Problem Solving

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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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