Anonamy wrote:
Is there a 2 min solution for this problem? The above calculations seem time-intensive.
Hi
Anonamy,
Initially we need to check which of these packs will provide us with the highest value for money (Minimum unit price of a hot dog )
LCM of 8 , 20 and 250 is 1000
Total cost of 1000 hot dogs
-when all hot dogs are bought in 8-pack = 1.55* (1000/8) = 1.55 *125 = 193.75 $
-when all hot dogs are bought in 20-pack = 3.05 * (1000/20) = 3.05 * 50 = 152.5 $
-when all hot dogs are bought in 250-pack = 22.95 * 4 = 91.8 $Though i have shown the calculations here , you need not do the above on the test . One can use estimation here .
Price of 8-pack = $1.55
Price of 20-pack = $3.05
20 is 2.5 times 8 , so we can estimate here that 1.55*2.5 ~ 3.75+ (+ signifies slightly more) . More than cost of 8 - pack.
Now , comparing 20 -pack vs 250 - pack
250 is 12.5 times 20 . Even if we estimate it as 12 .
We can estimate price as 12* 3.05 ~ 36+ (+ signifies slightly more) .
At this step we know that in order to buy greatest number of hot dogs we need to maximize the number of 250 pack , then 20 pack and then 8 pack .( with the amount remaining after each successive steps)
To maximize number of hot dogs with 200$
Total number of hot dogs bought in 250-pack = 22.95*8 =183.6$
Amount remaining = 200 - 183.6 = 16.4$
With this we can buy 5 of 20-pack = 3.05*5 15.25 $
Amount remaining = 16.4 - 15.25 = 1.15$
This amount is too less to buy any 8- pack .
Since two answers are really close - 2100 and 2108 , i would not recommend estimation here .
Greatest number of hot dogs one can buy with 200 $ = 250*8 + 20*5 = 2100
Answer B
_________________
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
+1 Kudos if you find this post helpful