Question

Critical Thinking: I am a 7-digit number. All my digits are non-zero and distinct, My ones digit is four times the tens digit. • The sum of the ones and tens digits is equal to the sum of the lakhs and ten lakhs digits. • The sum of the ten thousands and thousands digits is equal to the double of the hundreds digit. • The ten lakhs digit is greater than the lakhs digit , and the ten thousands digit is greater than the thousands digit. Find which number I am. ​

Answer 1

3286714

Explanation:

Let the digits of the number be :

• ABCDEFG

Our given conditions :

• G = 4F [ones digit is four times the tens digit]
• G + F = B + A [sum of the ones and tens digits is equal to the sum of the lakhs and ten lakhs digits]
• C + D = 2E [sum of the ten thousands and thousands digits is equal to the double of the hundreds digit]
• A > B and C > D [ten lakhs digit is greater than the lakhs digit , and the ten thousands digit is greater than the thousands digit]

Solving :

• Condition 1 : G is either 1 or 2 and F is either 4 or 8
• For now, let G be 1 and F be 4
• Now G + F = A + B
• Then A + B = 5 [but not 1 + 4] ⇒ A can be 3 and B can be 2
• Now C + D = 2E and our remaining numbers are 5,6,7,8,9
• C and D can be 8 and 6, then their mean would be 7, which is E

Solution :

So, the number is :

• ABCDEFG
• 3286714