(N-1) = (N-2) - 1 is an equation with a unique solution?

[jimmy.steve88]

The answer explanation to a GMAT Prep question reads as follows:

"... combining 1/5(N-1) = P - 1 and 1/4(N-2) = P, it follows that (N-1) = (N-2) - 1. This is a linear equation in N and can be solved for a unique value of N."

First of all, when I combine the first two equations, I get 13/10 = (1/20)N, which gives me N = 26. How are they getting the equation (N-1) = (N-2) - 1, and how is that a linear equation with a unique solution? Isolating N, we get 0 = -2, which is false.

It's been a long day, and perhaps I am missing something obvious. But right now I am quite perplexed by this.

Thanks

[800_or_bust]

The answer explanation to a GMAT Prep question reads as follows:

"... combining 1/5(N-1) = P - 1 and 1/4(N-2) = P, it follows that (N-1) = (N-2) - 1. This is a linear equation in N and can be solved for a unique value of N."

First of all, when I combine the first two equations, I get 13/10 = (1/20)N, which gives me N = 26. How are they getting the equation (N-1) = (N-2) - 1, and how is that a linear equation with a unique solution? Isolating N, we get 0 = -2, which is false.

It's been a long day, and perhaps I am missing something obvious. But right now I am quite perplexed by this.

Thanks

You're correct about the first two equations implying that N = 26. It looks they meant to say 1/5(N-1) = 1/4(N-2) - 1, but forgot to include both fractions. Was this from the official GMAT Prep software?

[jimmy.steve88]

You're correct about the first two equations implying that N = 26. It looks they meant to say 1/5(N-1) = 1/4(N-2) - 1, but forgot to include both fractions. Was this from the official GMAT Prep software?

Yes, this was from the official GMAT Prep software. I think you're right; I'm noticing a number of typographical errors in their software (e.g. 3^3 and 5^3 are written as 33 and 53, etc.). It can be a bit frustrating...

[Matt@VeritasPrep]

I think they mean

(n - 1)/5 = p - 1
(n - 2)/4 = p

That would give us the unique solution n = 26, p = 6.