Q. 1
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the average of the first five consecutive odd positive integers (1, 3, 5, 7, 9)?
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Step-by-Step Explanation & Concept Rationale
The first five odd integers are , 3, 5, 7, 9$. Their sum is: \[1 + 3 + 5 + 7 + 9 = 25\] Their average is: \[\text{Average} = \frac{25}{5} = 5\] Thus, the correct option is (C).
Q. 2
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A batsman has a batting average of 36 runs in 16 innings. He scores 70 runs in the 17th inning. What is his new batting average?
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Step-by-Step Explanation & Concept Rationale
The total runs scored in the first 16 innings: \[16 \times 36 = 576\] Adding the 17th inning score: \[\text{Total Runs} = 576 + 70 = 646\] The new average after 17 innings is: \[\text{New Average} = \frac{646}{17} = 38\] Thus, the correct option is (B).
Q. 3
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A grocer had sales of Rs. 6,435, Rs. 6,927, Rs. 6,855, Rs. 7,230, and Rs. 6,562 for 5 consecutive months. What sale must he achieve in the sixth month to maintain an average sale of Rs. 6,500?
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Step-by-Step Explanation & Concept Rationale
The required total sale for 6 months is: \[6 \times 6500 = \text{Rs. } 39000\] The sum of sales for the first 5 months is: \[6435 + 6927 + 6855 + 7230 + 6562 = \text{Rs. } 34009\] Therefore, the sixth month sale must be: \[39000 - 34009 = \text{Rs. } 4991\] Thus, the correct option is (B).
Q. 4
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
The average score of a group of 5 people is 42, and the average score of another group of 8 people is 81. What is the combined average score of all 13 people?
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Step-by-Step Explanation & Concept Rationale
The total sum of scores is: \[\text{Total} = (5 \times 42) + (8 \times 81) = 210 + 648 = 858\] The combined average for the 13 people is: \[\text{Average} = \frac{858}{13} = 66\] Thus, the correct option is (C).
Q. 5
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
The average of three numbers is 77. The first number is twice the second number, and the second number is twice the third number. What is the first number?
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Step-by-Step Explanation & Concept Rationale
Let the third number be $. Then the second number is $, and the first number is (2x) = 4x$. The average is given by: \[\frac{4x + 2x + x}{3} = 77 \implies \frac{7x}{3} = 77 \implies 7x = 231 \implies x = 33\] Therefore, the first number is: \[4x = 4 \times 33 = 132\] Thus, the correct option is (C).
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