One of the best DS problems I have seen that is so compact yet complicated! I think if anybody receives such a question in actual GMAT exam and solves it under time scramble they deserve 700+ for sure.
All these problems require thinking from a bids eye point of view and not delve too deep.
Similar to distance/rate problems where multiple meeting points are given, such a problem requires to understand from a generalistic standpoint.
Statement 1: No more than 4.
Here we do see that only with 4 we can get it to 4*19 = 76 as the sum and remaining values will take up more than 19 ppl.
SUFFICIENT.
Statement 2:
You might be thinking and jumping to possiblities with 1x,2x,3x,4x,5x,6x,7x... and I think it is good to quickly do that for a few seconds to get the feel for the statement.
Because only then you will first realise that ALL are even or ALL are odd.
Possible confusions involve:
1) With even number multiple I can never even have an odd number so hmm 1 orange is never used in this case.
You might be quick to move on to odd multiples like 1/3/5 and so on and check if with 1 there is anyway to find solution to diophontine equations.
THIS IS COMPLEX. Also one would realise quickly that you could always form such an equation and have atleast 1 orange since u have a plethora od possibilities with odd multiples and there is no bound.
And the answer would be that statement 2 would be Insufficient which is why this statement is quite hard to decipher properly and I am sure the above pre thinking is what would happen to most.
HOWEVER,
They mentioned diff between any two is odd so why not simply consider every number to its merit and forget about the multiples completely. Because all we need to know is IF we can include that 1 orange guy or not. Why? 1 orange guy can have millions of possibilities so if anything the question is:
Can 1 orange guy even have 1 or completely have 0.
Now if one thinks on the odd number spectrum then you realise that wait, all odd number for 19 such numbers that has to be odd! But we have 76 as sum! SO not POSSIBLE.
Now that we thought of it this way it might sound really simple but the aim basically is to condense it into simpler sections, and as for this problem the point is difference between any two numbers has to be only even here 19[only odd] = Odd.
Hence SUFFICIENT.
Answer:
Option DBunuel
A fruit stand sold 76 oranges to 19 customers. How many customers bought only one orange?
(1) No customer bought more than 4 oranges.
(2) The difference between the number of oranges bought by any two customers is even.
Apr 28
17 Feb 2025, 11:49
