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Test: Divisibility/Multiples/Factors - GMAT MCQ


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10 Questions MCQ Test Practice Questions for GMAT - Test: Divisibility/Multiples/Factors

Test: Divisibility/Multiples/Factors for GMAT 2025 is part of Practice Questions for GMAT preparation. The Test: Divisibility/Multiples/Factors questions and answers have been prepared according to the GMAT exam syllabus.The Test: Divisibility/Multiples/Factors MCQs are made for GMAT 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Divisibility/Multiples/Factors below.
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Test: Divisibility/Multiples/Factors - Question 1

If n is the product of the squares of 4 different prime numbers, how many factors does n have?

Test: Divisibility/Multiples/Factors - Question 2

If x and y are consecutive positive integer multiples of 3, what is the greatest integer j such that xy/j is always an integer?

Test: Divisibility/Multiples/Factors - Question 3

What is the smallest prime factor of (842−132)?

Detailed Solution for Test: Divisibility/Multiples/Factors - Question 3

Step 1: Simplify the Expression
The expression 84² - 13² is a difference of squares, which can be factored using the formula:
a² - b² = (a + b)(a - b)

Applying this formula:
84² - 13² = (84 + 13)(84 - 13) = 97 × 71

Step 2: Analyze the Factors
Now, we have:
84² - 13² = 97 × 71

  • 97:
    • Prime Check: 97 is a prime number (it has no divisors other than 1 and itself).
  • 71:
    • Prime Check: 71 is also a prime number.

Step 3: Determine the Smallest Prime Factor
From the factorization:
84² - 13² = 97 × 71

Both 97 and 71 are prime numbers. Among these:
Smallest Prime Factor = 71

Test: Divisibility/Multiples/Factors - Question 4

Which of the following is the lowest positive integer that is divisible by 2, 3, 4, 5, 6, 7, 8, and 9?

Test: Divisibility/Multiples/Factors - Question 5

A beacon flashes its light every 12 seconds, another every 18 seconds and a third every minute. First time, the three beacons flash simultaneously at 6.30 pm. At what time will the three beacons flash simultaneously second time?

Test: Divisibility/Multiples/Factors - Question 6

What is the number of positive integers less than 500 which have an odd number of divisors?

Test: Divisibility/Multiples/Factors - Question 7

When integer n is divided by 15, the remainder is 5. Which of the following has a remainder of 10 when divided by 15 ?

I. 3n
II. 5n
III. 4n + 10

Test: Divisibility/Multiples/Factors - Question 8

How many multiples of 6 are less than 5000, and also multiples of 8?

Test: Divisibility/Multiples/Factors - Question 9

A positive integer n is completely divisible by 12 and 8. If √n lies between 5 and 8, exclusive, how many values of n are possible?

Test: Divisibility/Multiples/Factors - Question 10

What is the number of multiples of 6 from -35 to 69?

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