CAT 2022 Question Paper | Quant Slot 3

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 17 : The average of all 3-digit terms in the arithmetic progression 38, 55, 72, ..., is

Video Explanation

Explanatory Answer

The common difference of the AP, 38, 55, 72, … is 17.
The smallest 3-digit number in the AP is 106 and the largest 3-digit number in it is 990
We need to find the value of,
106 + 123 + … + 973 +990
= 106 + (106 + 17) + (106 + 2 *17) + …. + (106 + 52 *17)
= 53(106) + 17(1 + 2 + 3 + … + 52)
= 53(106) + 17 * $\frac { 52 * 53 } { 2 }$
Average of these 53 numbers is $\frac { S u m } { 53 } = 106 + 17 * \frac { 52 } { 2 } = 106 + 17 * 26 = 548$

The question is " The average of all 3-digit terms in the arithmetic progression 38, 55, 72, ..., is "

Hence, the answer is '548'

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