M43-36

Question

Emily paid for meals at five different restaurants in Paris last week. Did she spend more than the median amount at any of the five restaurants?

(1) Emily spent the same total amount at any three of the five restaurants.
 
(2) Emily did not spend less than the average (arithmetic mean) amount at any of the restaurants.

Bunuel · Accepted Answer

Your examples do not satisfy the first statement.

Statement 1 says Emily spent the same total amount at any three of the five restaurants.

This means every combination of three bills must have the same total. For $100, $100, $100, $200, $300, the total of the first three is $300, but the total of the last three is $600. For $100, $200, $300, $300, $300, the total of the first three is $600, but the total of the last three is $900. For Statement 1 to be true, all bills must be the same.

Bunuel · Answer

Official Solution:

Emily paid for meals at five different restaurants in Paris last week. Did she spend more than the median amount at any of the five restaurants? 
 
(1) Emily spent the same total amount at any three of the five restaurants. 
 
This implies that all amounts must be equal. If this were not true, then at least two of the amounts would have been different, say  x < y . In this case, the sum of two amounts plus  x  would be less than the sum of the same two amounts plus  y , making the statement false. Therefore, all amounts must be equal. Consequently, Emily did not spend more than the median amount at any of the five restaurants. Sufficient.
 
(2) Emily did not spend less than the average (arithmetic mean) amount at any of the restaurants.
 
This implies that she also did not spend more than the average amount at any of the restaurants. Therefore, all amounts must be equal. Consequently, Emily did not spend more than the median amount at any of the five restaurants. Sufficient.

Answer: D

tintin9799 · Answer

Bunuel  did not understand why it is implicit for all amounts to be equal ?

Bunuel · Answer

The amounts must be equal because of the specific conditions given in each statement: 1. Statement (1): If Emily spent the same total amount at any three of the five restaurants, then all amounts must be equal. If one amount were different (e.g., x < y), then the total of three amounts containing x would be less than the total of three amounts containing y. This would contradict the statement. Hence, all amounts are equal. 2. Statement (2): If Emily did not spend less than the average at any restaurant, then no amount is below or above the average. This is only possible if all amounts are equal because any variation would create values below or above the average. In both cases, equality of amounts is the only scenario consistent with the given conditions. Check similar question here: https://gmatclub.com/forum/m43-433371.html

7seven7 · Answer

Hi  Bunuel , can you please explain what I missed in Stmt1 ?

Stem:  Emily paid for meals at five different restaurants in Paris last week.  
Q:  Did she spend more than the median amount at any of the five restaurants?  
Stmt:  Emily spent the same total amount at any three of the five restaurants.

For finding median, amounts would be in sorted order (will do with increasing).

If bill amounts are: $100, $100, $100, $200, $300 -> Then yes, she spent more ($200/$300) than median($100) amount.
 If bill amounts are: $100, $200, $300, $300, $300 -> Then no, she did not spent more than median($300) amount.

I agree that Stmt2 is sufficient on it own but not able to understand Stmt1.
Could you please help ?

Regards,
7seven7

HNS · Answer

Hi  Bunuel ,

I think that the wording of statement A is creating a confusion. "(1) Emily spent the same total amount at any three of the five restaurants." Cannot it mean that Emily had spent the same amount at any three restaurants ? What you are suggesting is something like "The sum of money that Emily had spent on any three restaurants is same".

Bunuel · Answer

It might sound confusing, but the only correct reading of that sentence is the one in the solution:

the combined total for any chosen set of 3 restaurants is the same as for any other set of 3.
 
It does not mean “she spent the same amount at three restaurants.”

M43-36

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