Math Gangsta SAT/ACT Practice Problem 52

Practice Problem #52

Each of the variables t, w, x, y, and z represents a different positive real number.
Given the equations below, which of the 4 variables w, x, y, and z necessarily has the greatest value?

1.23w = t
1.01x = t
0.99y = t
0.23z = t

Now I solve it step by step.

Since each expression equals t, I solve each one for the variable.

w = t / 1.23
x = t / 1.01
y = t / 0.99
z = t / 0.23

Now here’s the key idea:

All of these are equal to t divided by a number.

When you divide by a SMALLER positive number, you get a LARGER result.

So I compare the denominators:

1.23
1.01
0.99
0.23

The smallest number is 0.23.

That means:

z = t / 0.23

will be the largest value.

Final Answer: I (z)

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