Math Help - trick to solve?

Hey guys,

I'm studying for the gre and am wondering if there's any trick to solving a problem like this w/o doing the actual math:

Which is greater:

210,000 X 95,250

or

210,250 X 95,000


What is the general trick?

Thanks!

Hmm. Generally, I'd say that you're looking at an extremum problem, essentially. You're looking at the product of two numbers, x * y, such that x + y = const. It's like maximizing the area of a rectangle given that the perimeter is constant. What's your gut instinct?

well if you imagine 210,000 x 95250 as 210000 x (95000+250) = 210000 x 95000 + 210000 x 250 and
210250 x 95000 as 95000 x (210000+250) = 210000 x 95000 + 95000 x 250 the answer should become obvious?

Hello, sfspitfire23!

Which is greater: .[1] 210,000 × 95,250 .or .[2] 210,250 × 95,000 ?

We have:

[1] (210,000) × (95,000 + 250) . and .[2] (210,000 + 250) × (95,000)


Let: .x = 210,000, .y = 95,000


Then we have: .x·(y+250) .[?] .(x+250)·y

. . . . . . . . . . . xy + 250x .[?] .xy + 250y

. . . . . . . . . . . . . . .250x .[?] .250y

. . . . . . . . . . . . . . . . . x .[?] .y


Since x > y, then: .[1] .> .[2]