Correct Answer: C

Rationale: The smallest group is Group Gamma, which had 1/6 of the total number of patients. To determine the smallest group, compare the fractions representing the portions of patients in each group. 1/6 is smaller than 1/3 and 1/2, making Group Gamma the smallest. Group Alpha and Group Beta have larger fractions of patients, making them larger groups compared to Group Gamma.

Correct Answer: B

Rationale: To solve the equation x + x * x - x / x, follow the order of operations (PEMDAS/BODMAS). First, perform the multiplication: x * x = x^2. Then, perform the division: x / x = 1. Substituting these back into the equation gives x + x^2 - 1. Therefore, the equation simplifies to x + x^2 - 1. By evaluating this further, the final result is 3. Choices A, C, and D are incorrect because they do not correctly apply the order of operations to solve the equation.

Correct Answer: B

Rationale: To calculate the price after the 15% discount on a $100 item, you first find 15% of $100, which is $15. Then, subtract $15 from the original price: $100 - $15 = $85. Therefore, the correct answer is $85. Choice A ($90), Choice C ($80), and Choice D ($75) are incorrect as they do not reflect the correct calculation of applying a 15% discount to the original $100 price.

Correct Answer: A

Rationale: After 35% of the staff are on vacation, 65% remain. Since 20% of the remaining staff are certified, you multiply 0.20 by 65% (0.20 * 65% = 0.13 or 13%). Therefore, the correct answer is 0.13 or 13%. Choices C and D are incorrect as they do not represent the correct calculation for the percentage of certified staff available. Choice B is incorrect because it incorrectly states the calculated percentage as 0.13 instead of 0.07.

Correct Answer: A

Rationale: The correct equation that models the relationship between x and y when y is three times x is y = 3x. This equation represents that y is equal to three times x. Choice B (x = 3y) incorrectly reverses the relationship, stating that x is equal to three times y. Choice C (y = x + 3) and Choice D (y = x / 3) do not correctly represent a relationship where y is three times x, making them incorrect choices.