Data Insights (DI) Butler 2024 A car mechanic observed that although there is no direct formula to calculate the resale value of a car, the value of car did depreceate by almost 5% of initial cost every year. The less the age of car, the more the resale value. Thus, he found the linear relationship to be y = 5x, where y is the depreceated value as % of the original price and x is the age of the car in years. Based on the information above, select for y the depreceated value as % of the original value and for x the the age of the car consistent with that depreceated value. Make only two selections, one for each.

The percentage can only be a multiple of 5, hence we only look at 40, 50 or 60. For the years, 1 or 2 is a very small number given the % options, hence years has to be 12. 12*5=60. Hence y= 60% and x= 12 years Posted from my mobile device

I like to find one "anchor" for 2PA questions where I can so that I can solve the problem sequentially, rather than popcorning around from number to number. This is a good problem to illustrate what I mean. Really, we're just being asked for possible values of y given some x. And we know that y is always going to be a multiple of 5 (i.e. always ending in a 0 or 5). The challenge is that it is on us to determine two values that satisfy y = 5x. First of all, let's eliminate 1, 2, and 12 as potential options for the value of y, since we're dealing with integer values for x (that will always produce a units digit of 0 or 5 for y). Next, let's move onto x. Since we know y = 5x, let's start by plugging in 1 for x; this results in y being 5. With x = 1 as our "anchor," we can see that there is no value of 5 for y, we move on and recognize x cannot be 1. Similarly, x cannot be 2, since there is no value of 10 for y. However, if x is 12, we see that y is 60, which is a possible option. This leaves an (x,y) pair of (12,60). The math here wasn't complicated, but it's really easy to get tangled in your own work on these 2PA questions. To get out of this, we set x as our anchor, plugged values, and arrived at the correct pairing.