Number & Arithmetic — practice questions, page 6
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QuestionWhat is the largest prime factor of 2¹² − 1?QuestionThree-fifths of a number exceeds two-sevenths of the same number by 44. What is the number?QuestionThe four-digit number 52x6 is divisible by 12. What is the digit x?QuestionFor how many positive integers n does n! end in exactly three zeros?QuestionFind |−7| − |−3| × (−2), remembering that multiplication comes before subtraction.QuestionWhich is the smallest positive integer having exactly 12 positive divisors?QuestionRationalise each term and add: 1/(1 + √2) + 1/(√2 + √3) + 1/(√3 + √4) = ?QuestionHow many three-digit numbers are divisible by 17?QuestionThe squares of two consecutive whole numbers add up to 365. What is the larger of the two squares?QuestionThe numeral 1101101 is written in base two. What is its value in base ten?QuestionFor some pair of whole numbers, which of the following could be the HCF and the LCM?QuestionIf p and p + 2 are both prime and p is greater than 3, then p + 1 is always a multiple of:QuestionWhat is the sum of the digits of the number 10²⁵ − 25?QuestionWhat is the least number that must be taken away from 7581 so that the result is a perfect square?QuestionTwo whole numbers N and M are each divided by 7. The first leaves remainder 3 and the second…QuestionWhich of these numbers equals the sum of all its factors apart from itself?QuestionHow many digits long is the number 2¹⁰ × 5⁷ once it has been multiplied out?QuestionMeera spends exactly ₹100 on pens costing ₹7 each and notebooks costing ₹11 each, buying at least…QuestionHow many different pairs of whole numbers have HCF 9 and LCM 1188?QuestionIf √x + 1/√x = 3, what is the value of x + 1/x?QuestionThe fraction 17/40 has a terminating decimal expansion. How many digits does it have after the…QuestionHow many two-digit prime numbers have digits adding up to 10?QuestionWhat is the smallest five-digit number that is exactly divisible by 12, 15 and 18?QuestionHow many pairs of positive integers (x, y) satisfy 3x + 5y = 100?QuestionThe value of 24! is written out in full, but one of its digits has been smudged and cannot be…
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