Aptitude-Numbers

(11) What is the sum of the first 10 even numbers?

• (a) 100
• (b) 110
• (c) 120
• (d) 90

Answer

Correct Answer: (b) 110
The sum of the first 10 even numbers is 2 + 4 + 6 + \ldots + 18 + 20 = 110.

(12) If the 7th term of an arithmetic sequence is 58 and the common difference is 3, what is the first term?

• (a) 40
• (b) 34
• (c) 37
• (d) 43

Answer

Correct Answer: (a) 40
Using the formula a_n = a_1 + (n - 1)d, the first term is a_1 = a_7 - 6d = 58 - 6 \times 3 = 40.

(13) What is the 5th term of a geometric sequence where the first term is 2 and the common ratio is 4?

• (a) 256
• (b) 128
• (c) 512
• (d) 1024

Answer

Correct Answer: (c) 512
The 5th term is found using the formula a_n = a_1 \cdot r^{(n-1)}, which gives a_5 = 2 \cdot 4^{4} = 512.

(14) If the product of a number and 3 is 72, what is the number?

• (a) 24
• (b) 36
• (c) 18
• (d) 30

Answer

Correct Answer: (a) 24
The equation 3x = 72 can be solved for x to find the number, which is x = \frac{72}{3} = 24.

(15) What is the least common multiple (LCM) of 8 and 12?

• (a) 48
• (b) 24
• (c) 36
• (d) 96

Answer

Correct Answer: (b) 24
The LCM of 8 and 12 can be found using the formula \text{LCM}(a, b) = \frac{|a \cdot b|}{\gcd(a, b)}, which gives \text{LCM}(8, 12) = \frac{8 \cdot 12}{\gcd(8, 12)} = 24.