Question : $3^{11}+3^{12}+3^{13}+3^{14}$ is divisible by:
Option 1: 7
Option 2: 8
Option 3: 11
Option 4: 14
Correct Answer: 8
Solution : Given: $3^{11}+3^{12}+3^{13}+3^{14}$ = $3^{11}(1+3+3^2+3^3)$ = $3^{11}(40)$ Since 40 is divisible by 8, Therefore, the above expression is also divisible by 8. Hence, the correct answer is 8.
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Question : $4^{11}+4^{12}+4^{13}+4^{14}$ is divisible by:
Option 2: 14
Option 3: 17
Option 4: 9
Question : If the six-digit number 479xyz is exactly divisible by 7, 11, and 13, then {(y + z) ÷ x} is equal to:
Option 1: $4$
Option 2: $\frac{11}{9}$
Option 3: $\frac{7}{13}$
Option 4: $\frac{13}{7}$
Question : The number 1563241234351 is:
Option 1: divisible by 11 but not by 3
Option 2: neither divisible by 3 nor by 11
Option 3: divisible by both 3 and 11
Option 4: divisible by 3 but not by 11
Question : If the 7-digit number $x$468$y$05 is divisible by 11, then what is the value of ($x$ + $y$)?
Option 1: 12
Option 3: 8
Option 4: 10
Question : If the six-digit number 5x2y6z is divisible by 7, 11 and 13, then the value of $(x-y+3 z)$ is:
Option 2: 4
Option 3: 0
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