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Solution
If the average of a set of 9 numbers is 99, their sum is 9 × 99 = 891. If deleting 1 number reduces the average of the remaining 8 numbers to 89, the sum of those 8 numbers must be 8 × 89 = 712. The deleted number was 891 – 712 = 179. The answer is (179).

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Here, x² – y² = (x + y)(x – y) = 10 × 11 = 110. Add the two equations: 2x = 21, so x
= 10.5. Since 10.5 + y = 10, then y = -0.5. Using your calculator, you get: x² – y² =
(10.5)2 = 110.25 – 0.25 = 110. The answer is (110).

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Solution
If the average of 5 numbers (a, b, c, d, e) is 95, the sum of these numbers is 5 × 95 = 475. Similarly, the sum of the 3 numbers a, b, and e whose average is 100 is 300, leaving 175 (475 – 300) as the sum of the 2 remaining numbers, c and. The average of these 2 numbers is their sum divided by 2: average of c and d = 175 ÷ 2 = 87.5.
The answer is (87.5).

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Solution
If f(x) = x +5, then f(3a) = 3a + 5 and f(2a) = 2a + 5. Therefore , f(3a) + 2 = f(2a)
+ 3 ⇒3a + 5 + 2 = 2a + 5 + 3 ⇒3a + 7 = 2a + 8 a = 1.
The answer is (A).