Bunuel wrote:
If a, b, c and g are non-zero integers, 3 ≥ c ≥ – 9 , 5 ≥ a ≥ –2 , 10 ≥ b ≥ –1 , 4 ≥ g ≥ 1, then which of the following expresses the smallest possible value of ag/(bc)?
A. –90
B. –20
C. –10
D. 1/90
E. 15/4
Because we want the smallest possible value of ag/bc, we can first see that the value of the fraction will have to be negative. Thus, either the product ag will be negative, or bc will be negative. Additionally, we want the absolute value of the entire fraction to be as large as possible, but still in keeping with the given constraints.
Let’s start with the product ag:
We are given that 5 ≥ a ≥ –2 and 4 ≥ g ≥ 1
If we let a = 5 and g = 4, we have ag = 20.
Let’s now move to the denominator bc:
We are given that 3 ≥ c ≥ – 9 and 10 ≥ b ≥ –1
If we let c = 1 and b = -1, we have bc = -1.
Thus, the smallest value of ag/bc = 20/-1 = -20.
Answer: B
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