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01 Jun 2020, 03:53
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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:
25%
(medium)
Question Stats:
79% (01:39) correct
21%
(01:36)
wrong
based on 296
sessions
History
Date
Time
Result
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What is the value of S if S=\(1+ \frac{43}{83} + \frac{32}{91} + \frac{29}{120} + \frac{15}{79}\) ?
A) 1 to 1.5
B) 1.5 to 2
C) 2 to 2.5
D) 2.5 to 3
E) 3 to 3.5
A) 1 to 1.5
B) 1.5 to 2
C) 2 to 2.5
D) 2.5 to 3
E) 3 to 3.5
01 Jun 2020, 06:32
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43/83 ~ 43/86 = 1/2 = 0.5
32/91 ~ 32/96 = 1/3 = 0.333....
29/120 ~ 30/120 = 1/4 = 0.25
15/79 ~ 15/75 = 1/5 = 0.2
so those four fractions sum to something close to 1.3, and adding the 1, we should get something around 2.3.
32/91 ~ 32/96 = 1/3 = 0.333....
29/120 ~ 30/120 = 1/4 = 0.25
15/79 ~ 15/75 = 1/5 = 0.2
so those four fractions sum to something close to 1.3, and adding the 1, we should get something around 2.3.
07 Apr 2023, 00:56
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coreyander
Solution:
- Since the answer options are not exact values, we can approximate the fractions a little
- Given \(S=1+ \frac{43}{83} + \frac{32}{91} + \frac{29}{120} + \frac{15}{79}\)
\(≈1+ \frac{40}{80} + \frac{30}{90} + \frac{30}{120} + \frac{15}{75}\)
\(≈1+\frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5}\)
\(≈1+0.5+0.33+0.25+0.2\)
\(≈2.28\) (between 2 to 2.5)
Hence the right answer is Option C
07 Apr 2023, 04:35
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coreyander
Looking at the expression with so many large prime numbers, I know that I am not supposed to do any calculations with them. It just won't be possible in under 2 mins without a calculator. So then I would consider approximating. And that is when I would notice that all the fractions are close to standard fractions of 1/2, 1/3, 1/4 and 1/5.
Thereafter, it is a simple matter of adding them up.
