Same as what cbenk did, just a little more elaboration. Division is probably the easiest way I can think of solving this, afterall we are dealing with primes! Plus the question provides you with a hint that of the four prime numbers, two are common to each of the products represented.
Let the prime numbers be: A, B, C, and D. From the question we know,
A*B*C=4,199...(i)
B*C*D=7,429...(ii)
Dividing (i) by (ii),
[(A*B*C)/(B*C*D)]=[4,199/7,429]
[A/D]=[4,199/7,429]= 13/23
Since they are primes, you can safely state that the smallest number is 13 and the largest is 23.
Note:
4,199=13*17*19
7,429=13*17*19*23
Doesn't take that long to figure out the factorization, I started with 7, and found a factor when I got to 13. Once I figured this out, the rest of the math is really not neessary since 13 was the first prime factor (lowest as well) and the question tells you that the numbers are a product of consecutive primes. Naturally, feel free to double check on the test if you have time but you should also have some level of confidence that if your starting logic is correct then there really is no need to do all the math. So, once you figure out that 4,199=13*_*_, so can safely assume that the blanks are 17 and 19. Same thing with 7,429 since the first number of the product is the same as for 4,199. Hope this makes sense.
