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Numbers high level Exercise 2 - 3

13. If the first 99 natural numbers are written side by side to form a new number 123456..........9899, then find the remainder when this number is divided by 11.
a. 5
b. 6
c. 7
d. 8


14.123456789101112.... . 434445 . Find the remainder when divided by 45?
a. 0
b. 10
c. 20
d. 30


15. Find the value of $\displaystyle\frac{{LCM{\rm{ (1, 2, 3, 4,}}.........{\rm{100)}}}}{{LCM{\rm{ (51, 52, 53, }}......{\rm{100)}}}}$


16.  Find the number of combinations of (a, b, c) if LCM (a, b) = 1000, LCM (b, c) = 2000, LCM (c, a) = 2000
a.  70
b.  80
c.  90
d.  100


17.  The letters A, B, C, D, E, F and G represent distinct digits chosen from (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) such that A*B*C = B*G*E = D*E*F, where ‘*’ means multiplication. What does the letter G represent?
a*b*c=b*g*e=d*e*f
a.   4
b.   3
c.   2
d.   5


18. Find the remainder when 39! is divided by 41.
a. 1
b. 11
c. 39
d. 40