What is the Smallest Prime Factor of 5^8+10^6–50^3? GMAT Problem Solving

Question: What is the smallest prime factor of \(5^8+10^6-50^3\)?

1. 2
2. 3
3. 5
4. 7
5. 11

“What is the smallest prime factor of \(5^8+10^6-50^3\)?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer:

Approach Solution 1:

3 is the smallest prime factor

\(5^8+10^6-50^3=5^6*81\)

And since 97 is a prime number, 3 is the smallest prime.

Correct option: B

Approach Solution 2:

\(5^8\)has 5 as a prime factor

\(10^6\)has 2 and 5 as a prime factor

\(50^3\)has 2 and 5 as a prime factor

Thus only 2 and 5 are possible answers. The answer is 2 if the solution is even and 5 if the solution is odd.

Eliminate BDE.

\(5^8\)is odd because products of odd integers are always odd

\(10^6\)and \(50^3\) are even because products of even integers are always even

Odd + Even – Even = Odd

Correct option: C

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