero)
Hope that helps.