bhumika.k.shah wrote:The combined weight of 10 cars is 14000 pounds. No car weighs more than 50% more than any other car. What is the maximum possible weight for the heaviest car?
(A) 1,600
(B) 1,700
(C) 1,800
(D) 1,900
(E) 2,000
HOWWWWWWWWWW TO SOLVEEEEE!!!
For having the heaviest possible single car, let the remaining 9 cars weigh x pounds each, and the single heaviest car weighs h pounds, such that:bhumika.k.shah wrote:The combined weight of 10 cars is 14000 pounds. No car weighs more than 50% more than any other car. What is the maximum possible weight for the heaviest car?
(A) 1,600
(B) 1,700
(C) 1,800
(D) 1,900
(E) 2,000
HOWWWWWWWWWW TO SOLVEEEEE!!!
sars72 wrote:take the mean weight of the 10 cars to be variable M
let H be the weight of the heaviest car
let L be the weight of the leasy heavy (lightest) car
-> 10M= 14000 -> M = 1400
No car weighs more than 50% more than any other car -> H <= 1.5L
lets start of with the higher value choices and eliminate 1 by 1
start off with choice (E) 2000
H = 2000 pounds; since it is no heavier by 50% of any other car
--> 2000< 1.5L --> 1333 <= L, which means that the lightest car should be greater than or equal to (4000/3)
So, to check if this answer is plausible, we assume that all other cars weigh he minimum possible which is (4000/3)
-> (4000/3)*9 = 12000
Add this to the heaviest car which is 2000 -> 12000 + 2000 = 14000; 14000 is the total weight given in the question
So, it is possible for the heaviest car to weight 2000
Since this is the highest answer choice, this is the answer we are looking for and we do not need proceed further.
Answer is (E) 2000
ajith wrote:bhumika.k.shah wrote:The combined weight of 10 cars is 14000 pounds. No car weighs more than 50% more than any other car. What is the maximum possible weight for the heaviest car?
(A) 1,600
(B) 1,700
(C) 1,800
(D) 1,900
(E) 2,000
HOWWWWWWWWWW TO SOLVEEEEE!!!
Now if only one car had 1.5 times weight of the other 9 and if that car had 1.5 x weight of the others. and if all the other cars had the same weight x
10.5 x = 14000
x= 4000/3
the heaviest car weighs 4000/3*1.5 = 2000
now since 2000 is the maximum weight that is in the choices select E
It's just the explanation that looks long. It will take two mins max to solve this. In any case, Sanju's is explanation is much more straightforward and you can see how simple he has made the problem. I went about solving the problem in a round about fashion.bhumika.k.shah wrote:How do u expect to solve such sums in less than 2 mins ???
sorry, didnt explain that.. I divided both sides of the inequality 2000< 1.5L by 1.5 i.e. 3/2bhumika.k.shah wrote:how did u get this 4000/3 ??
--> 2000< 1.5L --> 1333 <= L, which means that the lightest car should be greater than or equal to (4000/3)
Classic silly mistake. The mean value of 1400 is for that 10 cars combined. By doing the calculation involving (1400*8), you are assuming that the mean value of the 8 cars is also 1400. You cannot take out 2 cars and assume that the mean of the remaining cars will remain the same.MFCR wrote:I think the correct answer is 1600 because if the 10 cars weight 14000 in total, the average weight is 1400. If there is one car heavier, there is another one ligther, and the other 8 cars have the average weight of 1400. I mean:
8*1400=11200 pounds
14000-11200=2800 pounds (the total possible weight of other 2 cars, called A and B). And if the weight of one of them (i.e, A) is 1.5 the another one (B), we have the following:
A+B=2800 , if B=1,5A => A+1,5A=2800 => 2,5A=2800 => A=1120 ; B= 1120+1,5= 1680
And now: (1400*8)+1680 (Car B) +1120 (Car A)=14000
sanju09 wrote:For having the heaviest possible single car, let the remaining 9 cars weigh x pounds each, and the single heaviest car weighs h pounds, such that:bhumika.k.shah wrote:The combined weight of 10 cars is 14000 pounds. No car weighs more than 50% more than any other car. What is the maximum possible weight for the heaviest car?
(A) 1,600
(B) 1,700
(C) 1,800
(D) 1,900
(E) 2,000
HOWWWWWWWWWW TO SOLVEEEEE!!!
9 x + h = 14000 and h ≤ 1.5 x. For maximum h, we must take h = 1.5 x
Now, 9 x + 1.5 x = 14000
Or x = 14000/10.5 and h = [spoiler]2,000 [/spoiler]pounds.
[spoiler]E[/spoiler]
