Bunuel wrote:

A cafeteria offers seven types of sandwiches, each with a fixed price and a fixed set of ingredients (no additions or substitutions). If the average price among the seven sandwiches is $2.25 do any sandwiches cost less than $1.75?

(1) The maximum price of a sandwich is $2.70.

(2) The median price of a sandwich is $2.70.

This is how i solved....

I am basically using what brent did but adding my test cases for even more simplification.....

So as Brent mentioned

" Target question: Do any sandwiches cost less than $1.75?

Given: The average price among the seven sandwiches is $2.25

So, (TOTAL cost of all 7 sandwiches)/7 = $2.25

So, TOTAL cost of all 7 sandwiches = (7)($2.25) = $15.75

Statement 1: The maximum price of a sandwich is $2.70

This statement doesn't FEEL sufficient, so I'll TEST some values.

Notice the Max cost = 2.7 and the average cost is 2.25 here the difference is 0.45

Let's assume all 7 sandwiches cost 2.25 each except the 7th one which cost = 2.70 so in order to maintain the avg we need to deduct 0.45 ( 2.70 - 2.25 ) from one of the other sandwiches...

so let's test some values 2.25 - 0.45 = 1.80 So, in this case, no sandwich is below 1.75

Here the valus are 1.80 ,2,25, 2,25,2,25,2,25,2,25 and 2.70 = And overall avg of 2.25

But we can also deduct more from one sandwich eg 2.25 - 0.55 =1.70 and add also subtract the 0.10 from another sandwich ie 2.25- 0.10 = 2.15

So now the set is 1.70 , 2.15, 2.25 .2.25 2.25 ,2,25 and 2.70 and yet we are at the overall avg of 2.25 per sandwich,,,

There are several scenarios that satisfy statement 1 and the given information (that the TOTAL cost of all 7 sandwiches = $15.75). Here are two:

Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Is perfectly explained by brent below

" Is it also possible to have a situation in which there are NO sandwiches that cost less than $1.75?

Let's find out.

Let's arrange the 7 sandwich prices in ASCENDING order with a median price of $2.70.

We get: _ _ _ $2.70 _ _ _

We're trying to create a scenario in which there are NO sandwiches that cost less than $1.75. This means we're trying to MAXIMIZE the values to the LEFT of the median. To do this, we must MINIMIZE the values to the RIGHT of the median.

Since the values to the RIGHT of the median must be $2.70 or greater, we can MINIMIZE these values by making them all $2.70.

We get: _ _ _ $2.70 $2.70 $2.70 $2.70

4 x $2.70 = $10.80, so we have already accounted for $10.80 of the total $15.75

$15.75 - $10.80 = $4.95, so the remaining 3 prices must add to $4.95

At this point, we might recognize that it is IMPOSSIBLE to achieve our goal of creating a scenario in which there are NO sandwiches that cost less than $1.75

Here's why.

If all 3 remaining prices were $1.75, then we would need $5.25 (3 x $1.75 = $5.25). However, we only have $4.95 left.

So, at least one of the 3 remaining prices will be LESS THAN $1.75

So, statement 2 guarantees that there IS a sandwich that costs less than $1.75

Since we can answer the target question with certainty, statement 2 is SUFFICIENT "

Answer: B