Problem Solving

Crack this one

rahuljones1 wrote:Crack this one

Let I be false. Then no home sold for more than 165,000.
15 x 150000 = 2250000 =Total value of all homes.
If median is 130,000, the first seven homes will have 130,000 since I must max to cover more ground and since first 7 can’t sell for greater since 130000.

So H1-H7 sold for 130000, H8 is median, 130,000. Total is 130000 x8=1,040,000. Subtract this from 2,2500000=1,210,000.
If the remaining 7 houses each sell for 165000 then, 7 x1650000=1155000<1210000. So I must be True.


H1-H7 – 130,000
H8---- 130,000
H9-H14 165,000
H15 ---220,000>165,000

Use this distribution to answer the rest of the question.

II must be true. Since 165,000>130,000 <150,000

III is false b/c none of the homes in the distribution above sold for less than 130,000

Choose I and II

II must be true. Since 165,000>130,000 <150,000

Not quite. An example:

H1,H2,...,H8 = 130K
H9, H10,..., H14 = 170K
H15 = 190K

avenus wrote:

II must be true. Since 165,000>130,000 <150,000

Not quite. An example:

H1,H2,...,H8 = 130K
H9, H10,..., H14 = 170K
H15 = 190K

But this doesn't disprove what I wrote.
170K>130K<150K<190K.
At least one is greater than 130K. and one at least one is less than $150K. Isnt' 130K<150K?

dtweah wrote:

avenus wrote:

II must be true. Since 165,000>130,000 <150,000

Not quite. An example:

H1,H2,...,H8 = 130K
H9, H10,..., H14 = 170K
H15 = 190K

But this doesn't disprove what I wrote.
170K>130K<150K<190K.
At least one is greater than 130K. and one at least one is less than $150K. Isnt' 130K<150K?

yeah, I guess 130K is usually <150K but statement II goes "At least one of the homes was sold for more than 130K and less than 150K". It's referring to the same home.
It doesn't say "At least one of the homes was sold for more than 130K and one of the homes was sold for less than 150K"

I stick with (A), I only.

Thankyou guys ..... your explanation is very helpful .... thanks !!

I stick with A only too.

Because statement 2 says that "At least one of the homes was sold for more than 130K and less than 150K” so in this case, let’s say that all the first 8 houses were sold for 130K, which leaves 1,210,000 if you divide this by 7 (the remaining homes) you will get 172K. So you see, one of the rest of the houses don’t necessarily have to be between 130k & 150k. It could be, but doesn’t have to be. A is correct.