Q1
Let D be a recurring decimal of the form, D = 0.a1a2a1a2a1a2 ......., where digits a1 and a2 lie between 0 and 9. Further, at most one of them is zero. Then which of the following numbers necessarily produces an integer, when multiplied by D?
Answer: C
D = 0.a1a2a1a2a1a2.....
∴100D = a1a2∙a1a2.....
100D – D = 99D = a1a2, which is an integer.
∴ If D is multiplied by 99 or any multiple of 99 it will result in an integer.
From the options given, it is clear that 198 (= 99 × 2) will necessarily produce an integer, when multiplied by D.
Hence, option (c).