CAT 2024 Question Paper | Quant Slot 1

CAT Questions

CAT 2024 Quant was dominated by Algebra followed by Arithmetic. 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 9 :The sum of all four-digit numbers that can be formed with the distinct non-zero digits $a, b, c$, and $d$, with each digit appearing exactly once in every number, is $153310+n$, where $n$ is a single digit natural number. Then, the value of $(a+b+c+d+n)$ is

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Video Explanation

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Explanatory Answer

With 4 digits a,b,c and d we can form 24 four-digit numbers. E.g. abcd, abdc, acbd,,,… dcba​
Sum of all these 24 numbers will be (a+b+c+d)*6*(1) + (a+b+c+d)*6*(10) + (a+b+c+d)*6*(100) + (a+b+c+d)*6*(1000)​ = 1111*(a+b+c+d)*6.
Now dividing 153310 by 1111 the remainder is 1103.
Adding 8 will make it exactly divisible by 1111. So, the value of n is 8.
153318/1111= 138.
(a+b+c+d)*6 = 138.
(a+b+c+d)= 23.
The required value of (a+b+c+d+n)= 23+8=31.

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The question is "The sum of all four-digit numbers that can be formed with the distinct non-zero digits $a, b, c$, and $d$, with each digit appearing exactly once in every number, is $153310+n$, where $n$ is a single digit natural number. Then, the value of $(a+b+c+d+n)$ is "

Hence, the answer is '31'

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