Number properties

[sud21]

What is the smallest prime factor of 5^8 +10^ 6 -50^ 3 ?

2

3

5

7

11

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Hi sud21,

These types of questions are essentially about 're-organizing' the information (in this case, by factoring and using exponent rules).

We start with

5^8 + 10^6 - 50^3

We can leave the first term 'as is' and re-write the second and third 'terms'...

5^8 + (2^6)(5^6) - (2^3)(5^3)(5^3) =

5^8 + (2^6)(5^6) - (2^3)(5^6)

Next, we can factor 5^6 out of each term....

(5^6)[5^2 + 2^6 - 2^3]

Since the terms in the bracket are relatively small, we can calculate and simplify...

(5^6)[25 + 64 - 8]

(5^6)[81]

The 81 can be rewritten....

(5^6)[3^4]

Thus, the smallest prime factor is 3...

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

[Matt@VeritasPrep]

5� + 10� - 50³ =

5� * (5² + 2� - 2³) =

5� * (25 + 64 - 8) =

5� * 81 =

5� * 3�