CAT 2021 Question Paper | Quant Slot 2

CAT Previous Year Paper | CAT Quant Questions | Question 12

CAT 2021 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 12 : 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

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Explanatory Answer

For a 4-digit number we can make 4 placeholders to represent the four digits
__ __ __ __
Now, we know that the sum of the thousands, hundreds and the tens place digit is 14, and the sum of the hundreds, tens and the units place digit is 15.

So we can conclude that the unit's digit is one unit greater than the thousandth place.
Four Digits
To maximize the 4-digit number the value of a should be as large as possible. And the value of the tens digit can be 9 at most. So the maximum value of a is 4.

Four Digits
Four Digits
To satisfy the sum of the thousands, hundreds and the tens place digit, the value of the hundreds place should be equal to 1.
Hence the largest possible number is 4195

The answer is '4195'

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