QUANTITATIVE ABILITY I - Number Theory & Divi

1.Use the shortcut for checking divisibility by 11 to determine if 123456 is divisible by 11. 2.Determine the number of factors of 360 using the prime factorization shortcut. Show your steps. 3.Use modular arithmetic to find the remainder when 83 is divided by 9. Explain your process. 4.Find the greatest common divisor (GCD) of 252 and 336 using the Euclidean algorithm. Show the steps involved. II. Divisibility Rules & Unit Place Deduction 1. Check if 5832 is divisible by 6. Use the divisibility rules for 2 and 3 to justify your answer. Determine if the number 1234567 is divisible by 9. Use the digit sum rule and explain your calculation. 2.A number ends in 4 and is divisible by 8. What can you conclude about this number? Provide an example of such a number. 3.If a number is divisible by both 4 and 9, is it always divisible by 36? Justify your answer with examples. 4.Find the smallest number that, when divided by 5, leaves a remainder of 3, and when divided by 7, leaves a remainder of 5. Use the Chinese Remainder Theorem.

QUANTITATIVE ABILITY I - LCM & HCF

1.Find the LCM and HCF of 45 and 60 using prime factorization. Show all steps. 2.Two numbers have an LCM of 72 and an HCF of 12. If one of the numbers is 24, find the other number. 3.Use the relationship between LCM and HCF to find the LCM of 28 and 35, given that their HCF is 7. 4.A gardener is planting trees in rows. The rows must be 12 trees long or 16 trees long. What is the minimum number of trees that can be in each row such that it is a multiple of both 12 and 16?