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29 May 2018, 02:35
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
47% (02:36) correct
53%
(02:53)
wrong
based on 47
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Not Attempted Yet
Edward invested five-ninths of his money at an annual rate of \(2r%\) compounded semi-annually, and the remaining money at an annual rate of\(r%\) compounded annually. If after one year, Edward’s money had grown by one-third, the value of \(r\) is equal to which of the following?
A) 10%
B) 15%
C) 20%
D) 25%
E) 33%
PS: Any tricks to solve this question in less than 2 minutes?
A) 10%
B) 15%
C) 20%
D) 25%
E) 33%
PS: Any tricks to solve this question in less than 2 minutes?
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Original investment be 90
Five-ninths = 50 and remaining i.e four-ninths = 40
Investment 01: 50(1+2r/2)^(2*1) = 50(1+r)^2 ...(1)
Investment 02: 40(1+r) ... (2)
Investment 1+2 = 4/3 of 90
50(1+r^2+2r) + 40 +40r = 120
50r^2 + 140r - 30 = 0
5r^2+14r - 3 = 0
(r+3) (5r-1) = 0
Therefore, r=1/5 or 20%
Answer: C
Five-ninths = 50 and remaining i.e four-ninths = 40
Investment 01: 50(1+2r/2)^(2*1) = 50(1+r)^2 ...(1)
Investment 02: 40(1+r) ... (2)
Investment 1+2 = 4/3 of 90
50(1+r^2+2r) + 40 +40r = 120
50r^2 + 140r - 30 = 0
5r^2+14r - 3 = 0
(r+3) (5r-1) = 0
Therefore, r=1/5 or 20%
Answer: C
05 Jun 2018, 06:22
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PoetVogon
Hi, I like your explanation but I can't follow your last step:
5r^2+14r + 3 = 0 [it should be -3 here but thats probably just a typo
(r+3) (5r-1) = 0
I solved it via the pq-method but that obviously takes a bit time. So can you please elaborate on your method?
