Correct Answer: A

Rationale: To find the value of X, set up a proportion: 5/30 = X/1. Cross-multiply to get 5 = 30X. Divide both sides by 30, which gives X = 5/30 = 0.1667. When rounded to the nearest tenth, X is 0.2, which is equivalent to 6 when rounded to a whole number. Therefore, the value of X is 6.

Correct Answer: C

Rationale: To convert 0.004 to a ratio, you first express it as a fraction, which is 4/1000. Simplifying this fraction gives 1/250. Therefore, the correct ratio for 0.004 is 1:250. This ratio represents the relationship between the parts, where for every 1 unit in the first part, there are 250 units in the second part. It's essential to simplify fractions to their lowest terms to express the ratio in its simplest form.

Correct Answer: C

Rationale: To solve this proportion, set up the equation: 15/1000 = x/100. Cross multiply to get 15 * 100 = 1000 * x. Simplifying gives x = 1. Therefore, the correct answer is 1. The ratio 15:1000 is equivalent to the ratio 1:67. By setting up the proportion, we find that x = 1, making Option C the correct answer. This question assesses your understanding of ratios and proportions. Remember, when solving proportions, cross multiplication is a useful method to find the unknown value. In this case, the proportion is between 15 and 1000 in the first set, and x and 100 in the second set. By applying the cross multiplication method, you can determine that x equals 1, making Option C the correct answer.

Correct Answer: C

Rationale: To add mixed numbers, convert them to improper fractions. 5 1/3 = 16/3 and 3 1/2 = 7/2. Find a common denominator, in this case, 6: 16/3 = 32/6 and 7/2 = 21/6. Add the fractions: 32/6 + 21/6 = 53/6, which simplifies to 8 5/6. Therefore, the sum of 5 1/3 + 3 1/2 is 8 5/6.

Correct Answer: D

Rationale: To determine the largest decimal among the options, you need to compare them by looking at the digits after the decimal point. When comparing 0.6, 0.667, 0.0688, and 0.68, consider that 0.6 is equivalent to 0.600, 0.667 remains 0.667, 0.0688 is already in its most precise form, and 0.68 is the same as 0.680. By comparing them, you can see that 0.68 is the largest decimal among the options provided. Remember, when comparing decimals, it's important to line up the decimal points to make accurate comparisons.