The CAT QA section requires speed and accuracy, along with a thorough understanding of the Arithmetic Progression. This article provides a set of MCQs on Arithmetic Progression to help you understand the topic and improve your problem-solving skills with the help of detailed solutions by ensuring conceptual clarity, which will help you in the CAT 2025 exam preparation
Whether you're revising the basics or testing your knowledge, these MCQs will serve as a valuable practice resource.
The CAT 2025 exam is expected to follow a similar trend to the CAT 2024, with 22 questions from the QA section out of a total of 68 questions.
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CAT MCQs on Arithmetic Progression
1. 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
A
\(y ,x\), and \(z\) are in arithmetic progression
B
\(\sqrt{x}, \sqrt{y}\) , and \(\sqrt{z}\) are in arithmetic progression
C
\(x ,y\), and \(z\) are in arithmetic progression
D
\(\sqrt x, \sqrt z\) , and \(\sqrt y\) are in arithmetic progression
2. 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
A
79
B
83
C
84
D
86
3. If \((2n+1)+(2n+3)+(2n+5)+….+(2n+47)=5280,\) then what is the value of \(1+2+3+….n?\)
A
4851
B
1458
C
4718
D
4378
4. If log8 9, log8 (2y+7) and log8 (3y+6) are in arithmetic progression with non-zero common difference, find the value of y.
A
1
B
2.25
C
–1.25
D
1.25
5. 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 \((a_1 + a_2 + …. + a_n ) > 1830?\)
A
8
B
9
C
10
D
11
6. 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
If the sum of the numbers in the new sequence is 450, then a5 is
A
81
B
41
C
61
D
51
7. The value of the sum 7 x 11 + 11 x 15 + 15 x 19 + ...+ 95 x 99 is
A
80707
B
80773
C
80730
D
80751
8. 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
A
20
B
23
C
48
D
45
9. 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 \(x_{100}\).
A
-194
B
206
C
204
D
-196
10. Suppose x1, x2, x3, …, x100 are in arithmetic progression such that x5 = -4 and 2x6 + 2x9 = x11 + x13. Then, x100 equals ?
A
206
B
-196
C
204
D
-194
11. What is the sum of all the 2-digit numbers which leave a remainder of 6 when divided by 8?
A
612
B
594
C
324
D
872
12. What is the sum of all two-digit numbers that give a remainder of 3 when they are divided by 7?
A
666
B
676
C
683
D
777
13. 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?
A
19
B
20
C
22
D
18
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