This strikes me as a CAT question, not a GMAT one, but here's a nifty method:
A number that gives a remainder of r when divided by d is of the form dk + r, where k is an integer. (For example, 17 divided by 5 is 3 with a remainder of 2, so 17 is of the form 5*3 + 2.)
Let's start with that property.
Since we really have one number, we can set the successive division by working back to front: we start with the final division (the number is of the form 7k + 2), then plug that into the second to last division (that number is 3*(7k+2) + 1).
(If this is abstract, illustrate it with real numbers. 125 divided by 4 is 31, with a remainder of 1, so I can say 125 = 4*31 + 1. 31 divided by 6 is 5 with a remainder of 1, so 31 = 5*6 + 1. To recreate the number, I take the final equation and plug it into the earlier one: 125 = 4*(5*6+1)+1.)
Putting it all together, our equation is
Final division: 7k + 2
Second to last division: 3(7k + 2) + 1, or 21k + 7
Third to last division: 5(21k + 7) + 4, or 105k + 39
First division: 4(105k + 39) + 3, or 420k + 159
Setting k = 0 to minimize the number, we get 159. Too cool!
Rich's method (testing the answer choices) also works, and is a practical solution on test day.
