Number & Arithmetic — practice questions, page 5
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If 1/(2 + 1/(3 + 1/x)) = 7/16, then x equals:A student says: "My number leaves remainder 4 when divided by 6 and remainder 3 when divided by…The digits of a two-digit number add up to 12, and the tens digit is to the units digit as 1 : 3.…The greatest number that divides 62, 132 and 237 leaving the same remainder in each case is used…If x² − y² = 91 and x + y = 13, where x and y are positive integers, then x − y equals:The value of 0.444… + 0.222… − 0.111… (each of the digits repeating for ever) is:The value of 1/(1 + 1/(1 + 1/(1 + 1))) is:How many perfect squares between 1 and 500 end in the digit 5?On rationalising the denominator, (√7 + √3)/(√7 − √3) becomes:The value of a^(1/2) × a^(2/3) ÷ a^(1/6), when a = 64, is:If 1/(3 − 2√2) = a + b√2 where a and b are rational numbers, then a + b equals:For how many prime numbers p is p² + 2 also a prime number?A quick test for 7 says: chop off the last digit, double it, and subtract it from what is left;…Which fraction sits exactly halfway between 1/3 and 1/2?The largest power of 12 that divides 100! exactly is 12^k. What is k?What is the greatest four-digit number that is a multiple of 88?Two whole numbers, each greater than 1, are co-prime and their LCM is 143. What is their sum?A whole number is divisible by 4 and is also divisible by 6. Which of these must it be divisible…What is the least number that must be ADDED to 2497 to make it exactly divisible by 23?How many perfect squares lie strictly between 100 and 1000?A four-digit number is made by writing the same two-digit number twice over, as in 5757 or 2323.…Three consecutive odd numbers add up to 129. What is the smallest of them?Every factor of 36 is written on its own card, and then all the cards are multiplied together. The…Which digit stands in the 100th place after the decimal point in 5/7?Three logs of timber measuring 42 m, 49 m and 63 m are to be sawn into planks that are all the…
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