Math: 45cfb9de

ID: 45cfb9de

(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Algebra)

Comment: Use the inequalities against the question.

Method 1: It is obvious that the bus travels faster than Adam does on foot: a 5-minute ride versus a 20-minute walk. If the question is asking about the wait time, w, Adam would have to wait for the bus before it would be faster to walk, then we want that wait time to be greater than something. Conceptually, (A) and (C) do not make sense. (Sometimes it helps to consider extremes. A wait time of 0 minutes for the bus would clearly get Adam to school faster than his walking ever could.) Between (B) and (D), work out the algebra.

(B) w - 5 > 20 --> w > 25

Implication: If Adam had to wait for more than 25 minutes for a 5-minute bus ride to get to school, then the 20-minute walk would be faster.

(D) w + 5 > 20 --> w > 15

Implication: If Adam had to wait for more than 15 minutes for a 5-minute bus ride to get to school, then the 20-minute walk would be faster.

We can see that the latter option, (D), is the one we want, because in terms of total travel time, a 15-minute wait for the bus plus a 5-minute ride would be 20 minutes, as would the walk on its own, so 20 minutes is a pivotal point, and if Adam waits more than 15 minutes for the bus, he would be better off walking. It is not that (B) is untrue in the sense that it would still be faster to walk, but the wait need not be greater than 25 minutes. (This would be true if it took Adam 30 minutes to walk.) The answer is (D), and this one can be done and dusted with nothing more than mental math (addition/subtraction).

Method 2: Graph the four inequalities and essentially look for the one that traces the same logic as above. It must fit known information. Also, remember that Desmos uses x or y, rather than w. Since there is only one variable, it should not be too confusing. I will model y, since "less than = down" makes more sense intuitively to me.

The first graph models answer choices (A) through (C) because adding (D) would create an overlap that might prove confusing. It should be clear that the two less than answers, (A) and (C), would not work, since they show that a value of 0 would be valid (not to mention negative values), which cannot be true. (B) indicates a crucial value at y = 25, and, for the reason I gave earlier, that does not have to be true for the walk to take less time. 

Getting rid of (A) and (B) from earlier, you can add the inequality in (D) and deduce that the black shading fits the given situation, and (D) must be the answer.

Method 3: You could model the situation in your own way, perhaps using words, and then match to an answer. For instance,

walk (20 minutes) < bus (5 minutes) + wait (w)

20 < 5 + w (answer choice (D))

15 < w

This method could be just as fast as the first method above, but many people find it challenging to directly translate words into mathematical symbols in this manner, so I mention here just to prove a point.