If Jack buys 5 pieces of three different items priced $20, $80 and $10

Question

If Jack buys 5 pieces of three different items priced $20, $80 and $100, does he buy at least one piece of each item?

(1) Three of 5 pieces are priced at $100 each.
(2) Average cost of 5 pieces is greater than $80.

self made

NandishSS · Answer

(1) Three of 5 pieces are priced at $100 each.

It can be 3 $100 and 2 items of $20 & $800 Gives Yes

It can be all 5 $100 Gives No

(2) Average cost of 5 pieces is greater than $85.

It says total cost is more than 425

It can be 3 $100 and 2 items of $20 & $800 Gives Yes

It can be all 5 $100 Gives No

Combining both doesn't give any info

Hence E

niks18 · Answer

Statement 1:  other two items can be priced at $80 each or one can be of $20 & the other of $80.  Insufficient

Statement 2:   Average >80 =>  total price >400

Now if all three items are bought then cost of 3 items will be  =20+80+100=200

so the total cost of remaining two items has to be at least 201. But maximum cost of any item is 100, hence we can reach only upto 200, resulting in total cost of 400. But we know total price >400

Hence all three items were not bought.  Sufficient 
 
Option  B

chetan2u · Answer

Hi  niks18 ,

most of the time you are right there, but here you have missed a point in statement II

(1) Three of 5 pieces are priced at $100 each. 
other 2 could be 20 and 80 ..yes
other two can be both same type... No
insuff

(2) Average cost of 5 pieces is greater than $80. 
 TRICK lies here..
 Max average when all three items are there : one each of 20 and 80 and remaining three of 100  , so  \frac{20+80+3*100}{5}=80 
BUT the average is >80
so there is no item of $20.. ans is always NO
sufficient 
B

niks18 · Answer

Yup agreed. I actually got confused between the earlier average posted 85 & the edited one 80. I changed the value but did not check the approach

chetan2u · Answer

actually, irrespective of 80 or 85 it is going to be B.
changed it to 80 to make it a bit more tricky for those getting at 80, otherwise 85 is straight B.

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If Jack buys 5 pieces of three different items priced $20, $80 and $10

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If Jack buys 5 pieces of three different items priced $20, $80 and $10

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