I am little confused with these two problems:
First is GMAT prep question:
When a certain tree was first planted, it was 4 feet tall, and the heigth of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year. By how many feet did the height of the tree increased each year?
Answers: (A) 3/10 (B)2/5 (C)1/2 (D) 2/3 (E) 6/5
Here is the second question from GMAT club advanced workshop:
The population of Linterhast was 3,600 people in 1990 and 4,800 people in 1993. If the population growth rate per thousand is constant, then what will be the population in 1996?
Answers: (A) 6,000 (B) 6,400 (C) 7,200 (D) 8,000 (E) 9,600
but I ended up with A
My interpretation for the first question:
Let x = amount of yearly growth, in feet.
Yr0 = 4
Yr1 = 4+x
Yr2 = 4+x+x=4+2x
Yr3 = 4+x+x+x=4+3x
Yr4 = 4+x+x+x+x=4+4x
Yr5 = 4+x+x+x+x+x=4+5x
Yr6 = 4+x+x+x+x+x+x=4+6x
We are told the amount at the end of Year 6 is 6/5 of the amount at the end of year 4. Thus we can write:
4+6x = 6/5 (4+4x)
5(4+6x) = 6(4+4x)
20+30x = 24+24x
Interpretation for the second question:
Let x = amount of yearly growth
1990 = 3600
1991 = 3600+x
1992 = 3600+x+x=3600+2x
1993 = 3600+x+x+x=3600+3x = 4800
1994 = 3600+x+x+x+x=3600+4x
1995 = 3600+x+x+x+x+x=3600+5x
1996 = 3600+x+x+x+x+x+x=3600+6x
My initial solution:
3600+3x = 4800
So, 1996= 3600+6*400=6000
Then after knowing that I missed the question I solved this way:
(3600+6x) = 4800/3600*(3600+3x)
So, 1996= 3600+6*600=7200
Found the answer with the logic here is just:
I get the logic of the solution but how my other interpretations are not correct since from the GMAT logical sense my other interpretations are correct, even though these two problems are quite identical.
Thus, why my some interpretations are correct in GMAT prep and incorrect in GMAT club problem.