CAT 2025 Slot 3 QA Q20 Number Systems

Question 20 of the Quantitative Ability (QA) section, CAT 2025 Slot 3, with CAT's official answer and a worked solution.

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 tens place is 6 more than the digit in the units place. The difference between the largest and smallest possible value of the number is
  1. A
    4078
  2. B
    3289
  3. C
    811
  4. D
    735

Answer: (C) 811 Number Systems MCQ

Solution

  1. Digits \(a b c d\): \(a + b + c = 15\), \(b + c + d = 16 \Rightarrow d = a + 1\); also \(c = d + 6\).
  2. \(c \le 9 \Rightarrow d \le 3\); \(a \ge 1 \Rightarrow d \ge 2\).
  3. \(d = 2\): \(a = 1, c = 8, b = 6\) gives 1682. \(d = 3\): \(a = 2, c = 9, b = 4\) gives 2493.
  4. Difference \(= 2493 - 1682 = 811\).

Same concept in other years

More Number Systems questions from CAT

All 40 Number Systems questions asked since 2017.