单选题 Jordan has taken 5 math tests so far this semester. If he gets a 70 on his next test, it will lower the average (arithmetic mean) of his test scores by 4 points. What is his average now?

(A) 74
(B) 85
(C) 86
(D) 90
(E) 94

【正确答案】 E

【答案解析】If a represents Jordan's average after 5 tests, then he has earned a total of 5a points [TAC-TIC E1]. A grade of 70 on the sixth test will lower his average 4 points to a -4. Therefore,
[*].
**Assume Jordan's average is a because he earned a on each of his first 5 tests. Since after getting a 70 on his sixth test his average will be a -4, the deviation on each of the first 5 tests is 4, for a total deviation above the average of 20 points. So, the total deviation below must also be 20 [KEY FACT E3]. Therefore, 70 is 20 less than the new average of a -4:
[*]
**Use TACTIC 1, Chapter 11: backsolve. Start with Choice C, 86. If his 5-test average was 90, he had 450 points and a 70 on the sixth test would give him a total of 520 points, and an average of 520 -6 = 86.666. So, the 70 lowered his average 3.333 points. That's not enough. Eliminate Choices A, B, and C.
Try Choices D or E. Choice E, 94, works.