Mansoor50
*** please note that thisquestions has been asked before but the topic was locked ***
The number of cars present at a particular time was measured at 3,999 different locations on Tuesday and on Wednesday. The number of locations that had more cars on Wednesday was 15% higher than the number of locations that had more cars on Tuesday. How many of the locations had more cars on Tuesday?
1,159
1,333
1,860
2,460
2,829
I am unable to understand the logic that higher-on-tuesday locations plus higher-on-wednesday locations is 3999.
and this iswhere i am getting stuck.
my logic:
total locs=3999. X is the number of higher locs and Y are the rest, thus
x+y=3999
if x increases by 15% this means x->1.15x
and if the number of higher locations increases, then the rest must drop by 15%, thus y->.85y
so we have
1. x+y=3999
2. 1.15x + .85y = 3999
What is wrong with my logic!!
The problem with your logic is as follows :
Since you have assumed x to be the locations which has more cars on Tuesday,
and y are the rest of the location
Hence, x + y =3999 is correct.
When 15% of the locations have more cars on Wednesday,
the number of locations reducing in y is not necessary 15%.
So writing 1.15x + 0.85y = 3999 is wrong.
The reason is the percentage decrease in y will be 15% only if x=y
But, that is not possible since we cannot have a fraction as the number of locations!
Now coming to the solution :
x+y = 3999
On Wednesday, there is a 15% increase in the locations,
going by the answer choices for the locations that had more cars on Tuesday.
Only
1860 or 2460 is possible, since 15% of the other 3 answer options will not yield an integer.
The increase in the locations in x must be equal to the decrease in location of y(in order for the sum to be 3999)
Testing 1860, 15% is 279. Hence making the total 2139(which is 1860 lesser than 3999)
1860(x) + 2139(y) = 2139(x) + 1860(y) = 3999
Hence,
Option C is the correct answer.
Hope it helps!