CAT 2017 Question Paper | Quants Slot 1

CAT Questions

The questions that come from Progression in CAT involves concept based on Arithmetic progressions and Geometric progressions. In CAT Exam, one can generally expect to get 1~2 questions from Progressions. The question is about Sum of a progression. With some simple but very powerful ideas, one can cut down on a lot of work when it comes to progression.

Question 34 : Let a₁, a₂,.......a_3n be an arithmetic progression with a₁ = 3 and a₂ = 7. If a₁ + a₂ + ......+a_3n = 1830, then what is the smallest positive integer m such that m (a₁ + a₂ + ..... + a_n) > 1830 ?

1. 8
2. 9
3. 10
4. 11

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question from Progressions

Let us assume 3n = k
⟹ \\frac{k}{2}) (2a + (k – 1)d) = 1830 we know that a = 3, d = 4
⟹ \\frac{k}{2}) (2(3) + (k – 1)4) = 1830
⟹ \\frac{k}{2}) (6 + 4k – 4) = 1830
⟹ k (2k + 1) = 1830
⟹ 2k² + k = 1830
⟹ 2k² + k – 1830 = 0
By factorizing we can find that k = 30, n = 10
⟹ \\frac{10}{2}) (2(3) + 4(9)) = 5(6 + 36)
⟹ 5(42) = 210
⟹ m (a₁ + a₂ + ..... + a_n) > 1830
⟹ 210 × m > 1830
⟹ m = 9, since 210 × 9 = 1890

The question is "Let a₁, a₂,.......a_3n be an arithmetic progression with a₁ = 3 and a₂ = 7. If a₁ + a₂ + ......+a_3n = 1830, then what is the smallest positive integer m such that m (a₁ + a₂ + ..... + a_n) > 1830 ?"

Hence, the answer is 9

Choice B is the correct answer