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McGraw Hill Integrated II, 2012 View details

5. Quadratic Inequalities

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Exercise 64 Page 213

Divide 116 with the given integers.

D

Practice makes perfect

We can look at the options one by one and try to find the other integer that falls outside the range by dividing 116 with the given numbers and taking the integer part of the result.

Option	n	116/n	Product	Is it between 107 and 116?
A	5	116/5=23.2	23* 5=115	Yes
B	10	116/10=11.6	11* 10=110	Yes
C	12	116/12≈ 9.67	9* 12=108	Yes
D	15	116/15≈ 7.73	7* 15=105	No
E	23	116/23≈ 5.04	5* 23=115	Yes

We can see that for four of the numbers we could find a pair such that the product is between 107 and 116. The only number for which there is no such pair is 15. The correct answer is D.