CAT Quantitative Aptitude Questions | CAT Algebra - Progressions questions

The question is about Arithmetic Progression. Four terms in an AP is given and we need to find out the relationship between the terms formed by multiplying three terms at a time. With some simple but very powerful ideas, one can cut down on a lot of working when it comes to progressions. For example, anchoring a progression around its middle term can be very useful. CAT Exam tests the idea of progression often in the CAT Quantitative Aptitude section and this could also be tested in DI LR section of the CAT Exam as a part of a puzzle.

Question 10: a, b, c and d are in A.P., What can we say about terms bcd, acd, abd and abc?

1. They are also in A.P.
2. They are also in H.P.
3. They are also in G.P.
4. They are not in an A.P., G.P. or H.P.

Video Explanation

Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Progressions: One simple division will lead to the solution.

a, b, c and d are in A.P.
Dividing through out this A.P. by abcd, we get
\\frac{a}{abcd}\\) , \\frac{b}{abcd}\\) , \\frac{c}{abcd}\\) , \\frac{d}{abcd}\\) are in A.P.
\\frac{1}{bcd}\\) , \\frac{1}{acd}\\) , \\frac{1}{abd}\\) , \\frac{1}{abc}\\) are in A.P.
=> bcd, acd, abd and abc are in H.P.

The question is "a, b, c and d are in A.P., What can we say about terms bcd, acd, abd and abc?"

Hence the answer is "They are in H.P."

Choice B is the correct answer.