Re: A car mechanic observed that although there is no direct formula to c
[#permalink]
13 Feb 2024, 12:03
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.