What percent of y is x ?
(1) y is 10 more than x divided by 2.
(2) The ratio of x to y is the same as the ratio of 2 more than x to 3 more than y.
This one is from a Kaplan test. I chose (D): either statement.
Before you steam ahead and say OA is correct, please read my reasoning and try to refute it.
As a ratio/percentage question, if you find y/x, you also have the percentage.
OA says that [spoiler]only (B) is sufficient[/spoiler]. The reasoning: "This is a ratio problem. There are two variables, so normally we'd need two distinct equations to get their values. In this case, however, knowing the relationship between the variables is all we need. Statement (1 ) translates to y -10 = x + 2. Since the relationship between the two unknowns depends on a constant, the ratio between the two changes as the values of x and y change. Insufficient. Statement (2) can be rewritten as x * y = (x + 2) * (y + 3). Cross-multiplying and simplifying gives us 3x * 2 = y. Sufficient."
Now, if I look at y=x/2+10, I know that there is no straight y/x in there. But look at it as a function, and try to graph it. This being a first degree function, the graph is a straight line with the slope of 1/2 the coefficient of x, and which crosses the y axis at y=10.
This 1/2 coefficient is exactly what we are asked to find: y/x. The constant term (here 10) is completely irrelevant, it can be anything. It only decides where the graph crosses the y axis, the slope is the same and only dependent on the coefficients of x and y.
So, what I say is that given y=x/2+10, or for any y=x/2+constant, y/x=1/2 or y=50%*x, thus (2) is sufficient.
So, where am I wrong? Or where are they?
(1) y is 10 more than x divided by 2.
(2) The ratio of x to y is the same as the ratio of 2 more than x to 3 more than y.
This one is from a Kaplan test. I chose (D): either statement.
Before you steam ahead and say OA is correct, please read my reasoning and try to refute it.
As a ratio/percentage question, if you find y/x, you also have the percentage.
OA says that [spoiler]only (B) is sufficient[/spoiler]. The reasoning: "This is a ratio problem. There are two variables, so normally we'd need two distinct equations to get their values. In this case, however, knowing the relationship between the variables is all we need. Statement (1 ) translates to y -10 = x + 2. Since the relationship between the two unknowns depends on a constant, the ratio between the two changes as the values of x and y change. Insufficient. Statement (2) can be rewritten as x * y = (x + 2) * (y + 3). Cross-multiplying and simplifying gives us 3x * 2 = y. Sufficient."
Now, if I look at y=x/2+10, I know that there is no straight y/x in there. But look at it as a function, and try to graph it. This being a first degree function, the graph is a straight line with the slope of 1/2 the coefficient of x, and which crosses the y axis at y=10.
This 1/2 coefficient is exactly what we are asked to find: y/x. The constant term (here 10) is completely irrelevant, it can be anything. It only decides where the graph crosses the y axis, the slope is the same and only dependent on the coefficients of x and y.
So, what I say is that given y=x/2+10, or for any y=x/2+constant, y/x=1/2 or y=50%*x, thus (2) is sufficient.
So, where am I wrong? Or where are they?
