1. If z = x + y and x is 2.5 percent of z, where x, y, and z are positive numbers, which of the following is the ratio of y to x?
Answer: C
The ratio of y to x is 39 to 1.
To find the ratio of y to x, we can start by using the equation z = x + y and the information that x is 2.5 percent of z. By substituting the values and solving for the ratio, we determine that the ratio of y to x is 39 to 1.
A) 41 to 1
This option suggests that y is 41 times larger than x. However, based on the calculations derived from the relationships between x, y, and z, this ratio does not hold true, as the actual ratio is found to be lower.
B) 40 to 1
A ratio of 40 to 1 implies that y is 40 times greater than x. While this is a plausible option, it does not align with the calculations derived from the equations provided, which show that the ratio is actually less than this value.
C) 39 to 1
This is the correct ratio of y to x. Given that x is 2.5 percent of z, we can derive y by substituting the values accordingly and simplifying, leading to the conclusion that y is indeed 39 times greater than x.
D) 35 to 1
A 35 to 1 ratio indicates that y is 35 times greater than x. This does not match the calculated ratio, which shows that y actually has a greater comparative value to x than this option suggests.
E) 32 to 1
This option indicates a ratio of 32 to 1, suggesting that y is only 32 times larger than x. The calculations reveal that this is also incorrect, as the actual ratio is significantly higher.
Conclusion
The calculation confirms that the correct ratio of y to x is 39 to 1, as derived from the relationship of x being 2.5 percent of z. All other options misrepresent this relationship, either by overestimating or underestimating the comparative size of y relative to x. Thus, C is the only viable answer.