Let 1/3 + 1/5 + 1/7 + 1/9 + 1/11 = m/3*5*7*9*11, where m is a positive

Question

If  \frac{1}{3} + \frac{1}{5} + \frac{1}{7} + \frac{1}{9} + \frac{1}{11} = \frac{m}{3*5*7*9*11} , what is the remainder when m is divided by 5?

A. 0
B. 1
C. 2
D. 3
E. 4

This is a  PS Butler Question

Check the links to other Butler Projects: 
 
   Data Sufficiency Butler 
   Critical Reasoning Butler  
   Sentence Correction Butler  
   Reading Comprehension Butler  
   Integrated Reasoning Butler

d7633056 · Answer

sorry if this is a stupid question. just trying to disambiguate the notation presented here on the right hand side for myself? is it to be considered  \frac{m}{3*5*7*9*11}  or  \frac{m}{3}*5*7*9*11 ?

Bunuel · Answer

______________________________
Fixed the formatting. Thank you!

gmatophobia · Answer

We can take the LCM of the fractions on the RHS. The numerator of each term ( \frac{1}{3}, \frac{1}{7}   and  \frac{1}{9} ) will have 5 in the numerator. The only term that will not have 5 in its numerator is 1/5.

The denominators of the RHS and LHS will cancel out.

The numerator of 1/5 will be 7 * 3 * 9 * 11

The remainder of m when divided by 5 is the same as the remainder when (7*3*9*11) is divided by 5.

We can use the multiplicative property -

Remainder of ( \frac{7*3*9*11}{5} ) = Rem( \frac{7}{5} ) * Rem( \frac{3}{5} ) * Rem( \frac{9}{5} ) * Rem( \frac{11}{5} )

= 2 * 3 * 4 * 1

= Rem( \frac{24}{5} ) = 4

Option E

sumit99kr · Answer

Multiply both sides by 3x5x7x9x11.

It will result m = 5k + 3x7x9x11

Just find the remainder for 3x7x9x11 when divided by 5 using remainder theorem, it will be 4.

Alternatively 3x7x9x11 will have it's units digit as 9.
Thus 9/5 will leave remainder as 4.

Hence E is the correct answer.

Posted from my mobile device

BrushMyQuant · Answer

\frac{1}{3} + \frac{1}{5} + \frac{1}{7} + \frac{1}{9} + \frac{1}{11} = \frac{m}{3*5*7*9*11}

Multiplying with 3*5*7*9*11 on both the sides we get

\frac{ 3*5*7*9*11 }{3} + \frac{ 3*5*7*9*11 }{5} + \frac{ 3*5*7*9*11 }{7} + \frac{ 3*5*7*9*11 }{9} + \frac{ 3*5*7*9*11 }{11} = \frac{ 3*5*7*9*11 * m}{3*5*7*9*11}

=> Integer Multiple of 5(i.e 5*7*9*11) + 3*7*9*11 + Integer Multiple of 5(i.e 3*5*9*11) + Integer Multiple of 5(i.e 3*5*7*11) + Integer Multiple of 5(i.e 3*5*7*9) = m
Remainder of m by 5 = 0 + Remainder of 3*7*9*11 by 5 + 0 + 0 + 0 = Remainder of 3*7*9*11 by 5

Remainder of 3*7*9*11 by 5  = Remainder of units' digit of 3*7*9*11 by 5 = Remainder of 1 by 5 = 1

So,  Answer will be B 
Hope it helps!

Watch the following video to MASTER Remainders

https://www.youtube.com/watch?v=P0S6j2uTaj4

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

Let 1/3 + 1/5 + 1/7 + 1/9 + 1/11 = m/357911, where m is a positive

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions