1. Question: Find the unit's digit in the product (256 xx 27 xx 159 xx 182).
Product of unit's digits in given numbers = ( 6 xx 7 xx 9 xx 2) = 756
:. Unit digit in the given product is 6.

Explanation: Not available

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2. Question: Find the unit's digit in the product ( 3^67 xx 6^39 xx 7^53 )
Clearly, unit digit in 3^4 is 1.
∴ Unit digit in 3^64 is 1.
∴ Unit digit in 3^67 is 7. [Because Unit digit in 1 xx 3 xx 3 xx 3 is 7 ]
Clearly, unit digit in every power of 6 is 6
∴ Unit digit in 6^39 is 6.
Clearly, unit digit in 7^4 is 1.
∴ Unit digit in 7^52 is 1.
∴ Unit digit in 7^53 is 7. [Because Unit digit in 1 xx 7 is 7 ]
∴ Unit digit in given product = Unit digit in ( 7 xx 6 xx 7 ) = 4.

Explanation: Not available

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3. Question: Prime numbers less than 100
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

Test : Let p be a given number. Find a whole number nearly greater than the square root of p.
Let k > sqrt p .
Test whether p is divisible by any prime number less than k. If yes, then p is not prime. Otherwise, p is prime.

Explanation: Not available

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4. Question: Which of the following numbers is not divisible by 2?
3567516, 9130525, 7870823 and 1371594 
Clearly, the unit's digit of 9130525 is 5, which is not divisible by 2.
So, 9130525 is not divisible by 2.
Each one of the other numbers has a unit divisible by 2.
So, each one other than 9130525 is divisible by 2.

Explanation: Divisibility By 2 : A number divisible by 2, if its unit digit is any of 0, 2, 4, 6, 8.

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5. Question: Which of the following numbers is divisible by 3 ?
1) 541326, 2) 5967013 
1) Sum of digits in 541326 is 21, which is divisible by 3.
Hence, 5967013 is not divisible by 3.
Explanation: Not available