CAT 2021 Slot 2 · Quant · Question 12
CAT 2021 Slot 2 previous year question on Numbers Basics, with the answer and a step-by-step solution.
For a 4-digit number, the sum of its digits in the thousands, hundreds and tens places is 14, the sum of its digits in the hundreds, tens and units places is 15, and the tens place digit is 4 more than the units place digit. Then the highest possible 4-digit number satisfying the above conditions is
Answer & solution
Answer: 4195
Let the number be \overline{abcd}. The conditions are a+b+c=14, b+c+d=15 and c=d+4.
Subtracting the first two gives a-d=-1, so a=d-1.
From the second, b=15-c-d=15-\left( d+4 \right)-d=11-2d.
To make the number largest we want a as large as possible, so we want d as large as possible. The limits are b\ge 0, giving d\le 5, and c=d+4\le 9, also giving d\le 5.
So d=5, and then a=4, b=1, c=9. The number is 4195.
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