SAT Mathematics Practice Test 5

Question : 41 of 58

Marks: +1, -0

${a-b}/a=c$
In the equation above, if a is negative and b is positive, which of the following must be true?

Solution:

The equation can be rewritten as

1-b/a=c

,or equivalently

1-c=b/a

. Since

a < 0

and

b > 0

it follows that

b/a < 0

, and so

1-c < 0

, or equivalently

c > 1

Choice B is incorrect. If

c=1,

then

a−b=a,

b=0.

But it is given that

b > 0

, so

c = 1

cannot be true. Choice C is incorrect. If

c=−1

, then

a−b=−a,

2a=b

. But this equation contradicts the premise that

a < 0

and

b > 0

, so

c=−1

cannot be true. Choice D is incorrect. For example, if

c=−2,

then

a−b=−2a,

3a=b.

But this contradicts the fact that a and b have opposite signs, so

c < −1

cannot be true.

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