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Mathematics Solved Questions Bank & Study Material (2026) - Apex Rankers
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93 Total Solved Questions
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Q. 1
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Amna is 18 times older than her daughter Raiza. If Raiza is 6 years old, how old is Amna?
A
90 years
B
100 years
C
108 years
✓ Correct
D
118 years
💡
Step-by-Step Explanation & Concept Rationale
Raiza is $ years old. Amna\'s age is: \[18 \times 6 = 108\text{ years}\] Thus, the correct option is (C).
Q. 2
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Ali is 18 years older than Rehan. 8 years ago, Ali was 6 times as old as Rehan. What is Ali\'s present age?
A
25 years
B
28 years
C
29.6 years
✓ Correct
D
31 years
💡
Step-by-Step Explanation & Concept Rationale
Let Rehan\'s present age be $. Then Ali\'s present age is + 18$. 8 years ago: \[(R + 18) - 8 = 6(R - 8)\] \[R + 10 = 6R - 48 \implies 5R = 58 \implies R = 11.6\text{ years}\] Therefore, Ali\'s present age is: \[R + 18 = 11.6 + 18 = 29.6\text{ years}\] Thus, the correct option is (C).
Q. 3
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
A father is 7 times as old as his daughter. 7 years ago, he was 11 times as old as his daughter. What is the present age of the daughter?
A
15.5 years
B
17.5 years
✓ Correct
C
20 years
D
25 years
💡
Step-by-Step Explanation & Concept Rationale
Let the daughter\'s present age be $. The father\'s present age is $. 7 years ago: \[7d - 7 = 11(d - 7)\] \[7d - 7 = 11d - 77 \implies 4d = 70 \implies d = 17.5\text{ years}\] Thus, the correct option is (B).
Q. 4
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
A person is $\frac{2}{5}$ as old as his mother. After 8 years, he will be $\frac{1}{2}$ as old as his mother. What is the present age of the mother?
A
30 years
B
35 years
C
40 years
✓ Correct
D
45 years
💡
Step-by-Step Explanation & Concept Rationale
Let the mother\'s present age be $. The son\'s present age is $\frac{2}{5}M$. After 8 years: \[\frac{2}{5}M + 8 = \frac{1}{2}(M + 8)\] \[\frac{2}{5}M + 8 = \frac{1}{2}M + 4 \implies 8 - 4 = \frac{1}{2}M - \frac{2}{5}M \implies 4 = \frac{1}{10}M \implies M = 40\] Thus, the mother is $ years old. Thus, the correct option is (C).
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Q. 1
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
If $\frac{x}{z} = 8$, $\frac{x}{y} = 8$, and $\sqrt{x} = 4$, find the value of $z$.
A
1
B
2
✓ Correct
C
3
D
4
💡
Step-by-Step Explanation & Concept Rationale
Given $\sqrt{x} = 4 \implies x = 4^2 = 16$. Substituting $x = 16$ into $\frac{x}{z} = 8$: \[\frac{16}{z} = 8 \implies 8z = 16 \implies z = 2\] Thus, the correct option is (B).
Q. 2
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
If $\frac{x}{2} = 0$, find the value of $1 + x + x^2 + 3x^3$.
A
1
✓ Correct
B
2
C
3
D
4
💡
Step-by-Step Explanation & Concept Rationale
From $\frac{x}{2} = 0$, we get $x = 0$. Substituting $x = 0$ into the polynomial expression: \[1 + (0) + (0)^2 + 3(0)^3 = 1 + 0 + 0 + 0 = 1\] Thus, the correct option is (A).
Q. 3
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
If $\frac{x}{y} = 8$ and $x = 16$, what is the value of $y$?
A
1
B
2
✓ Correct
C
3
D
4
💡
Step-by-Step Explanation & Concept Rationale
Substitute $x = 16$ into the given equation: \[\frac{16}{y} = 8 \implies 8y = 16 \implies y = \frac{16}{8} = 2\] Thus, the correct option is (B).
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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)?
A
3
B
4
C
5
✓ Correct
D
6
💡
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?
A
37
B
38
✓ Correct
C
39
D
40
💡
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?
A
Rs. 4,800
B
Rs. 4,991
✓ Correct
C
Rs. 5,000
D
Rs. 5,120
💡
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?
A
60
B
65
C
66
✓ Correct
D
70
💡
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?
A
110
B
120
C
132
✓ Correct
D
140
💡
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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Q. 1
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Solve the decimal addition: $2.31 + 3.21$
A
5.42
B
5.51
C
5.52
✓ Correct
D
5.62
💡
Step-by-Step Explanation & Concept Rationale
Adding the decimal values directly: \[2.31 + 3.21 = 5.52\] Thus, the correct option is (C).
Q. 2
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Solve the decimal addition: $0.001 + 2.1$
A
2.11
B
2.101
✓ Correct
C
2.011
D
3.1
💡
Step-by-Step Explanation & Concept Rationale
Align the numbers by the decimal point: \[2.100 + 0.001 = 2.101\] Thus, the correct option is (B).
Q. 3
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Solve the decimal subtraction: $2.5213 - 1.001$
A
1.5203
✓ Correct
B
1.5212
C
1.5113
D
1.4203
💡
Step-by-Step Explanation & Concept Rationale
Align the numbers by the decimal point: \[2.5213 - 1.0010 = 1.5203\] Thus, the correct option is (A).
Q. 4
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Calculate the product: $1.31 \times 0.3$
A
0.39
B
0.393
✓ Correct
C
3.93
D
39.3
💡
Step-by-Step Explanation & Concept Rationale
First multiply $131 \times 3 = 393$. Since there are $2 + 1 = 3$ decimal places in total, place the decimal point $3$ places from the right: \[1.31 \times 0.3 = 0.393\] Thus, the correct option is (B).
Q. 5
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Calculate the product: $0.08 \times 0.2$
A
0.16
B
0.016
✓ Correct
C
0.0016
D
1.6
💡
Step-by-Step Explanation & Concept Rationale
First multiply the whole numbers: $8 \times 2 = 16$. Next, count the total number of decimal places: $2 + 1 = 3$ decimal places. Therefore: \[0.08 \times 0.2 = 0.016\] Thus, the correct option is (B).
Q. 6
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Solve the decimal division: $\frac{0.08}{0.2}$
A
0.04
B
0.4
✓ Correct
C
4
D
40
💡
Step-by-Step Explanation & Concept Rationale
Multiply numerator and denominator by $100$: \[\frac{0.08}{0.2} = \frac{8}{20} = \frac{4}{10} = 0.4\] Thus, the correct option is (B).
Q. 7
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Solve the decimal division: $\frac{0.002}{0.8}$
A
0.025
B
0.0025
✓ Correct
C
0.00025
D
0.25
💡
Step-by-Step Explanation & Concept Rationale
Multiply numerator and denominator by $1000$: \[\frac{0.002}{0.8} = \frac{2}{800} = \frac{1}{400} = 0.0025\] Thus, the correct option is (B).
Q. 8
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Solve the decimal division: $\frac{0.8}{0.002}$
A
4
A
4
A
4
A
4
A
4
B
40
B
40
B
40
B
40
B
40
C
400
✓ Correct
C
400
✓ Correct
C
400
✓ Correct
C
400
✓ Correct
C
400
✓ Correct
D
4000
D
4000
D
4000
D
4000
D
4000
💡
Step-by-Step Explanation & Concept Rationale
To divide decimals, multiply both numerator and denominator by $1000$ to eliminate the decimal points: \[\frac{0.8}{0.002} = \frac{0.8 \times 1000}{0.002 \times 1000} = \frac{800}{2} = 400\] Thus, the correct option is (C).
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Q. 1
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Is 7 a factor of 63?
A
Yes
✓ Correct
B
No
C
Only under approximation
D
Cannot be determined
💡
Step-by-Step Explanation & Concept Rationale
Dividing 63 by 7: \[63 \div 7 = 9\] Since 63 is divisible by 7 without any remainder, 7 is a factor of 63. Thus, the correct option is (A).
Q. 2
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Which of the following statements is true regarding the number 20?
A
It is a prime number
B
It is a composite number
✓ Correct
C
It is an odd number
D
It is neither prime nor composite
💡
Step-by-Step Explanation & Concept Rationale
A composite number is a positive integer that has at least one divisor other than 1 and itself. Since 20 has divisors $1, 2, 4, 5, 10, 20$, it is a composite number. Thus, the correct option is (B).
Q. 3
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Which of the following statements is true regarding the number 17?
A
It is a prime number
✓ Correct
B
It is a composite number
C
It is neither prime nor composite
D
It is an even number
💡
Step-by-Step Explanation & Concept Rationale
A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. Since 17 is only divisible by 1 and 17, it is a prime number. Thus, the correct option is (A).
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Q. 1
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Four angles $a, b, c, d$ lie sequentially on a straight line. What is the average of $a, b, c,$ and $d$?
A
40°
B
45°
✓ Correct
C
50°
D
60°
💡
Step-by-Step Explanation & Concept Rationale
Since the angles lie on a straight line, their total sum is $a + b + c + d = 180^\circ$. Their average is: \[\text{Average} = \frac{a + b + c + d}{4} = \frac{180^\circ}{4} = 45^\circ\] Thus, the correct option is (B).
Q. 2
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Angles around a point are $85^\circ, 105^\circ, 60^\circ,$ and $a$. Find the value of angle $a$.
A
100°
B
105°
C
110°
✓ Correct
D
115°
💡
Step-by-Step Explanation & Concept Rationale
The sum of all angles around a point is $360^\circ$: \[85^\circ + 105^\circ + 60^\circ + a = 360^\circ \implies 250^\circ + a = 360^\circ \implies a = 110^\circ\] Thus, the correct option is (C).
Q. 3
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Angles on a straight line are given as $30^\circ, 60^\circ,$ and $a$. Find the value of angle $a$.
A
60°
B
70°
C
80°
D
90°
✓ Correct
💡
Step-by-Step Explanation & Concept Rationale
Angles on a straight line sum to $180^\circ$: \[30^\circ + 60^\circ + a = 180^\circ \implies 90^\circ + a = 180^\circ \implies a = 90^\circ\] Thus, the correct option is (D).
Q. 4
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
If the circumference of a circle is $3\pi$, find its area.
A
$\frac{3\pi}{4}$
B
$\frac{9\pi}{4}$
✓ Correct
C
$\frac{9\pi}{2}$
D
$3\pi$
💡
Step-by-Step Explanation & Concept Rationale
The circumference is $C = 2\pi r = 3\pi \implies r = \frac{3}{2}$. The area of the circle is: \[A = \pi r^2 = \pi \left(\frac{3}{2}\right)^2 = \frac{9\pi}{4}\] Thus, the correct option is (B).
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Q. 1
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the highest common factor (HCF) of 16 and 36?
A
2
B
4
✓ Correct
C
8
D
16
💡
Step-by-Step Explanation & Concept Rationale
Prime factorizations: \[16 = 2^4\] \[36 = 2^2 \times 3^2\] The common prime factor with the smallest exponent is $2^2 = 4$. Thus, the HCF is $4$. Thus, the correct option is (B).
Q. 2
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the highest common factor (HCF) of 36 and 82?
A
2
✓ Correct
B
4
C
6
D
18
💡
Step-by-Step Explanation & Concept Rationale
Prime factorizations: \[36 = 2^2 \times 3^2\] \[82 = 2 \times 41\] The common prime factor is $2^1 = 2$. Thus, the HCF is $2$. Thus, the correct option is (A).
Q. 3
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the highest common factor (HCF) of 6 and 12?
A
2
B
3
C
6
✓ Correct
D
12
💡
Step-by-Step Explanation & Concept Rationale
Since 6 divides 12 evenly ($12 \div 6 = 2$), the highest common factor is $6$. Thus, the correct option is (C).
Q. 4
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the highest common factor (HCF) of 50, 70, and 85?
A
5
✓ Correct
B
10
C
15
D
25
💡
Step-by-Step Explanation & Concept Rationale
Prime factorizations: \[50 = 2 \times 5^2\] \[70 = 2 \times 5 \times 7\] \[85 = 5 \times 17\] The only common prime factor is $5$. Therefore: \[\text{HCF} = 5\] Thus, the correct option is (A).
Q. 5
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the highest common factor (HCF) of 17, 23, 27, and 29?
A
1
✓ Correct
B
3
C
9
D
17
💡
Step-by-Step Explanation & Concept Rationale
The numbers 17, 23, and 29 are prime numbers. Since there is no common factor greater than 1 dividing all four numbers: \[\text{HCF}(17, 23, 27, 29) = 1\] Thus, the correct option is (A).
Q. 6
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the highest common factor (HCF) of 10, 20, 25, and 35?
A
2
B
5
✓ Correct
C
10
D
15
💡
Step-by-Step Explanation & Concept Rationale
Prime factorizations: \[10 = 2 \times 5\] \[20 = 2^2 \times 5\] \[25 = 5^2\] \[35 = 5 \times 7\] The common prime factor with the smallest exponent is $5^1 = 5$. Thus, the HCF is $5$. Thus, the correct option is (B).
Q. 7
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the Highest Common Factor (HCF) of $10$ and $12$?
A
1
B
2
✓ Correct
C
4
D
6
💡
Step-by-Step Explanation & Concept Rationale
Prime factorizations: $10 = 2 \times 5$ and $12 = 2^2 \times 3$. The only common prime factor is $2^1 = 2$. Therefore, $\text{HCF}(10, 12) = 2$. Thus, the correct option is (B).
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Q. 1
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A company paid total interest of Rs. 183.3 lakh over a period of 5 years. What is the average interest paid per year?
A
32.5 lakh
B
36.66 lakh
✓ Correct
C
41.6 lakh
D
49.4 lakh
💡
Step-by-Step Explanation & Concept Rationale
The average annual interest payment is: \[\text{Average} = \frac{\text{Total Interest}}{\text{Number of Years}} = \frac{183.3}{5} = 36.66\text{ lakh}\] Thus, the correct option is (B).
Q. 2
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
A company distributed Rs. 17 lakh in bonuses against a total salary expense of Rs. 1710 lakh. Bonus is approximately what percentage of total salary?
A
0.5%
B
1%
✓ Correct
C
2%
D
5%
💡
Step-by-Step Explanation & Concept Rationale
Calculate the percentage: \[\text{Percentage} = \frac{17}{1710} \times 100\% \approx 0.994\% \approx 1\%\] Thus, the correct option is (B).
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Q. 1
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the least common multiple (LCM) of 3 and 6?
A
3
B
6
✓ Correct
C
9
D
18
💡
Step-by-Step Explanation & Concept Rationale
Since 6 is a multiple of 3: \[\text{LCM}(3, 6) = 6\] Thus, the correct option is (B).
Q. 2
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the least common multiple (LCM) of 8 and 16?
A
8
B
16
✓ Correct
C
24
D
32
💡
Step-by-Step Explanation & Concept Rationale
Since 16 is divisible by 8: \[\text{LCM}(8, 16) = 16\] Thus, the correct option is (B).
Q. 3
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the least common multiple (LCM) of 8, 16, and 32?
A
16
B
32
✓ Correct
C
48
D
64
💡
Step-by-Step Explanation & Concept Rationale
All numbers are powers of 2 ($8 = 2^3$, $16 = 2^4$, $32 = 2^5$). The LCM is the highest power of 2: \[\text{LCM} = 2^5 = 32\] Thus, the correct option is (B).
Q. 4
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the least common multiple (LCM) of 6, 12, 24, and 48?
A
12
B
24
C
48
✓ Correct
D
96
💡
Step-by-Step Explanation & Concept Rationale
Since 6, 12, and 24 are all divisors of 48, the least common multiple of the set is: \[\text{LCM}(6, 12, 24, 48) = 48\] Thus, the correct option is (C).
Q. 5
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the least common multiple (LCM) of 4, 6, and 12?
A
6
B
12
✓ Correct
C
24
D
48
💡
Step-by-Step Explanation & Concept Rationale
Prime factorizations: \[4 = 2^2\] \[6 = 2^1 \times 3^1\] \[12 = 2^2 \times 3^1\] The LCM is: \[\text{LCM} = 2^2 \times 3^1 = 4 \times 3 = 12\] Thus, the correct option is (B).
Q. 6
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the least common multiple (LCM) of 18, 24, and 36?
A
36
B
48
C
72
✓ Correct
D
144
💡
Step-by-Step Explanation & Concept Rationale
Prime factorizations: \[18 = 2^1 \times 3^2\] \[24 = 2^3 \times 3^1\] \[36 = 2^2 \times 3^2\] Taking the highest powers of each prime factor: \[\text{LCM} = 2^3 \times 3^2 = 8 \times 9 = 72\] Thus, the correct option is (C).
Q. 7
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the least common multiple (LCM) of 5, 15, 20, and 30?
A
30
B
45
C
60
✓ Correct
D
120
💡
Step-by-Step Explanation & Concept Rationale
Prime factorizations: \[5 = 5^1\] \[15 = 3^1 \times 5^1\] \[20 = 2^2 \times 5^1\] \[30 = 2^1 \times 3^1 \times 5^1\] The LCM is: \[\text{LCM} = 2^2 \times 3^1 \times 5^1 = 4 \times 3 \times 5 = 60\] Thus, the correct option is (C).
Q. 8
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the least common multiple (LCM) of 7, 14, and 13?
A
91
B
156
C
182
✓ Correct
D
210
💡
Step-by-Step Explanation & Concept Rationale
Find the prime factorizations: \[7 = 7^1\] \[14 = 2^1 \times 7^1\] \[13 = 13^1\] The LCM is the product of the highest powers of all prime factors: \[\text{LCM} = 2^1 \times 7^1 \times 13^1 = 14 \times 13 = 182\] Thus, the correct option is (C).
Q. 9
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the Least Common Multiple (LCM) of $2$ and $3$?
A
1
B
3
C
5
D
6
✓ Correct
💡
Step-by-Step Explanation & Concept Rationale
Since $2$ and $3$ are distinct prime numbers, their LCM is their product: \[\text{LCM}(2, 3) = 2 \times 3 = 6\] Thus, the correct option is (D).
Q. 10
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the Least Common Multiple (LCM) of $4$ and $6$?
A
6
B
10
C
12
✓ Correct
D
24
💡
Step-by-Step Explanation & Concept Rationale
Prime factorization: $4 = 2^2$ and $6 = 2 \times 3$. Taking the highest power of each prime factor: \[\text{LCM}(4, 6) = 2^2 \times 3 = 4 \times 3 = 12\] Thus, the correct option is (C).
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Q. 1
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the equation of a straight line having a slope of $-2$ and a $y$-intercept of $3$?
A
y = -2x + 3
✓ Correct
B
y = 2x + 3
C
y = x + 3
D
y = -x + 3
💡
Step-by-Step Explanation & Concept Rationale
Using the slope-intercept form equation of a line $y = mx + c$, where slope $m = -2$ and $y$-intercept $c = 3$: \[y = -2x + 3\] Thus, the correct option is (A).
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Q. 1
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
What is the fractional or decimal equivalent of 100%?
A
1
✓ Correct
B
10
C
0.1
D
100
💡
Step-by-Step Explanation & Concept Rationale
By definition of percent: \[100\% = \frac{100}{100} = 1\] Thus, the correct option is (A).
Q. 2
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Convert the fraction $\frac{1}{2}$ to a percentage:
A
50%
✓ Correct
B
25%
C
75%
D
100%
💡
Step-by-Step Explanation & Concept Rationale
To convert a fraction to a percentage, multiply by $100\%$: \[\frac{1}{2} \times 100\% = 50\%\] Thus, the correct option is (A).
Q. 3
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
What is 80% of 20?
A
12
B
16
✓ Correct
C
18
D
20
💡
Step-by-Step Explanation & Concept Rationale
Calculate: \[80\% \times 20 = 0.80 \times 20 = 16\] Thus, the correct option is (B).
Q. 4
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
What is 60% of 20?
A
10
B
12
✓ Correct
C
14
D
16
💡
Step-by-Step Explanation & Concept Rationale
Calculate: \[60\% \times 20 = 0.60 \times 20 = 12\] Thus, the correct option is (B).
Q. 5
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
What is 40% of 60?
A
18
B
20
C
24
✓ Correct
D
28
💡
Step-by-Step Explanation & Concept Rationale
Calculate: \[40\% \times 60 = 0.40 \times 60 = 24\] Thus, the correct option is (C).
Q. 6
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
What is 45% of 90?
A
38.5
B
40.5
✓ Correct
C
42.5
D
45.0
💡
Step-by-Step Explanation & Concept Rationale
Calculate: \[45\% \times 90 = \frac{45}{100} \times 90 = 0.45 \times 90 = 40.5\] Thus, the correct option is (B).
Q. 7
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
What percent of 125 is 50?
A
25%
B
30%
C
40%
✓ Correct
D
50%
💡
Step-by-Step Explanation & Concept Rationale
The percentage is calculated as: \[\left(\frac{50}{125}\right) \times 100\% = \left(\frac{2}{5}\right) \times 100\% = 40\%\] Thus, the correct option is (C).
Q. 8
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Ali secured 72% marks in an annual examination. If his score was 864 marks, what were the total maximum marks of the examination?
A
1,000
B
1,100
C
1,150
D
1,200
✓ Correct
💡
Step-by-Step Explanation & Concept Rationale
Let the maximum marks be $M$. \[0.72 \times M = 864 \implies M = \frac{864}{0.72} = 1200\] Thus, the maximum marks were 1,200. Thus, the correct option is (D).
Q. 9
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
In a college with a total enrollment of 1,335 students, 60% are boys. How many girls are enrolled in the college?
A
480
B
534
✓ Correct
C
600
D
801
💡
Step-by-Step Explanation & Concept Rationale
The percentage of girls in the college is: \[100\% - 60\% = 40\%\] \[\text{Number of Girls} = 1335 \times 0.40 = 534\] Thus, the correct option is (B).
Q. 10
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A sports team lost 75% of the matches it played this season. If the team won 45 matches and drew none, what is the total number of matches played?
A
120
B
135
C
150
D
180
✓ Correct
💡
Step-by-Step Explanation & Concept Rationale
Since the team lost 75% of matches and drew none, the winning percentage is: \[100\% - 75\% = 25\%\] Let total matches be $N$: \[0.25 N = 45 \implies N = \frac{45}{0.25} = 45 \times 4 = 180\] Thus, the correct option is (D).
Q. 11
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Convert the percentage $10\%$ into a simplified fraction.
A
1/2
B
1/5
C
1/10
✓ Correct
D
1/20
💡
Step-by-Step Explanation & Concept Rationale
Convert $10\%$ to a fraction: \[10\% = \frac{10}{100} = \frac{1}{10}\] Thus, the correct option is (C).
Q. 12
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
What is the fraction equivalent of $15\%$ in simplest form?
A
1/4
B
3/20
✓ Correct
C
5/20
D
3/10
💡
Step-by-Step Explanation & Concept Rationale
Convert $15\%$ to a fraction and divide numerator and denominator by $5$: \[15\% = \frac{15}{100} = \frac{3}{20}\] Thus, the correct option is (B).
Q. 13
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
The percentage $25\%$ is equal to which simplified fraction?
A
1/3
B
1/4
✓ Correct
C
1/5
D
2/5
💡
Step-by-Step Explanation & Concept Rationale
Convert $25\%$ to a simplified fraction: \[25\% = \frac{25}{100} = \frac{1}{4}\] Thus, the correct option is (B).
Q. 14
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Which fraction represents $20\%$?
A
1/2
B
1/4
C
1/5
✓ Correct
D
1/10
💡
Step-by-Step Explanation & Concept Rationale
Convert $20\%$ to a fraction: \[20\% = \frac{20}{100} = \frac{1}{5}\] Thus, the correct option is (C).
Q. 15
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
If a student's marks are expressed as $\frac{1}{4}$ of the total, what is the percentage?
A
20%
B
25%
✓ Correct
C
30%
D
40%
💡
Step-by-Step Explanation & Concept Rationale
Multiply the fraction by $100\%$: \[\frac{1}{4} \times 100\% = 25\%\] Thus, the correct option is (B).
Q. 16
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Convert the fraction $\frac{1}{10}$ into a percentage.
A
1%
B
5%
C
10%
✓ Correct
D
15%
💡
Step-by-Step Explanation & Concept Rationale
To convert a fraction to a percentage, multiply by $100\%$: \[\frac{1}{10} \times 100\% = 10\%\] Thus, the correct option is (C).
Q. 17
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
What is $20\%$ of $80$?
A
12
B
14
C
16
✓ Correct
D
18
💡
Step-by-Step Explanation & Concept Rationale
Calculate $20\%$ of $80$: \[\text{Value} = \frac{20}{100} \times 80 = \frac{1}{5} \times 80 = 16\] Thus, the correct option is (C).
Q. 18
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
What is $20\%$ of $60$?
A
10
B
12
✓ Correct
C
14
D
16
💡
Step-by-Step Explanation & Concept Rationale
Calculate $20\%$ of $60$: \[\text{Value} = \frac{20}{100} \times 60 = \frac{1}{5} \times 60 = 12\] Thus, the correct option is (B).
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Q. 1
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
An article with a cost price of Rs. 2,000 was sold for Rs. 2,500. What is the profit percentage?
A
20%
B
25%
✓ Correct
C
30%
D
35%
💡
Step-by-Step Explanation & Concept Rationale
The profit earned is: \[\text{Profit} = 2500 - 2000 = \text{Rs. } 500\] \[\text{Profit Percentage} = \frac{\text{Profit}}{\text{Cost Price}} \times 100\% = \frac{500}{2000} \times 100\% = 25\%\] Thus, the correct option is (B).
Q. 2
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A television set is purchased for Rs. 8,000 and sold at a 10% loss. What is the selling price?
A
Rs. 7,000
B
Rs. 7,100
C
Rs. 7,200
✓ Correct
D
Rs. 7,500
💡
Step-by-Step Explanation & Concept Rationale
The cost price is $\text{CP} = \text{Rs. } 8000$ and loss is \%$. \[\text{Loss} = 8000 \times 0.10 = \text{Rs. } 800\] \[\text{Selling Price (SP)} = 8000 - 800 = \text{Rs. } 7200\] Thus, the correct option is (C).
Q. 3
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A merchant bought a chair for Rs. 1,540 and sold it to earn a profit of 25%. What is the selling price?
A
Rs. 1,850
B
Rs. 1,900
C
Rs. 1,925
✓ Correct
D
Rs. 2,000
💡
Step-by-Step Explanation & Concept Rationale
The cost price is $\text{CP} = \text{Rs. } 1540$ and profit is \%$. \[\text{Profit} = 1540 \times 0.25 = \text{Rs. } 385\] \[\text{Selling Price (SP)} = \text{CP} + \text{Profit} = 1540 + 385 = \text{Rs. } 1925\] Thus, the correct option is (C).
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Q. 1
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
A high-speed printer prints 4 pages in 15 seconds. At this constant rate, how many seconds will it take to print 25 pages?
A
60 seconds
B
75 seconds
C
93.75 seconds
✓ Correct
D
100 seconds
💡
Step-by-Step Explanation & Concept Rationale
The time required per page is $\frac{15}{4} = 3.75\text{ seconds}$. For 25 pages: \[\text{Total Time} = 25 \times 3.75 = 93.75\text{ seconds}\] Thus, the correct option is (C).
Q. 2
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
If the proportion is $7 : 4 = 21 : x$, what is the value of $x$?
A
8
B
10
C
12
✓ Correct
D
14
💡
Step-by-Step Explanation & Concept Rationale
In a proportion, the product of extremes equals the product of means: \[\frac{7}{4} = \frac{21}{x} \implies 7x = 4 \times 21 = 84 \implies x = \frac{84}{7} = 12\] Thus, the correct option is (C).
Q. 3
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
On a map scale, a distance of 10 miles is represented by 1.5 cm. What distance on the map represents 40 miles?
A
3 cm
B
4.5 cm
C
6 cm
✓ Correct
D
7.5 cm
💡
Step-by-Step Explanation & Concept Rationale
Using direct proportion: \[\text{Map Distance} = \frac{1.5\text{ cm}}{10\text{ miles}} \times 40\text{ miles} = 1.5 \times 4 = 6\text{ cm}\] Thus, the correct option is (C).
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Q. 1
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
The total distance of a road trip is 3,000 miles. Ahmad drove $\frac{3}{4}$ of the total distance and Ali drove the remainder. How many miles did Ali drive?
A
500 miles
B
750 miles
✓ Correct
C
1,000 miles
D
2,250 miles
💡
Step-by-Step Explanation & Concept Rationale
The fraction of the distance driven by Ali is: \[1 - \frac{3}{4} = \frac{1}{4}\] \[\text{Ali's Distance} = \frac{1}{4} \times 3000 = 750\text{ miles}\] Thus, the correct option is (B).
Q. 2
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
The ratio of the weight of an object on the Moon to its weight on Earth is $1 : 6$. If an astronaut weighs 180 lbs on Earth, what is his weight on the Moon?
A
15 lbs
B
20 lbs
C
25 lbs
D
30 lbs
✓ Correct
💡
Step-by-Step Explanation & Concept Rationale
Using the given ratio: \[\text{Weight on Moon} = \frac{1}{6} \times \text{Weight on Earth} = \frac{1}{6} \times 180 = 30\text{ lbs}\] Thus, the correct option is (D).
Q. 3
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
If $a : b = 6 : 7$ and $b : c = 8 : 9$, find the compound ratio $a : b : c$.
A
48:56:63
✓ Correct
B
42:56:63
C
48:54:63
D
36:49:63
💡
Step-by-Step Explanation & Concept Rationale
To combine the ratios, make the term for $b$ common ($\text{LCM}(7, 8) = 56$): \[a : b = (6 \times 8) : (7 \times 8) = 48 : 56\] \[b : c = (8 \times 7) : (9 \times 7) = 56 : 63\] Therefore: \[a : b : c = 48 : 56 : 63\] Thus, the correct option is (A).
Q. 4
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
The ratio of books sold by shop A to shop B is $7 : 4$, and the ratio of books sold by shop B to shop C is $5 : 3$. If shop C sold 36 books, how many books did shop A sell?
A
70
B
84
C
105
✓ Correct
D
140
💡
Step-by-Step Explanation & Concept Rationale
Express the continuous ratio $A : B : C$: \[A : B = 7 : 4 = 35 : 20\] \[B : C = 5 : 3 = 20 : 12\] Thus: \[A : B : C = 35 : 20 : 12\] Given that shop C sold 36 books ($12x = 36 \implies x = 3$): \[A = 35 \times 3 = 105\] Thus, shop A sold 105 books. Thus, the correct option is (C).
Q. 5
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
The subscriber counts of three channels A, B, and C are in the ratio $2 : 5 : 6$. If the total number of subscribers across all three channels is 65,000, find the combined number of subscribers for channels A and C.
A
10,000
B
25,000
C
40,000
✓ Correct
D
55,000
💡
Step-by-Step Explanation & Concept Rationale
The sum of the ratio parts is: \[2 + 5 + 6 = 13\text{ parts}\] Value of one ratio part: \[\frac{65000}{13} = 5000\] The combined ratio parts for channels A and C is $2 + 6 = 8\text{ parts}$. \[\text{Combined Subscribers} = 8 \times 5000 = 40,000\] Thus, the correct option is (C).
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Q. 1
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Find the sum of the first 10 terms of the arithmetic sequence: , 7, 12, 17, \dots$
A
240
B
245
✓ Correct
C
250
D
260
💡
Step-by-Step Explanation & Concept Rationale
The first term is = 2$, common difference = 7 - 2 = 5$, and number of terms = 10$. Using the sum formula for an arithmetic progression: \[S_n = \frac{n}{2}[2a + (n-1)d]\] \[S_{10} = \frac{10}{2}[2(2) + (10-1)5] = 5[4 + 45] = 5 \times 49 = 245\] Thus, the correct option is (B).
Q. 2
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Find the 100th term of the arithmetic sequence: $15, 20, 25, 30, \dots$
A
500
B
510
✓ Correct
C
520
D
530
💡
Step-by-Step Explanation & Concept Rationale
First term $a = 15$ and common difference $d = 20 - 15 = 5$. The $n$-th term is $a_n = a + (n-1)d$. For $n = 100$: \[a_{100} = 15 + (100 - 1) \times 5 = 15 + 99 \times 5 = 15 + 495 = 510\] Thus, the correct option is (B).
Q. 3
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Find the sum of the first $50$ odd positive integers: $1 + 3 + 5 + 7 + \dots$
A
2400
B
2450
C
2500
✓ Correct
D
2600
💡
Step-by-Step Explanation & Concept Rationale
The sum of the first $n$ odd positive integers is given by $S_n = n^2$. For $n = 50$: \[S_{50} = 50^2 = 2500\] Or using arithmetic series formula: $S_{50} = \frac{50}{2}[2(1) + (50-1)2] = 25[2 + 98] = 25 \times 100 = 2500$. Thus, the correct option is (C).
Q. 4
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Find the 8th term in the geometric progression: $1, 3, 9, \dots$
A
2000
B
2187
✓ Correct
C
2200
D
2500
💡
Step-by-Step Explanation & Concept Rationale
First term $a = 1$, common ratio $r = 3$. The 8th term is: \[a_8 = a r^{8-1} = 1 \times 3^7 = 2187\] Thus, the correct option is (B).
Q. 5
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
In the geometric sequence $6, 12, 24, \dots$, what is the position (term number) of the value $1536$?
A
7th
B
8th
C
9th
✓ Correct
D
10th
💡
Step-by-Step Explanation & Concept Rationale
Here first term $a = 6$ and common ratio $r = \frac{12}{6} = 2$. The $n$-th term is: \[a_n = a r^{n-1} \implies 1536 = 6 \times 2^{n-1} \implies 2^{n-1} = \frac{1536}{6} = 256\] Since $256 = 2^8$, we have $n - 1 = 8 \implies n = 9$. Thus, the correct option is (C).
Q. 6
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Find the sum of the infinite geometric progression: $\frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \dots$
A
1/3
B
1/2
✓ Correct
C
2/3
D
1
💡
Step-by-Step Explanation & Concept Rationale
Here $a = \frac{1}{3}$ and common ratio $r = \frac{1}{3}$. Using $S_\infty = \frac{a}{1 - r}$: \[S_\infty = \frac{1/3}{1 - 1/3} = \frac{1/3}{2/3} = \frac{1}{2}\] Thus, the correct option is (B).
Q. 7
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
In the geometric sequence $1, 3, 9, 27, \dots$, find the common ratio ($r$).
A
2
B
3
✓ Correct
C
6
D
9
💡
Step-by-Step Explanation & Concept Rationale
The common ratio $r$ is the quotient of any term divided by the preceding term: \[r = \frac{3}{1} = \frac{9}{3} = \frac{27}{9} = 3\] Thus, the correct option is (B).
Q. 8
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Find the value of the 10th term in the geometric sequence: $1, 3, 9, \dots$
A
$3^8$
B
$3^9$
✓ Correct
C
$3^{10}$
D
$3^{11}$
💡
Step-by-Step Explanation & Concept Rationale
Here the first term is $a_1 = 1$ and common ratio is $r = \frac{3}{1} = 3$. The $n$-th term is $a_n = a_1 r^{n-1}$. For $n = 10$: \[a_{10} = 1 \times 3^{10-1} = 3^9\] Thus, the correct option is (B).
Q. 9
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
If the first term of a geometric sequence is $a_1 = 6$ and the common ratio is $r = 2$, find the 9th term.
A
768
B
1024
C
1536
✓ Correct
D
3072
💡
Step-by-Step Explanation & Concept Rationale
The formula for the $n$-th term of a geometric progression is $a_n = a_1 r^{n-1}$. For $n = 9$: \[a_9 = 6 \times 2^{9-1} = 6 \times 2^8 = 6 \times 256 = 1536\] Thus, the correct option is (C).
Q. 10
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Calculate the sum of the infinite geometric series: $\frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \dots$
A
1/3
B
1/2
✓ Correct
C
2/3
D
1
💡
Step-by-Step Explanation & Concept Rationale
The first term is $a = \frac{1}{3}$ and common ratio is $r = \frac{1/9}{1/3} = \frac{1}{3}$. Using the infinite sum formula $S_\infty = \frac{a}{1 - r}$: \[S_\infty = \frac{\frac{1}{3}}{1 - \frac{1}{3}} = \frac{\frac{1}{3}}{\frac{2}{3}} = \frac{1}{2}\] Thus, the correct option is (B).
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Q. 1
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Find the arithmetic mean of $2, 8, 5, 9, 6,$ and $12$.
A
6
B
7
✓ Correct
C
8
D
9
💡
Step-by-Step Explanation & Concept Rationale
The arithmetic mean is: \[\text{Mean} = \frac{2 + 8 + 5 + 9 + 6 + 12}{6} = \frac{42}{6} = 7\] Thus, the correct option is (B).
Q. 2
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Find the median of the set: $4, 2, 7, 3, 10, 9, 13$.
A
4
B
7
✓ Correct
C
9
D
10
💡
Step-by-Step Explanation & Concept Rationale
Arranging the $7$ numbers in ascending order: \[2, 3, 4, 7, 9, 10, 13\] The 4th (middle) number is $7$. Thus, the correct option is (B).
Q. 3
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Find the median of the following set of values: $45, 91, 62, 71, 55$.
A
55
B
62
✓ Correct
C
71
D
91
💡
Step-by-Step Explanation & Concept Rationale
Arranging the $5$ numbers in ascending order: \[45, 55, 62, 71, 91\] The middle value (3rd element) is $62$. Thus, the correct option is (B).
Q. 4
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Find the mode of the dataset: $2, 5, 5, 6, 5, 7, 10, 11, 6, 5$.
A
2
B
5
✓ Correct
C
6
D
7
💡
Step-by-Step Explanation & Concept Rationale
The mode is the value that appears with the highest frequency. Counting the occurrences: $5$ appears $4$ times, $6$ appears $2$ times, and other numbers appear once. Hence, the mode is $5$. Thus, the correct option is (B).
Q. 5
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Find the arithmetic mean of $2, 8, 5, 9, 6,$ and $12$.
A
6
B
7
✓ Correct
C
8
D
9
💡
Step-by-Step Explanation & Concept Rationale
The arithmetic mean is calculated as: \[\text{Mean} = \frac{\sum x}{n} = \frac{2 + 8 + 5 + 9 + 6 + 12}{6} = \frac{42}{6} = 7\] Thus, the correct option is (B).
Q. 6
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Find the median of the dataset: $4, 2, 7, 3, 10, 9, 13$.
A
4
B
7
✓ Correct
C
9
D
10
💡
Step-by-Step Explanation & Concept Rationale
Arrange the $n = 7$ numbers in ascending order: \[2, 3, 4, 7, 9, 10, 13\] The median is the 4th (middle) value, which is $7$. Thus, the correct option is (B).
Q. 7
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Determine the median of the set of marks: $45, 91, 62, 71, 55$.
A
55
B
62
✓ Correct
C
71
D
91
💡
Step-by-Step Explanation & Concept Rationale
First arrange the $n = 5$ numbers in ascending order: \[45, 55, 62, 71, 91\] The median is the middle $\left(\frac{n+1}{2}\right) = 3\text{rd}$ term, which is $62$. Thus, the correct option is (B).
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