X = 0. p q p q p q p q p q...... is a number where p and q are digits from 0 to 9 such that both p and q are not 0 simultaneously. Which of the following when multiplied by X will result in an integer value?
A. p q
B. 1/(p q)
C. 1/99
D. 198
E. 10 p + q
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not 0 simultaneously
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rossmj
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ANS D
Repeating decimals like this occur when we divde by 9
1/9=.111111
2/9=.22222
Similarly when a number is divded by 99 we get
11/99=.11111111
12/99=.12121212
1/99=.0101010101
so if we multiply by 198 we are multiplying an integer by 2 which will yield an integer.
Repeating decimals like this occur when we divde by 9
1/9=.111111
2/9=.22222
Similarly when a number is divded by 99 we get
11/99=.11111111
12/99=.12121212
1/99=.0101010101
so if we multiply by 198 we are multiplying an integer by 2 which will yield an integer.
