hD13
A group of people decided to cut 128 trees in a certain number of days. For the first 4 days, they were able to achieve their planned per day target. However, for the remaining days, the group was able to cut 4 more trees daily than planned. In this way, the group could cut 164 trees one day before the planned finish date. What was the number of trees the group was planning to cut per day?
(A) 6
(B) 7
(C) 8
(D) 12
(E) 16
Posted from my mobile device Logical thinking ( Options )As we have 128 trees cut over a certain period of days, we can safely assume that number of days and number of trees per day should be factors of 128.
\(128 = 2^7 \), so the answer should have only 2s in it.
Eliminate A, B and D.
C) 8
So 8 trees per day for 16 days.
Number of trees = 4*8+(16-1-4)*(8+4)=32+11*12=164...Matches the quantity given in question
Algebraic Let the number of days be n, so trees per day = \(\frac{128}{n}\)
First 4 days: \(4*\frac{128}{n}\)
Next n-1-4 days: \((n-5)*(\frac{128}{n}+4)\)
Total = \((n-5)*(\frac{128}{n}+4)+4*\frac{128}{n}=164\)
\((n-5)(128+4n)+4*128=164n..........128n+4n^2-5*4n-5*128+4*128=164n.........32n+n^2-5n-160+128=41n\)
\(n^2-14n-32=0.......n^2-16n+2n-32=0.....(n-16)(n+2)=0\)
So, n=16 or -2..
Number of days = 16, so trees per day = 128/16=8
C