**A.**0.154

**B.**0.1818

**C.**0.667

**D.**2

**E.**3.03

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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?

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**A.**0.154

**B.**0.1818

**C.**0.667

**D.**2

**E.**3.03

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A fast approach is to use some estimation.e-GMAT wrote: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

E = 1/2 + 1/4 + 1/6 + 1/8 + 1/10 + 1/12 + 1/14 + 1/16 + 1/18 + 1/20

â‰ˆ 0.5 + 0.25 + 0.15 + 0.1 + 0.1 + 0.1 + 0.05 + 0.05 + 0.05 + 0.05

â‰ˆ1.4

The reciprocal of E â‰ˆ1/1.4 â‰ˆ0.7

Check the answer choices . . . answer = C

Cheers,

Brent

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**Posts:**645**Joined:**26 Jul 2010**Location:**US**Thanked**: 527 times**Followed by:**227 members

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.

We need to determine

- "¢ Among the given options, which one can be a possible value of the reciprocal of E.

As E equals the sum of the reciprocals of the first 10 even natural numbers, we can write E in the following manner:

- "¢ E = 1/2 + 1/4 + 1/6 + 1/8 + 1/10 + 1/12 + 1/14 + 1/16 + 1/18 + 1/20

Or, E = 1/2 (1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10)

- "¢ If all 10 terms were equal to 1/10, then E would be 1/2 x 10 x 1/10 = 1/2.
- o But since the actual terms are more, we can say that the value of E is greater than 1/2.

- o But since the actual terms are less, we can say that the value of E is less than 5.

- "¢ 1/2 < E < 5

Or, 2 > 1/E > 1/5

Or, 2 > 1/E > 0.2

Hence, the correct answer is option C.

Answer: C