Question #c77ef2fb - SAT Suite Question Bank

ID: c77ef2fb

Modded SAT Question Bank by Abdullah Mallik

Blood volume, $V sub B$ , in a human can be determined using the equation $V sub B equals, the fraction with numerator V sub P, and denominator 1 minus H, end fraction$ , where $V sub P$ is the plasma volume and H is the hematocrit (the fraction of blood volume that is red blood cells). Which of the following correctly expresses the hematocrit in terms of the blood volume and the plasma volume?

$H equals, 1 minus the fraction V sub P over V sub B$
$H equals, the fraction V sub B over V sub P$
$H equals, 1 plus the fraction V sub B over V sub P$
$H equals, V sub B, minus V sub P$

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Correct Answer: A

Rationale

Choice A is correct. The hematocrit can be expressed in terms of the blood volume and the plasma volume by solving the given equation $V sub B equals, the fraction with numerator V sub P, and denominator 1 minus H, end fraction$ for H. Multiplying both sides of this equation by $open parenthesis, 1 minus H, close parenthesis$ yields $V sub B, times, open parenthesis, 1 minus H, close parenthesis, equals V sub P$ . Dividing both sides by $V sub B$ yields $1 minus H equals, the fraction V sub P, over V sub B$ . Subtracting 1 from both sides yields $negative H equals, negative 1 plus, the fraction V sub P over V sub B$ . Dividing both sides by $negative 1$ yields $H equals, 1 minus, the fraction V sub P over V sub B$ .

Choices B, C, and D are incorrect and may result from errors made when manipulating the equation.

Question Difficulty: Medium