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The unit digit and tens digit of a two-digit number is a consecutive prime number. It is more than 7 tens and less than 8 tens. The sum of its digits is 12. The product of the digit is 35, then what is the number?

The unit digit and tens digit of a two-digit number is a consecutive prime number. It is more than 7 tens and less than 8 tens. The sum of its digits is 12. The product of the digit is 35, then what is the number? Correct Answer 75

Given:

Digit of number  are consecutive prime. 

Sum of digit = 12

Number is more than 7 tens and less than 8 tens

Product of digit = 35

Concept:

Prime number: 

  • A number which can be divided by only 1 and number itself called prime number.
  • For example 2, 3, 5, 7, 11 etc.
  • 2 is smallest prime number which is even and 3 is smallest prime number which is odd.


Calculation:

Let the number is ab.

According to question, sum of digit is 12. Hence,

a + b = 12      ---(1)

Also product of digit are 35. Hence,

ab = 35          ---(2)

According to question, number is more than 7 tens and less than 8 tens. Hence,

, 70 < ab < 80

Hence, possible number can be, 

 71, 72, 73, 74, 75, 76, 77, 78, 79

we can see that, 75 satisfy both equation (1) and (2). Also 5 and 7 are two consecutive prime numbers.

Therefore 75 will be correct answer.


Shortcut Trick 

According to question, sum and product of digit are 12 and 35 respectively. Also number is b/w 70 and 80.

Hence, from the option, we can see that, 75 is the number which satisfy all condition. 

Hence, 75 will be correct answer.

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