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# CAT Past Year Questions: Factors & Divisibility Notes | Study Quantitative Aptitude (Quant) - CAT

## Document Description: CAT Past Year Questions: Factors & Divisibility for CAT 2022 is part of Quantitative Aptitude (Quant) preparation. The notes and questions for CAT Past Year Questions: Factors & Divisibility have been prepared according to the CAT exam syllabus. Information about CAT Past Year Questions: Factors & Divisibility covers topics like and CAT Past Year Questions: Factors & Divisibility Example, for CAT 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for CAT Past Year Questions: Factors & Divisibility.

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Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:How many factors of 24 × 35 × 104 are perfect squares which are greater than 1?



Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:How many pairs (m, n) of positive integers satisfy the equation m2 + 105 = n2?



Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:In a six-digit number, the sixth, that is, the rightmost, digit is the sum of the first three digits, the fifth digit is the sum of first two digits, the third digit is equal to the first digit, the second digit is twice the first digit and the fourth digit is the sum of fifth and sixth digits. Then, the largest possible value of the fourth digit is?



Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:If m and n are integers such that (√2)19 34 42 9m 8n = 3n 16m (∜64) then m is



Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157 : 3, then the sum of the two numbers is



Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:The number of integers x such that 0.25 < 2x < 200, and 2x + 2 is perfectly divisible by either 3 or 4, is



Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:A sequence of 4 digits, when considered as a number in base 10 is four times the number it represents in base 6. What is the sum of the digits of the sequence?



Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:Which of the following will completely divide (10690 – 4990)?



Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:Let P be the set of all odd positive integers such that every element in P satisfies the following conditions.
I. 100 ≤ n < 1000
II. The digit at the hundred’s place is never greater than the digit at tens place and also never less than the digit at units place.

How many elements are there in P?



Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:A four-digit number is divisible by the sum of its digits. Also, the sum of these four digits equals the product of the digits. What could be the product of the digits of such a number?



Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:P is the product of the first 100 multiples of 15 and Q is the product of the first 50 multiples of 2520. Find the number of consecutive zeroes at the end of P2/Q × 101767



Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:The number of factors of the square of a natural number is 105. The number of factors of the cube of the same number is ‘F’. Find the maximum possible value of ‘F’.



Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:‘ab’ is a two-digit prime number such that one of its digits is 3. If the absolute difference between the digits of the number is nota factor of 2, then how many values can ‘ab’ assume?



Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:If E = 3 + 8 + 15 + 24 + … + 195, then what is the sum of the prime factors of E?



Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:The number 44 is written as a product of 5 distinct integers. If ‘n’ is the sum of these five integers then what is the sum of all the possible values of n?



Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:All the two-digit natural numbers whose unit digit is greater than their ten’s digit are selected. If all these numbers are written one after the other in a series, how many digits are there in the resulting number?



Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:A positive integer is equal to the square of the number of factors it has. How many such integers are there?



Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:If ‘a’ is one of the roots of x5 – 1 = 0 and a ≠ 1, then what is the value of a15 + a16 + a17 +.......a50?



The document CAT Past Year Questions: Factors & Divisibility Notes | Study Quantitative Aptitude (Quant) - CAT is a part of the CAT Course Quantitative Aptitude (Quant).
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