What is the 99th digit after the decimal point in the

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Tue Aug 07, 2018 7:49 pm

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What is the 99th digit after the decimal point in the decimal expansion of 2/9 + 3/11?

A. 1
B. 2
C. 4
D. 7
E. 9

OA C

Source: Manhattan GMAT

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Tue Aug 07, 2018 9:12 pm

BTGmoderatorDC wrote:What is the 99th digit after the decimal point in the decimal expansion of 2/9 + 3/11?

A. 1
B. 2
C. 4
D. 7
E. 9

OA C

Source: Manhattan GMAT

2/9 = 0.2222...; we see that the 99th digit would be '2.'
3/11 = 0.2727...; we see that the digits at odd places are 2,' while that at even places are '7.' Since 99 is odd, the 99th digit would be '7.'

Thus, the 99th digit after the decimal point in the decimal expansion of 2/9 + 3/11 = 2 + 2 = 4.

The correct answer: C

Hope this helps!

-Jay
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swerve: Legendary Member; Posts: 2535; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Wed Aug 08, 2018 10:17 am

$$\frac{2}{9}=0.2222222...............2$$
$$\frac{3}{11}=0.27272727...............27$$
Addition (does not have carries)
$$\frac{2}{9}+\frac{3}{11}=0.49494949..........49$$
Odd's have 4.

99th would have 4. Therefore, C is the correct answer. Regards!

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8136; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Sun Aug 26, 2018 6:35 pm

BTGmoderatorDC wrote:What is the 99th digit after the decimal point in the decimal expansion of 2/9 + 3/11?

A. 1
B. 2
C. 4
D. 7
E. 9

2/9 + 3/11 = 22/99 + 27/99 = 49/99 = 0.494949....

SInce each odd-positioned digit to the right of the decimal point has a value of 4, the 99th digit is 4.

Alternate Solution:

We see that 2/9 = 0.222... and 3/11 = 0.272727...

If we add the two decimal expressions, we see that we obtain 0.494949... Since all the odd-positioned digits to the right of the decimal point have a value of of 4, the 99th digit is 4.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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