What is the remainder when 45647^(1+4+9+...+625) is divided by 34?

sry cal mistakewhen u first divide 45647 with 34 remainder is 1919^9=171 & 34x5=170the exponent of 45647 is 25x13x17so the remainder of (25x13x17) with 9 will be 8so remaining will be 19^8/34so remainder will be 15

Explanation:- 45647 when divided by 34 leaves a remainder of 19.and In the power we are getting square of nos 1+2^2+3^2......25^2 using sum formula we get this as 5525 so question reduces to 19^5525 divided by 34 we can further apply euler no concept to find that 16th power will give remainder of 1 so question becomes (19^5)/34 gives rem 15

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Some apples were distributed evenly among some boys. If eight more apples were distributed ,each boy would have got four apples . If the number of apples distributed had been two less, each Boy would have got three apples. How many apples were distributed?

Let number of apples be x Now, x + 8/4 = × - 2/3 Hence, x = 32

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Weightage of Number system in CAT?

Hai Vikash, Around 2-4 questions come from Number Systems every year. The major areas covered in Number Systems are Basics of Numbers, Divisibility Rules, Divisibility and Factors, HCF / LCM, Finding Out Last Digit, Finding Out Last Two Digits, Number of Trailing Zeroes, Highest Power of a Number in a Factorial, Finding out Remainders, Base Systems.