Samwong wrote:

What is the 101st digit after the decimal point in the decimal representation of \(\frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \frac{1}{37}\) ?

A) 0

B) 1

C) 5

D) 7

E) 8

Official Explanation:

\(\frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \frac{1}{37}=\frac{333}{999} + \frac{111}{999} + \frac{37}{999} + \frac{27}{999}=\frac{508}{999}=0.508508...\) .

102nd digit will be 8, thus 101st digit will be 0.

The correct answer is A.

It took me a while to see that 1/27 is equal to 37/999 and that 1/37 is equal to 27/999. What clue in the question indicates that you need to make that conversion? What is the shortcut for that conversion?

\(\frac{1}{3} =\frac{1*333}{3*333}=\frac{27}{999}\).

\(\frac{1}{9} =\frac{1*111}{9*111}=\frac{27}{999}\).

\(\frac{1}{27} =\frac{1*37}{27*37}=\frac{27}{999}\).

\(\frac{1}{37} =\frac{1*27}{37*27}=\frac{27}{999}\).

Following link might help for this problem:

math-number-theory-88376.html (check Converting Fractions chapter).

_________________

New to the Math Forum?

Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:

GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:

PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.

What are GMAT Club Tests?

Extra-hard Quant Tests with Brilliant Analytics