In a six-digit number, the sixth, that is, the rightmost, digit is the

1.	In a six-digit number, the sixth, that is, the rightmost, digit is the sum of the first three digits, the fifth digit is the sum of first two digits, the third digit is equal to the first digit, the second digit is twice the first digit and the fourth digit is the sum of fifth and sixth digits. Then, the largest possible value of the fourth digit is (type in box)
Answer» Calculation: Let the first digit be 'a' Now according to the question, Third digit = The first digit ⇒ a The second digit = 2 × The first digit ⇒ 2 × a ⇒ 2a The sixth digit = The sum of (first digit + second digit + third digit) ⇒ a + 2a + a ⇒ 4a The fifth digit = The sum of first two digit ⇒ a + 2a ⇒ 3a The fourth digit = The sum of (fifth digit + sixth digit) ⇒ 3a + 4a ⇒ 7a So we can see our fourth digit should be a multiple of 7 And we can say that the largest possible value of the fourth digit will be 7 when the value of 'a' will be 1 Because if we put 'a' equal to 2 it will give the two-digit number equal to (7 × 2 = 14) for the fourth digit which is not possible. ∴ The largest possible value of the fourth digit is only 7.

In a six-digit number, the sixth, that is, the rightmost, digit is the sum of the first three digits, the fifth digit is the sum of first two digits, the third digit is equal to the first digit, the second digit is twice the first digit and the fourth digit is the sum of fifth and sixth digits. Then, the largest possible value of the fourth digit is (type in box)

Answer»

Calculation:

Let the first digit be 'a'

Now according to the question,

Third digit = The first digit

⇒ a

The second digit = 2 × The first digit

⇒ 2 × a

⇒ 2a

The sixth digit = The sum of (first digit + second digit + third digit)

⇒ a + 2a + a

⇒ 4a

The fifth digit = The sum of first two digit

⇒ a + 2a

⇒ 3a

The fourth digit = The sum of (fifth digit + sixth digit)

⇒ 3a + 4a

⇒ 7a

So we can see our fourth digit should be a multiple of 7

And we can say that the largest possible value of the fourth digit will be 7 when the value of 'a' will be 1

Because if we put 'a' equal to 2 it will give the two-digit number equal to (7 × 2 = 14) for the fourth digit which is not possible.

∴ The largest possible value of the fourth digit is only 7.