CAT Quantitative Ability Questions | CAT Number System questions
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CAT/2021.2
Question . 5
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
Explanatory Answer
Method of solving this CAT Quantitative Ability Question from Number System question
Correct Solution : 4195
Given the information:
The sum of the thousands, hundreds, and tens place digit is 14.
The sum of the hundreds, tens, and units place digit is 15.
Let's represent the four-digit number using placeholders:
From the given information, we can deduce the following relationships:
The unit's digit is one unit greater than the thousandth place digit.
The tens digit can be at most 9.
To maximize the four-digit number, we want to maximize the value of the thousands place digit (a) and the tens digit. So, the largest possible value for a is 4.
To satisfy the sum of the thousands, hundreds, and tens place digit, the value of the hundreds place digit should be 1. This is because the sum of 4 (thousands place), 1 (hundreds place), and the largest possible tens digit (9) equals 14.
Using the information above, we can determine the four-digit number as 4195.
Therefore, the largest possible four-digit number that satisfies the given conditions is 4195.
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