CAT 2025 Slot 3 QA Question 10: For a 4-digit number (greater than 1000), sum of the digits in the thousands, hundreds, and tens places is 15. Sum of the digits in the hundreds, tens, and units places is 16. Also, the digit in the t

Question

For a 4-digit number (greater than 1000), sum of the digits in the thousands, hundreds, and tens places is 15. Sum of the digits in the hundreds, tens, and units places is 16. Also, the digit in the t

Accepted Answer

Let the thousands, hundreds, tens and units digits be $a$, $b$, $c$ and $d$ respectively.
$a + b + c = 15$
$b + c + d = 16$
$c = d + 6$
Subtracting the first equation from the second gives $d-a = 1$, so $d = a + 1$.
$c = a + 7$
$b = 15 - a - c = 8 - 2a$
Since $c$ is a digit, $a$ can be $1$ or $2$.
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