(1/7)+(1/8)+(1/9) is in between?

Question

(\frac{1}{7})+(\frac{1}{8})+(\frac{1}{9})  is in between?
 
A.  (\frac{1}{6}) and (\frac{1}{5})  
B.  (\frac{1}{5}) and (\frac{1}{4})  
C.  (\frac{1}{4}) and (\frac{1}{3})  
D.  (\frac{1}{3}) and (\frac{1}{2})  
E.  (\frac{1}{2}) and 1

BrentGMATPrepNow · Accepted Answer

Let's examine EXTREME values.

If  all 3 values were equal to 1/9 (the smallest value), then the sum would be 1/9 + 1/9 + 1/9 = 3/9 =  1/3 
Of course, the 3 value are  not  equal to 1/9 (the smallest value), so  the original sum must be greater than  1/3

If  all 3 values were equal to 1/7 (the biggest value), then the sum would be 1/7 + 1/7 + 1/7 = 3/7 =  3/7 
Of course, the 3 value are  not  equal to 1/7 (the biggest value), so  the original sum must be less than  3/7

So, the sum must be BETWEEN  1/3  and  3/7 
Hmmm, this is not among the answer choices.

HOWEVER, since  3/7  is less than 1/2, we can also say that the sum must be BETWEEN  1/3  and 1/2

Answer:  D

Cheers,
Brent

soumik0503 · Answer

Option d.. 
1/7=0.1428
1/8=0.1250
1/9=0.1101

How I remember this.. Well Ive mucked up till 1/20...do let me know if any better approach to this is possible

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soumik0503 · Answer

Nice approach..

Thanks Brent.

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Abhishek009 · Answer

\frac{1}{7} + \frac{1}{8} + \frac{1}{9}

= \frac{72 + 63 + 56}{504}

= \frac{191}{504}

= 0.38

Thus, from the given options it is evident that the value ranges from  (\frac{1}{3}) to (\frac{1}{2})  , hence answer must be (D)

Utsharmakarsh · Answer

(17)+(18)+(19)(17)+(18)+(19) is in between?

A. (16)and(15)(16)and(15)
B. (15)and(14)(15)and(14)
C. (14)and(13)(14)and(13)
D. (13)and(12)(13)and(12)
E. (12)and1

+1 d..

umadurga · Answer

Nice approach by Brent.

broall · Answer

$\frac{1}{7}+\frac{1}{8}+\frac{1}{9}> \frac{3}{9}=\frac{1}{3}$

$\frac{1}{7}+\frac{1}{8}+\frac{1}{9}< \frac{3}{7} <\frac{1}{2}$

The answer is D.

MathRevolution · Answer

==>The sum of consecutive reciprocal numbers is decided by the first and the last number. In other words, you get 
(1/9)+(1/9)+(1/9)< (1/7)+(1/8)+(1/9)< (1/7)+(1/7)+(1/7), and if you reorganize this, from
=1/3=3/9=(1/9)+(1/9)+(1/9)<(1/7)+(1/8)+(1/9)<(1/7)+(1/7)+(1/7)=3/7<3/6=1/2, you get between (1/3) and (1/2).

The answer is D.
Answer: D

Madhavi1990 · Answer

Interesting question - can someone share more like these? I felt it was going beyond just series, but more about interpreting the question language as well.Thank you!

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(1/7)+(1/8)+(1/9) is in between?

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