Question

Every prime number greater than 10 has a digit in the ones place that is include in wich set of numbers A- 1,3,7,9 B-1,3,5,9 D-1,3,7

Answer 1

Prime numbers greater than 10 must end in the digits 1, 3, 7, or 9, as they need to be indivisible by 2 and 5, the smallest primes.

Step-by-step explanation:

The question is asking about the pattern of digits found in the ones place of prime numbers greater than 10. Every prime number greater than 10 must end with a digit that allows it to be indivisible by 2 or 5, the smallest prime numbers. Primes must be odd, hence they cannot end with 0, 2, 4, 6, or 8, as those are even numbers. Additionally, since all numbers ending in 5 are divisible by 5, the digit 5 is also eliminated as a possibility for the ones place of a prime number (except for the prime number 5 itself).

The only digits that can be in the ones place of a prime number greater than 10 are 1, 3, 7, and 9. This leads us to conclude that the set of digits in the ones place of prime numbers greater than 10 is represented by option A: 1, 3, 7, 9. This pattern is critical in identifying the primality of larger numbers through a simple observation of their last digit.

Answer 2

That's very interesting. I had never thought about it before.
Let's look through all of the ten possible digits in that place,
and see what we can tell:

-- 0:
A number greater than 10 with a 0 in the units place is a multiple of
either 5 or 10, so it's not a prime number.

-- 1:
A number greater than 10 with a 1 in the units place could be
a prime (11, 31 etc.) but it doesn't have to be (21, 51).

-- 2:
A number greater than 10 with a 2 in the units place has 2 as a factor
(it's an even number), so it's not a prime number.

-- 3:
A number greater than 10 with a 3 in the units place could be
a prime (13, 23 etc.) but it doesn't have to be (33, 63) .

-- 4:
A number greater than 10 with a 4 in the units place is an even
number, and has 2 as a factor, so it's not a prime number.

-- 5:
A number greater than 10 with a 5 in the units place is a multiple
of either 5 or 10, so it's not a prime number.

-- 6:
A number greater than 10 with a 6 in the units place is an even
number, and has 2 as a factor, so it's not a prime number.

-- 7:
A number greater than 10 with a 7 in the units place could be
a prime (17, 37 etc.) but it doesn't have to be (27, 57) .

-- 8:
A number greater than 10 with a 8 in the units place is an even
number, and has 2 as a factor, so it's not a prime number.

-- 9:
A number greater than 10 with a 9 in the units place could be
a prime (19, 29 etc.) but it doesn't have to be (39, 69) .

So a number greater than 10 that IS a prime number COULD have
any of the digits 1, 3, 7, or 9 in its units place.

It CAN't have a 0, 2, 4, 5, 6, or 8 .

The only choice that includes all of the possibilities is 'A' .