CAT 2023 Progression Question (Hard)

Question

Let both the series and be in arithmetic progression such that the common differences of both the series are prime numbers. If and , then equals

Accepted Answer

Step 1 Define both APs Let the first AP be a a n 1 d Let the second AP be b b n 1 d We re told - d and d are prime numbers - b 0 b b d 0 b d So b d n 1 d n 2 d Thus b 9 2 d 7d b 19 2 d 17d Step 2 Use condition a b a a 4d b 7d a 4d 7d 1 Step 3 Use condition a b a a 18d b 17d a 18d 17d 2 Now subtract

CAT 2023

Quantitative

Progression

Hard

Let both the series $a_1, a_2, a_3, \ldots$ and $b_1, b_2, b_3 \ldots$ be in arithmetic progression such that the common differences of both the series are prime numbers. If $a_5=b_9, a_{19}=b_{19}$ and $b_2=0$ , then $a_{11}$ equals

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