alphak3nny001 wrote:
Jose purchased both large dressers and small dressers to add to his antique furniture collection. The large dressers
cost $31 each, while the small dressers cost $25 each. If Jose did not purchase any other items, how many small
dressers did he buy?
(1) Jose purchased as many small dressers as large dressers.
(2) In total, Jose spent $280 at the flea market
Option A: Jose purchased as many small as large, so small can be 1 dress, 2 dress and so on....we cannot zero in at a particular number
Option B: Jose spent $280 and did not purchase any other items
Lets says number of large dress= x and number of small dress=y
so, 31x + 25y =280
now if you look at it the highest number of small dress that can be purchased is 11 as 11*25=$275 but in this fashion Jose will not be able to spend $280, similar highest large dress can be bought as 9*31=$279 , still $1 will be left
Hence there needs to be a split between the two, now $25 will have either 5 or 0 at the end in its multiple, while $31 has all the numbers from 1 to 9 at the end in its multiple.
How can we have those multiples of 25 an 31 which when added gives 0 at the end as we need $280 in total.....
Only 2 ways possible, either 5 from $25 multiple and 5 from $31 multiple.... or 0 from $25 multiple and 0 from $31 multiple....but $31 multiple cant come with 0 at the end as maximum large dress can be only 9 not 10.
Multiple of $31 possible in this scenario is only 5*$31=$155 so for small left amount will be $280-$155= $125.....
So small dress number will be 5....
Hence B is sufficient
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