Number & Arithmetic — practice questions, page 8
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QuestionWithout expanding fully, what is (√5 + √3)² + (√5 − √3)²?QuestionIf 2ˣ = 3ʸ = 6ᶻ, where x, y and z are all non-zero, which relation must hold?QuestionWhat is the sum of all the integers from −25 to 30 inclusive?Questiona and b are integers with a < 0 < b. Which of these expressions is negative for EVERY such pair?QuestionThe recurring decimal 0.363636… (the block 36 repeating) is written as a fraction in its lowest…QuestionEvery three-digit number whose digits are all the same — 111, 222, 333 and so on — has a common…QuestionA number leaves remainder 7 when divided by 12, and also leaves remainder 7 when divided by 18.…QuestionWhat is the remainder when 1! + 2! + 3! + … + 100! is divided by 15?Questionm and n range over all the integers — positive, negative or zero. What is the smallest POSITIVE…QuestionThe HCF of two whole numbers is 12, and the two numbers add up to 84. How many such pairs are there?QuestionHow many ordered pairs of positive integers (a, b) satisfy 1/a + 1/b = 1/6?QuestionWhich of these fractions has the LONGEST repeating block in its decimal expansion?QuestionThe four factorials 5!, 10!, 15! and 20! are all multiplied together. How many zeros does the…QuestionThe number 40! is divided by 18, the answer is divided by 18 again, and so on for as long as the…QuestionHow many of the whole numbers from 1 to 84 have no factor greater than 1 in common with 84?QuestionThe digits of 2¹⁰⁰⁰ are added together; the digits of that answer are added together; and so on…QuestionMany whole numbers can be broken up into a run of two or more consecutive whole numbers — for…QuestionA perfect square is written down, but only its last two digits can still be read. Which of these…QuestionIn the stack 7^7^7 the exponent is itself 7⁷, so the number is 7 raised to the power 823543. What…QuestionSplitting a number into blocks of three digits from the right and then alternately subtracting and…QuestionA fruit-seller has a basket of mangoes. Counted out in threes, 2 are left over; counted out in…QuestionThe number 10¹² + 10⁶ + 1 is written out in full. How many of its digits are zeros?QuestionA three-digit number is subtracted from the number written with its digits in reverse order, and…QuestionFor how many whole numbers n is n added to the sum of its own digits equal to 2016? (For instance…QuestionHow many divisors of 900 are smaller than 30 yet do not divide 30?
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