Number properties - tricky high-level question

[adgir]

Number 543xy2 is divisible by 42.

Find x and y, and write out how you found them (no calculator allowed).

[chieftang]

Well the obvious solution would be to test for divisibility by 7,3,2. Unfortunately, though, the test for 7 is not so straight forward. Is it doable? Yes. But I don't suspect this is a realistic GMAT question.

Incidentally, xy = 31.

Oh and interestingly, here is the original problem source: https://www.oei.es/oim/revistaoim/numero ... sjov18.pdf originally published around 2005.

It would appear as though "800score" has "borrowed" questions from various sources. Hmmm.

[ronnie1985]

x+y = 3*n-14
Putting n = 5, x+y = 1. If any one of x and y is 0, the other is 1, and none of 543012 or 543102 is divisible by 7. Hence try x+y = 4, then 543312 is divisible.
Trial and error method, not direct method.

[chieftang]

x+y = 3*n-14
Putting n = 5, x+y = 1. If any one of x and y is 0, the other is 1, and none of 543012 or 543102 is divisible by 7. Hence try x+y = 4, then 543312 is divisible.
Trial and error method, not direct method.

Yes it worked out early in this case, but x+y could actually be 1,4,7,10,13,16 before you do the tedious div7 check. So that's a lot of trial and error potential!! Imagine if the actual answer had been xy = 79 !