MGMAT FDP QBank

[PFWinkler]

Hello – I found this problem rather challenging. I understand the substitution of an integer in for Y to test cases, given that we have 9 different positive single digits (ie: if Y is 2 we would violate the condition within the statement). I am unable to understand how to determine any possible value of Z in this scenario. The answer key is rather vague (in my view), and I don’t really understand the meaning of ‘place values’ or what role they serve within the computation.

a b c
d e f

x y z

If, in the addition problem above, a, b, c, d, e, f, x, y, and z each represent different positive single digits, what is the value of z ?
(1) 3a = f = 6y
(2) f – c = 3

Specifically: This. How can we just add zero’s to random variables? Why make 2 -> 200, and why make B -> 10B etc?
In order to determine the possible values for z in this scenario, we need to rewrite the problem using place values as follows:
200 + 10b + c + 100d + 10e + 6 = 100x + 10 + z

Source: MGMAT. FDP Question Bank. Question 9 of 25.

[RonPurewal]

imagine you have a friend from ancient rome, where numbers are not written like ours. (in the number XLVIII, the letters are not "digits" in any meaningful sense.)

how would you explain to this friend what "387" means? (at first, (s)he will probably think it means 3 + 8 + 7.)

if you can explain to your friend how "387" works, then you'll realize why certain variables in this problem are being multiplied by 10 and/or 100.

[PFWinkler]

Thank you Ron. That was very helpful…though, intuitively I was unable to see that at first!

Thanks man,
-PFWIII

[RonPurewal]

you're welcome.