Number & Arithmetic — practice questions, page 7
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QuestionTaking √2 = 1.414, what is the value of 4/√2 correct to three decimal places?QuestionWhen 500! is written as a product of prime factors, how many times does the prime 7 appear?Question101 is a prime number. What is the remainder when 3¹⁰¹ is divided by 101?QuestionWhat is the remainder when 12! is divided by 13?QuestionA tower of powers is worked out from the TOP downwards, so 3^3^3 means 3 raised to the power 3³.…QuestionExactly one of these numbers has an ODD number of positive divisors. Which one?QuestionA number is called abundant when its proper divisors — all its divisors except the number itself —…QuestionThe reciprocal of every divisor of 24 is written down, and all of them are added together. What is…QuestionWritten in base six, how many zeros does 20! end with?QuestionCasting out nines is a quick check on a multiplication, because a number and its digit sum leave…QuestionFor every integer n the number n⁵ − n is a multiple of a fixed number. What is the LARGEST number…QuestionA number is divided by 4; the quotient is then divided by 5; and that quotient is divided by 6.…QuestionThe product of two numbers is 4107 and their HCF is 37. What is the larger of the two numbers?QuestionWhat is the longest rod that can measure each of the lengths 2 1/2 m, 3 3/4 m and 5 m an exact…QuestionA three-digit palindrome reads the same forwards and backwards, like 353 or 909. How many…QuestionOf the eleven fractions 1/2, 1/3, 1/4, …, 1/12, how many have a decimal expansion that terminates?QuestionWhich of these fractions is the closest approximation to √2?QuestionHow many of the whole numbers from 1 to 300 are divisible by none of 2, 3 and 5?QuestionThe number 20! ÷ (10! × 10!) works out to a whole number. What is the highest power of 2 that…Questionn is an odd positive integer. The number 7ⁿ + 3ⁿ is always divisible by:QuestionHow many of the numbers from 1 to 30 have exactly four positive divisors?QuestionThe number two hundred is rewritten in base seven. What does it look like?QuestionThe whole numbers from 1 to 100 are written out one after another. How many times does the digit 7…QuestionNumbers of the form 2ᵖ − 1 with p prime are often prime themselves — but not always. Which of…QuestionWhich of these numbers is both a perfect square AND a perfect cube?
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