A cafeteria offers seven types of sandwiches, each with a fixed price

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

Analyzing the question:
Average price is 2.25, therefore the sum is 7*2.25 = 14+1.4+0.35 = $15.75. Is there any that costs less than $1.75? Note it is relatively straightforward to find a case in which one is less than 1.75, so we should see if there is a case in which no sandwiches cost less than 1.75. If we can't, the statement would be sufficient. Also, note that the sandwiches do not have to have different prices.

Statement 1:
The max price is 2.7, which is 2.7-2.25 = 0.45 above the median. We can have one sandwich at 1.8 which is 0.45 below the average to even out with the one with maximum price, and have the rest at the average price so that all sandwiches cost more than $1.75. The key point here is that there is enough room to have all of the sandwiches at a high enough price. Insufficient.

Statement 2:
Again we should focus on finding a case in which all of the sandwiches cost above $1.75. Because the median is 2.70, we need at least three sandwiches priced greater than or equal to $2.7. We can set all of them to 2.7, the lowest price possible, to maximize the prices of the remaining sandwiches. Then we have the three lowest-priced sandwiches sum to = 15.75 - 2.7*4 = 15.75 - 10.8 = $4.95. This is not enough to price three sandwiches $1.75 each, therefore one of them must cost less than 1.75.

Ans: B

I am surprisingly little confused with these sort of probolems, Can you please share a link with similar questions?

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.