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Try this beautiful Problem based on Number theory from AMC 10A, 2002 Problem 15.

Using the digits $1,2,3,4,5,6,7$, and 9 , form 4 two-digit prime numbers, using each digit only once. What is the sum of the 4 prime numbers?

- 150
- 160
- 170
- 180
- 190

Arithmetic

Divisibility

Prime Number

Suggested Reading

Source of the Problem

Answer

Elementary Number Theory by David M. Burton.

AMC 10A 2002 Problem 15

190

Hint 1

Hint 2

Hint 3

Hint 4

First try to find the probable digits for the unit place of the prime number.

The two digit prime number should end with $1, 3, 7, 9$ since it is prime and should not divisible by $2$ or $5$.

So now try to find which two digit primes will work here.

So, the primes should be $23, 41, 59, 67$.

Now find the sum of them.

Content

[hide]

Try this beautiful Problem based on Number theory from AMC 10A, 2002 Problem 15.

Using the digits $1,2,3,4,5,6,7$, and 9 , form 4 two-digit prime numbers, using each digit only once. What is the sum of the 4 prime numbers?

- 150
- 160
- 170
- 180
- 190

Arithmetic

Divisibility

Prime Number

Suggested Reading

Source of the Problem

Answer

Elementary Number Theory by David M. Burton.

AMC 10A 2002 Problem 15

190

Hint 1

Hint 2

Hint 3

Hint 4

First try to find the probable digits for the unit place of the prime number.

The two digit prime number should end with $1, 3, 7, 9$ since it is prime and should not divisible by $2$ or $5$.

So now try to find which two digit primes will work here.

So, the primes should be $23, 41, 59, 67$.

Now find the sum of them.

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