The average of the first 8 prime numbers is: | Mathematics MCQ | Examoogle

Examoogle • User • info@examoogle.com • EE-2024-8821

Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked

MathematicsNumber System

The average of the first 8 prime numbers is:

9.5

10.125

11.25

12.5

Correct Answer

📐 MA • Math Direct FormulaMathematicsNumber System

Option B

10.125

Quick Summary:

Given: First 8 prime numbers: 2, 3, 5, 7, 11, 13, 17, 23

📐MAMath SolutionDirect Formula

📋 Given

First 8 prime numbers: 2, 3, 5, 7, 11, 13, 17, 23

🔢 Formula Used

Average=∑i=18pi8\text{Average} = \frac{\sum_{i=1}^{8} p_i}{8}Average=8∑i=18​pi​​

⚡ Exam Hall Shortcut / Speed Trick

Pair numbers (2+23, 3+17, 5+13, 7+11) to get sums 25,20,18,18; total 81, then divide 81 by 8 quickly to obtain 10.125.

⚠️ Common Student Trap / Pitfall

Including 19 as the 8th prime gives 9.625, which is not among the options.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

List the primes

Identify the first eight primes as given: $2,3,5,7,11,13,17,23$ .

p={2,3,5,7,11,13,17,23}p = \{2,3,5,7,11,13,17,23\}p={2,3,5,7,11,13,17,23}

Sum the primes

Add them either directly or by pairing: $2+23=25$ , $3+17=20$ , $5+13=18$ , $7+11=18$ , total $25+20+18+18=81$ .

∑pi=2+3+5+7+11+13+17+23=81\sum p_i = 2+3+5+7+11+13+17+23 = 81∑pi​=2+3+5+7+11+13+17+23=81

Compute the average

Divide the sum by the count $8$ : $81\div8 = 10.125$ .

Average=818=10.125\text{Average} = \frac{81}{8} = 10.125Average=881​=10.125

Select the option

The computed average matches option B.

10.125=Option B10.125 = \text{Option B}10.125=Option B

✅

B is correct because the average of the listed primes is $10.125$ .

Core Concepts Used

Click any tag to open in AI Tutor

💡 EXAM TIP

Average calculations frequently appear in series‑sum problems; remember to sum first then divide, which avoids errors in individual term averages.

Loading discussion...