Two ways to solve this question:
1) When there is a recurring number i.e non-terminating number, the number can be expressed in the below form
Suppose N = 0.abababababab......
N can be written as
===> __
==>0.ab
To convert any recurring number to fraction form, divide the number by 9,99,999,9999, depending on the no. of recurring digits.
Here we have two recurring digits, so N=ab/99,
Similarly if we have,
====> _____
M = 0.abcde, them M = abcde/99999
NOTE: this is only for numbers in the form of 0.abcdef..... , not for normal recurring number 123123123....
Now in this question, we have
===> ____
D= 0.a1a2
Therefore, D=a1a2/99
Lets try each option and multiple it by D
For C, we have (a1a2/99)*198 => 2* a1a2, this will be an integer.
So option C is correct, for other option we are getting fractional terms.
2) Second way
D= 0.a1a2a1a2a1a2.......
===> ____
D=0.a1a2
Now,
=========> ____
100D= a1a2.a1a2
Now, 100D - D => a1a2 ( Both recurring parts will be subtracted)
99D = a1a2
D = a1a2/99
Rest same as explained 1st way.
Thanks,
Jai
KUDOS if it Helped..!!!
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MODULUS Concept ---> http://gmatclub.com/forum/inequalities-158054.html#p1257636
HEXAGON Theory ---> http://gmatclub.com/forum/hexagon-theory-tips-to-solve-any-heaxgon-question-158189.html#p1258308