Progressions — XAT Previous-Year Questions

In a school, the number of students in each class, from Class I to X, in that order, are in an arithmetic progression. The total number of students from Class I to V is twice the total number of students from Class VI to X. If the total number of students from Class I to IV is 462, how many students are there in Class VI?

Suppose Haruka has a special key âˆ† in her calculator called delta key:

Rule 1: If the display shows a one-digit number, pressing delta key âˆ† replaces the displayed number with twice its value.

Rule 2: If the display shows a two-digit number, pressing delta key âˆ† replaces the displayed number with the sum of the two digits.

Suppose Haruka enters the value 1 and then presses delta key âˆ† repeatedly.

After pressing the âˆ† key for 68 times, what will be the displayed number?

Consider a_{n + 1} = $\frac{1}{1+{\displaystyle \frac{1}{a_n}}}$ for n = 1, 2, ...., 2008, 2009 where a₁ = 1. Find the value of a₁ a₂ + a₂ a₃ + a₃ a₄ + ... + a₂₀₀₈ a₂₀₀₉ 

A marble is dropped from a height of 3 metres onto the ground. After the hitting theground, it bounces and reaches 80% of the height from which it was dropped. This repeats multiple times. Each time it bounces, the marble reaches 80% of the height previously reached. Eventually, the marble comes to rest on the ground.
What is the maximum distance that the marble travels from the time it was dropped until it comes to rest?

Shireen draws a circle in her courtyard. She then measures the circle’s circumference and its diameter with her measuring tape and records them as two integers, A and B respectively. She finds that A and B are coprimes, that is, their greatest common divisor is 1. She also finds their ratio, A : B, to be: 3.141614161416… (repeating endlessly).
What is A - B?

If both the sequences x, a1, a2, y and x, b1, b2, z are in A.P. and it is given that y > x and z < x, then which of the following values can $\left\{\frac{(a1-a2)}{(b1-b2)}\right\}$ possibly take?

A man is laying stones, from start to end, along the two sides of a 200-meter-walkway. The stones are to be laid 5 meters apart from each other. When he begins, all the stones are present at the start of the walkway. He places the first stone on each side at the walkway’s start. For all the other stones, the man lays the stones first along one of the walkway’s sides, then along the other side in an exactly similar fashion. However, he can carry only one stone at a time. To lay each stone, the man walks to the spot, lays the stone, and then walks back to pick another. After laying all the stones, the man walks back to the start, which marks the end of his work. What is the total distance that the man walks in executing this work? Assume that the width of the walkway is negligible.

An antique store has a collection of eight clocks. At a particular moment, the displayed times on seven of the eight clocks were as follows: 1:55 pm, 2:03 pm, 2:11 pm, 2:24 pm, 2:45 pm, 3:19 pm and 4:14 pm. If the displayed times of all eight clocks form a mathematical series, then what was the displayed time on the remaining clock?

The sum of the series, (-100) + (-95) + (-90) + … + 110 + 115 + 120, is

Consider the set of numbers {1, 3, 3², 3³,…...,3¹⁰⁰}. The ratio of the last number and the sum of the remaining numbers is closest to:

What is the sum of the following series?
–64, –66, –68,……..….., –100