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04 Apr 2019, 22:05
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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:
85%
(hard)
Question Stats:
51% (02:24) correct
49%
(02:21)
wrong
based on 328
sessions
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The value of the variable E is determined by adding the reciprocals of the first 10 even natural numbers. Which of the following can be a possible value of the reciprocal of E?
A. 0.154
B. 0.1818
C. 0.667
D. 2
E. 3.03
A. 0.154
B. 0.1818
C. 0.667
D. 2
E. 3.03
10 Apr 2019, 21:40
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Solution
Given:
In this question, we are given that
- • The value of the variable E is determined by adding the reciprocals of the first 10 even natural numbers.
To find:
We need to determine
- • Among the given options, which one can be a possible value of the reciprocal of E.
Approach and Working:
As E equals the sum of the reciprocals of the first 10 even natural numbers, we can write E in the following manner:
- • E = \(\frac{1}{2}\) + \(\frac{1}{4}\) + \(\frac{1}{6}\) + \(\frac{1}{8}\) + \(\frac{1}{10}\) + \(\frac{1}{12}\) + \(\frac{1}{14}\) + \(\frac{1}{16}\) + \(\frac{1}{18}\) + \(\frac{1}{20}\)
Or, E = \(\frac{1}{2} (1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \frac{1}{7} + \frac{1}{8} + \frac{1}{9} + \frac{1}{10})\)
Now, if we observe the terms within the bracket carefully, we can see that 1 is the largest among all the 10 terms and \(\frac{1}{10}\) is the smallest among all the 10 terms.
- • If all 10 terms were equal to \(\frac{1}{10}\), then E would be \(\frac{1}{2} * 10 * \frac{1}{10}\) = \(\frac{1}{2}\).
- o But since the actual terms are more, we can say that the value of E is greater than \(\frac{1}{2}\).
- • Similarly, if all 10 terms were equal to 1, then E would be \(\frac{1}{2} * 10 * 1 = 5\).
- o But since the actual terms are less, we can say that the value of E is less than 5.
Combining the above results, we can say
- • \(\frac{1}{2} < E < 5\)
Or, \(2 > \frac{1}{E} > \frac{1}{5}\)
Or, \(2 > \frac{1}{E} > 0.2\)
From the given options, only 0.667 falls in the given range.
Hence, the correct answer is option C.
Answer: C
QOW Quant Workshop:
General Discussion
Archit3110
05 Apr 2019, 02:20
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Given
E= determined by adding the reciprocals of the first 10 even natural numbers ; 2,4,6,8,10..20
so E = (1/2+1/4+1/6+1/8+1/10+1/12+...+1/20)
or say
E = 1/2(1/1+1/2+1/3+1/4+1/5+1/6+...+1/10)
E= 1/2 ( 1+.5+.3+.25+.2+.16+....+.1)
E= ~ 3/2
reciprocal of E = 2/3 = ~ 0.66
IMO C
E= determined by adding the reciprocals of the first 10 even natural numbers ; 2,4,6,8,10..20
so E = (1/2+1/4+1/6+1/8+1/10+1/12+...+1/20)
or say
E = 1/2(1/1+1/2+1/3+1/4+1/5+1/6+...+1/10)
E= 1/2 ( 1+.5+.3+.25+.2+.16+....+.1)
E= ~ 3/2
reciprocal of E = 2/3 = ~ 0.66
IMO C
EgmatQuantExpert
