carcass wrote:
If \(\frac{a}{b}=\frac{2}{3}\) which of the following is not true ?
A) \(\frac{a+b}{b}=\frac{5}{3}\)
B) \(\frac{b}{b-a}=3\)
C) \(\frac{a-b}{b}=\frac{1}{3}\)
D) \(\frac{2a}{3b}=\frac{4}{9}\)
E) \(\frac{a+3b}{a}=\frac{11}{2}\)
We are given that a/b = 2/3 or 3a = 2b.
Let’s simplify each answer choice to determine which one cannot be manipulated to yield 3a = 2b.
A) (a + b)/b = 5/3
3(a + b) = 5b
3a + 3b = 5b
3a = 2b
Since we have 3a = 2b, answer choice A is not correct.
B) b/(b - a) = 3
b = 3(b - a)
b = 3b - 3a
3a = 2b
Since we have 3a = 2b, answer choice B is not correct.
C) (a - b)/b = 1/3
3(a - b) = b
3a - 3b = b
3a = 4b
Since we have 3a = 4b, answer choice C is correct.
Alternative solution:
Let’s test each answer choice to determine which one is not true (keep in mind that a/b = 2/3).
A) (a + b)/b = 5/3
(a + b)/b = a/b + b/b = 2/3 + 1 = 5/3 → This is true.
B) b/(b - a) = 3
Notice that b/(b - a) = 3 means (b - a)/b = 1/3 when we reciprocate both sides of the equation.
(b - a)/b = b/b - a/b = 1 - 2/3 = ⅓ → This is true.
C) (a - b)/b = 1/3
(a - b)/b = a/b - b/b = 2/3 - 1 = -1/3 → So (a - b)/b = 1/3 is not true. This is the correct answer choice.
Answer: C
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79% (01:07) correct 
