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29 Jan 2025, 09:55
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
100% (00:31) correct
0% (00:00) wrong based on 6 sessions
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If the average (arithmetic mean) of 5, 6, 7, and w is 10, what is the value of w?
A. 8
B. 13
C. 18
D. 22
E. 28
A. 8
B. 13
C. 18
D. 22
E. 28
01 Feb 2025, 08:01
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OE
Test Choice C: w = 18.
Is the average of 5, 6, 7, and 18 equal to 10?
No: \(\frac{5+6+7+18}{4}\) \(\frac{36}{4}=9\), which is too small. Eliminate C, and, since for the average to be 10, w must be greater than 18, eliminate A and B, as well.
Try D: \(\frac{5+6+7+22}{4}\) \(\frac{40}{4}=10\) w = 22. Is the average of 5, 6, 7, and 22 equal to 10?
Yes: . The answer is D.
Every problem that can be solved using TACTIC 1 can be solved directly, often in less time. So we stress: if you are confident that you can solve a problem quickly and accurately, just do so.
Here are two direct methods for solving Example 1, each of which is faster than backsolving. (See Section 12-E, on averages.) If you know either method you should use it, and save TACTIC 1 for those problems that you can’t easily solve directly.
DIRECT SOLUTION 1. If the average of four numbers is 10, their sum is 40. So, 5 + 6 + 7 + w = 40 ⇒ 18 + w = 40 ⇒ w = 22.
DIRECT SOLUTION 2. Since 5 is 5 less than 10, 6 is 4 less than 10, and 7 is 3 less than 10, to compensate, w must be 5 + 4 + 3 = 12 more than 10. So, w = 10 + 12 = 22.
Test Choice C: w = 18.
Is the average of 5, 6, 7, and 18 equal to 10?
No: \(\frac{5+6+7+18}{4}\) \(\frac{36}{4}=9\), which is too small. Eliminate C, and, since for the average to be 10, w must be greater than 18, eliminate A and B, as well.
Try D: \(\frac{5+6+7+22}{4}\) \(\frac{40}{4}=10\) w = 22. Is the average of 5, 6, 7, and 22 equal to 10?
Yes: . The answer is D.
Every problem that can be solved using TACTIC 1 can be solved directly, often in less time. So we stress: if you are confident that you can solve a problem quickly and accurately, just do so.
Here are two direct methods for solving Example 1, each of which is faster than backsolving. (See Section 12-E, on averages.) If you know either method you should use it, and save TACTIC 1 for those problems that you can’t easily solve directly.
DIRECT SOLUTION 1. If the average of four numbers is 10, their sum is 40. So, 5 + 6 + 7 + w = 40 ⇒ 18 + w = 40 ⇒ w = 22.
DIRECT SOLUTION 2. Since 5 is 5 less than 10, 6 is 4 less than 10, and 7 is 3 less than 10, to compensate, w must be 5 + 4 + 3 = 12 more than 10. So, w = 10 + 12 = 22.
