List of top Quantitative Aptitude Questions on Arithmetic Progression asked in CAT

In the sequence 1, 3, 5, 7, ..., k, ..., 57, the sum of the numbers up to k, excluding k, is equal to the sum of the numbers from k up to 57, also excluding k. What is k?

The terms \(x_5 = -4\), \(x_1, x_2, \dots, x_{100}\) are in an arithmetic progression (AP). It is also given that \(2x_6 + 2x_9 = x_{11} + x_{13}\). Find \(x_{100}\).

Suppose $x_1, x_2, x_3, \dots, x_{100}$ are in arithmetic progression such that $x_5 = -4$ and $2x_6 + 2x_9 = x_{11} + x_{13}$. Then, $x_{100}$ equals ?

Let both the series \(a_1,a_2,a_3,....\) and \(b_1,b_2,b_3,....\) 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

For some positive and distinct real numbers \(x ,y\), and \(z\) , if \(\frac{1}{\sqrt{ y}+ \sqrt{z}}\) is the arithmetic mean of \(\frac{1}{\sqrt{x}+ \sqrt{z}}\) and \(\frac{1}{\sqrt{x} +\sqrt{y}}\) , then the relationship which will always hold true, is

If \((2n+1)+(2n+3)+(2n+5)+….+(2n+47)=5280,\) then what is the value of \(1+2+3+….n?\)

The value of the sum 7 x 11 + 11 x 15 + 15 x 19 + ...+ 95 x 99 is

Let a1, a2, ... , a52 be positive integers such that a1 < a2 < ... < a52. Suppose, their arithmetic mean is one less than the arithmetic mean of a2, a3, ..., a52. If a52 = 100, then the largest possible value of a1 is

Let a1 , a2 , a3 , a4 , a5 be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with 2a3.
If the sum of the numbers in the new sequence is 450, then a5 is

Let \(a_1 , a_2 ,……..a_{3n}\) be an arithmetic progression with \(a_1 = 3\) and \(a_2 = 7.\) If \(a_1 + a_2 + ….+a_{3n} = 1830\), then what is the smallest positive integer m such that m \((a_1 + a_2 + …. + a_n ) > 1830?\)

What is the sum of all the 2-digit numbers which leave a remainder of 6 when divided by 8?

Let $a$, $b$, $c$, and $d$ be integers such that $a = 6b$, $a = 12c$, and $2b = 9d = 12e$. Then which of the following pairs contains a number that is not an integer?

Using only 2, 5, 10, 25, and 50 paisa coins, what will be the minimum number of coins required to pay exactly 78 paise, 69 paise and Rs. 1.01 to three different persons?

If $x$ and $y$ are integers, then the equation $5x + 19y = 64$ has:

In a coastal village, every year floods destroy exactly half of the huts. After the flood water recedes, the same number of huts destroyed are rebuilt. The floods occurred consecutively in the last three years — 2001, 2002 and 2003. If floods are expected again in 2004, the number of huts expected to be destroyed is:

What is the sum of all two-digit numbers that give a remainder of 3 when they are divided by 7?

A set of consecutive positive integers beginning with 1 is written on the blackboard. A student erased one number. The average of the remaining numbers is $35\frac{7}{17}$. What was the number erased?

Two men X and Y started working for a certain company at similar jobs on January 1, 1950. X asked for an initial salary of Rs. 300 with an annual increment of Rs. 30. Y asked for an initial salary of Rs. 200 with a rise of Rs. 15 every 6 months. Assume that the arrangements remained unaltered till December 31, 1959. Salary is paid on the last day of the month. What is the total amount paid to them as salary during the period?

A group of men decided to do a job in 8 days. But since 10 men dropped out every day, the job got completed at the end of the 12th day. How many men were there at the beginning?

If log₈ 9, log₈ (2y+7) and log₈ (3y+6) are in arithmetic progression with non-zero common difference, find the value of y.