PE 4 - Numbers | Algebra - Number Theory
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If S is the sum of all two-digit numbers that give a remainder of 5 when they are divided by 11, what is the remainder when S is divided by 11?
Solution
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ReportIn a garden there are 50 plants, planted in rows with the same number of plants in each row. The number of flowers on every plant of a row is the square of the row number. If the total number of flowers is 550, find the number of rows?
(a + b)! is divisible by which of the following? (a and b are positive integers)
- (a)
a!
- (b)
b!
- (c)
a! × b!
- (d)
All of the above
What is the remainder when 500-digit 1223334444…. is divided by 8?
If N is the smallest positive integer that is not prime and does not divide 30!. How many factors does N have?
The nine-digit number 6454389p6 is divisible by 36. Find the value of p.
- (a)
0
- (b)
9
- (c)
0 or 9
- (d)
None of these
n! has 249 zeros, value of n can be:
- (a)
845
- (b)
777
- (c)
1003
- (d)
941
- (e)
1108
What is the remainder when the series 11 + 22 + 33 + … + 99 is divided by 5?
- (a)
0
- (b)
1
- (c)
2
- (d)
3
If m and n are integers divisible by 7, which of the following is not necessarily true?
- (a)
(m – n) is divisible by 7
- (b)
(m2 – n2) is divisible by 49
- (c)
(m + n) is divisible by 14
- (d)
None of these