5. If the average of X, 2X+5, X+6 and 45 is 29, what’s X?
a. 15
b. 20
c. 24
d. 32
The average of X, 2X+5, X+6, and 45 equals 29. Solving yields X = 15 as the correct answer.
Step-by-Step Solution
Sum the four terms: X + (2X + 5) + (X + 6) + 45 = 4X + 56.
Divide by 4 for average: (4X + 56)/4 = 29.
Multiply both sides by 4: 4X + 56 = 116. Subtract 56: 4X = 60. Thus, X = 15 [execute_python].
Option Analysis
Verify each option by computing the average:
| Option | X Value | Terms | Average |
|---|---|---|---|
| a | 15 | 15, 35, 21, 45 | 29 |
| b | 20 | 20, 45, 26, 45 | 34 |
| c | 24 | 24, 53, 30, 45 | 38 |
| d | 32 | 32, 69, 38, 45 | 46 |
Only option a gives exactly 29 [execute_python].
The average of X, 2X+5, X+6 and 45 is 29 problem tests basic algebra skills vital for CSIR NET Life Sciences quantitative aptitude. Candidates often face such equations in exam sections requiring quick arithmetic and verification.
Equation Setup
Combine terms: X + 2X + 5 + X + 6 + 45 = 4X + 56. Average equation: (4X + 56)/4 = 29. Simplify to X = 15.
Why Options Fail
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b. 20 yields 34, exceeding 29.
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c. 24 gives 38, too high.
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d. 32 results in 46, furthest off [execute_python].
Practice plugging options first for speed, then solve algebraically for confirmation.
