Question #b1228811 - SAT Suite Question Bank

ID: b1228811

Modded SAT Question Bank by Abdullah Mallik

Marisa needs to hire at least 10 staff members for an upcoming project. The staff members will be made up of junior directors, who will be paid $640 per week, and senior directors, who will be paid $880 per week. Her budget for paying the staff members is no more than $9,700 per week. She must hire at least 3 junior directors and at least 1 senior director. Which of the following systems of inequalities represents the conditions described if x is the number of junior directors and y is the number of senior directors?

$640 x, plus 880 y, is greater than or equal to 9,700; x plus y is less than or equal to 10; x is greater than or equal to 3; y is greater than or equal to 1$
$640 x, plus 880 y, is less than or equal to 9,700; x plus y is greater than or equal to 10; x is greater than or equal to 3; y is greater than or equal to 1$
$640 x, plus 880 y, is greater than or equal to 9,700; x plus y is greater than or equal to 10; x is less than or equal to 3; y is less than or equal to 1$
$640 x, plus 880 y, is less than or equal to 9,700; x plus y is less than or equal to 10; x is less than or equal to 3; y is less than or equal to 1$

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Correct Answer: B

Rationale

Choice B is correct. Marisa will hire x junior directors and y senior directors. Since she needs to hire at least 10 staff members, $x plus y, is greater than or equal to 10$ . Each junior director will be paid $640 per week, and each senior director will be paid $880 per week. Marisa’s budget for paying the new staff is no more than $9,700 per week; in terms of x and y, this condition is $640 x plus 880 y, is less than or equal to 9,700$ . Since Marisa must hire at least 3 junior directors and at least 1 senior director, it follows that $x is greater than or equal to 3$ and $y is greater than or equal to 1$ . All four of these conditions are represented correctly in choice B.

Choices A and C are incorrect. For example, the first condition, $640 x plus 880 y, is greater than or equal to 9,700$ , in each of these options implies that Marisa can pay the new staff members more than her budget of $9,700. Choice D is incorrect because Marisa needs to hire at least 10 staff members, not at most 10 staff members, as the inequality $x plus y, is less than or equal to 10$ implies.

Question Difficulty: Medium