# CAT 2023 Question Paper | Quant Slot 2

###### CAT Previous Year Paper | CAT Quant Questions | Question 22

CAT 2023 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 22 : Let $a_n$ and $b_n$ be two sequences such that $a_n=13+6(n-1)$ and $b_n=15+7(n-1)$ for all natural numbers $n$. Then, the largest three digit integer that is common to both these sequences, is

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$a _ { n } = 13 + 6 ( n - 1 ) = 7 + 6 n$
$b _ { m } = 15 + 7 ( m - 1 ) = 8 + 7 m$
For some m, n, let $7 + 6 n = 8 + 7 m$
$6 n - 7 m = 1$
$n = 6 , m = 5$ works!
$a _ { 6 } = 43$ and $b _ { 5 } = 43$
Since, $L $cdot C $cdot M$ 6,7$ = 42$, the common terms of the series are of the form $43 + 42 k$
Let’s find the smallest 4-digit number of this form…
$$frac { 1000 } { 42 } $cong 23.80$ $43 + 42$ 23$ = 1009$
$$therefore 43 + 42$ 22 ) = 967$ is the largest 3-digit such value.

The question is " Let $a_n$ and $b_n$ be two sequences such that $a_n=13+6(n-1)$ and $b_n=15+7(n-1)$ for all natural numbers $n$. Then, the largest three digit integer that is common to both these sequences, is "

##### The answer is '967'

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