CAT 2022 Question Paper | Quant Slot 1

CAT Questions

CAT 2022 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 7 : The average of three integers is 13 . When a natural number \(n\) is included, the average of these four integers remains an odd integer. The minimum possible value of \(n\) is

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Video Explanation

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Explanatory Answer

Let the four integers be \(I_1, I_2, I_3\) and \(I_4\).
We know that the average of \(I_1, I_2, I_3\)is 13.
If \( I _ { 4 } \)is also 13, the average will be unchanged. The new average is also 13.
If \( I _ { 4 } \) is 13 + 4, the average will increase by 1. The new average is 14.
If \( I _ { 4 } \) is 13 + 4(2), the average will increase by 2. The new average is 15.
If \( I _ { 4 } \) is 13 + 4(x), the average will increase by x. The new average is 13 + x.
If \( I _ { 4 } \) is 13 - 4, the average will decrease by 1. The new average is 12.
If \( I _ { 4 } \) is 13 - 4(2), the average will decrease by 2. The new average is 11.
If \( I _ { 4 } \) is 13 - 4(x), the average will decrease by x. The new average is 13 - x.
We observe that for the average to remain odd and an integer, \( I _ { 4 } \) should be \( 13 \pm 8 x \) where x is a whole number. Since we intend to find the smallest value of \( I _ { 4 } \), the question transpires to be What is the maximum value of x such that 13 - 8x is a natural number?

The maximum value of x is 1. Therefore, the minimum value of 13 - 8x is 5.
That minimum value of \( I _ { 4 } \) such that it satisfies all the given conditions is 5.

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The question is " The average of three integers is 13 . When a natural number \(n\) is included, the average of these four integers remains an odd integer. The minimum possible value of \(n\) is "

Hence, the answer is '5'

Choice C is the correct answer.

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