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458 views

Divisibility of large number

This was a question asked in a competitive exam: $(300^{3000} -1 )$ is divisible by a) $401$ b) $501$ c) $301$ d) $901$ The answer is $301$. Not sure how they arrived at the answer. Can ...
256 views

Number of zeros not possible in $n!$ [duplicate]

Possible Duplicate: How come the number $N!$ can terminate in exactly $1,2,3,4,$ or $6$ zeroes but never $5$ zeroes? The number of zeros which are not possible at the end of the $n!$ is: ...
863 views

If a second car leaves later at a higher speed, how long will it take to catch up?

If a Skoda sets off at an average speed of 20 miles per hour at 7 am and a Porsche sets off at an average speed of 40 miles per hour at 4 pm in the same direction, at what time will the Porsche catch ...
226 views

Word based problem with percentages

If your salary is increased by 10% and then after 6 months by a further 50%, what is the overall % increase?
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If $f(x)$ is a polynomial satisfying $f(x)f(\frac 1x) = f(x)+f(\frac 1x)$ and $f(3)=28$, then how could we find $f(4)$?

If $f(x)$ is a polynomial satisfying $f(x)f(\frac 1x) = f(x)+f(\frac 1x)$ and $f(3)=28$, then how could we find $f(4)$ ?
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Finding remainders of large number

This question was asked in a competitive exam. Find the remainder of dividing $6^{83}+ 8^{83}$ by $49$ Are there any theorems/rules to compute the answer ?
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Finding last digit of numbers raised to large powers

This question came in a competitive exam I took recently. The last digit of LCM of $3^{2003} - 1$ and $3^{2003} + 1$ is is there any strategy by which we can quickly determine the answer? I am ...
215 views

HCF/LCM problem

Find the greatest number that will divide $x$, $y$ and $z$ leaving the same remainder in each case. Now the solution for this is obtained by finding the HCF of $(x – y)$, $(y – z)$ and $(z – x)$. ...