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What is the remainder when 77,777… up to 56 digits is divided by 19?

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Important Questions on Numbers and Their Properties

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IMPORTANT
Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 58
There are three consecutives odd integers such that the product is a prime number. Find the largest of the prime number.
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Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 60
A man took a five-digit number ending in 9 and raised it to an even power greater than 50. He then multiplied it with 17 raised to a multiple of 4. What is the last digit of the resulting number?
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Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 61
Rahul took an odd number of prime numbers and added them. He found the result to be even. Which of the following could be concluded?
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Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 62
When asked as to how many guavas Lovely has, she replies, 'if you add three-quarters of the number of guavas that I have to three-quarters of one guava, you will get the numbers of guavas I have'. How many guavas does she have?
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Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 66
What is the remainder when [100 !+1] is divided by 101?
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Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 67
A is a set of the first 10 natural numbers. B is a subset of A such that B consists of exactly 2 numbers, both co-primes to each other. Find the maximum number of such possible subsets.
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Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 68
When written in the lowest term, rational numbers A and B have denominators 60 and 70, respectively. Now, A and B have been added. What is the smallest possible denominator of (A+B)?
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Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 71
P, Q, R, S, and T are five prime numbers, where P<Q<R<S<T . It is also given that P+Q+R+S+T=482 . What is the value of P5?