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Questions and Answers
If the 5-digit number 593ab is divisible by 3, 7, and 11, what is the value of $a^2 - b^2 + ab$?
What is the greatest five-digit number that is completely divisible by 8, 15, 16, 21, and 5?
If a number of 54k31m82 is divisible by 11, what will be the maximum value of (k + m)?
When (2 – 1) is divided by 7, what is the remainder?
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Find the sum of all possible values of (a + b) so that the number 4a067b is divisible by 11.
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If a nine-digit number 7698x138y is divisible by 72, what is the value of $4x + y$?
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How many numbers between 500 and 900, both inclusive, are divisible by 12, 15, 20, and 30?
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Which of the following numbers is divisible by 88?
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If an eleven-digit number 6578x43267y is divisible by 72, what is the value of x + 6y?
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What is the smallest number that leaves a remainder of 5 when divided by both 72 and 96?
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How many six-digit numbers of the form 537xy5 are divisible by 125?
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What is the quotient when the largest number divisible by both 72 and 96 between 500 and 900 is divided by the smallest number divisible by both 72 and 96 between 500 and 900?
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If the number 7183 + 7383 is divided by 36, what will be the remainder?
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If the 11-digit number 645A42879B8 is divisible by both 8 and 9, what are the smallest possible values of A and B?
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If the 11-digit number 4y6884805x6 is divisible by 72, and x ≥ y, then the value of xy is:
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When a number is divided by 3, the remainder is 2. Again, when the quotient is divided by 7, the remainder is 5. What will be the remainder when the original number is divided by 21?
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If the nine-digit number 87605x31y is divisible by 72, then the value of 2x – 3y is:
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Which of the following numbers is divisible by both 2 and 3?
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Study Notes
Divisibility by Numbers
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Between 500 and 900, both inclusive, there are 35 numbers exactly divisible by 12, 15, 20, and 30.
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The numbers 12, 15, 20, and 30 are exactly divisible by 60.
Divisibility by Specific Numbers
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The number 6578x43267y is divisible by 72, then the value of x + 6y will be 5.
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The smallest number which when divided by 72 and 96, respectively, leaves a remainder 5 in each case is 725.
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The six-digit number 537xy5 is divisible by 125. There are 25 such six-digit numbers.
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The sum of all the possible values of (a + b), so that the number 4a067b is divisible by 11, is 37.
Divisibility by Primes
- When (2 – 1) is divided by 7, the remainder is 1.
- The sum of 3-digit numbers abc, cab, and bca is not divisible by 31.
Greatest Divisible Numbers
- The greatest five-digit number that is completely divisible by 8, 15, 16, 21, and 5 is not specified in the text.
- The nine-digit number 7698x138y is divisible by 72, then the value of 4x + y is not specified in the text.
Conditions for Divisibility
- If a number of 54k31m82 is divisible by 11, the maximum value of (k + m) is not specified in the text.
- The number 89x64287y is divisible by 72, then the value of (3x + 2y) is not specified in the text.
- The five-digit number 593ab is divisible by 3, 7, and 11, then the value of (a²– b²+ab) is not specified in the text.
Combinations of Divisibility
- The number 7183 + 7383 is divisible by 36, then the remainder is 13.
- The 11-digit number 4y6884805x6 is divisible by 72, and x ≠y, then the value xy is not specified in the text.
- The number 645A42879B8 is divisible by both 8 and 9, then the smallest possible values of A and B are not specified in the text.
Remainders
- When a number is divided by 3, the remainder is 2. Again, when the quotient is divided by 7, the remainder is 5. The remainder when the original number is divided by 21 is 8.
- If the nine-digit number 87605x31y is divisible by 72, then the value of 2x – 3y is not specified in the text.
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Description
Test your divisibility knowledge by finding numbers between 500 and 900 that are divisible by 9, as well as checking which numbers are divisible by 88. Also, identify specific numbers such as 12, 15, 20, and 30. Questions are drawn from SSC CHSL and SSC MTS exams.
