GRE Quant Problem Help Needed

[user1501]

Hi, can someone help me explain how we figured out that B was the answer instead of D in this quant problem? I don’t get how we can come to the conclusion that 3^750 is larger than 5^400 by logic? And how do we know that 2^1000 is not larger than 3^750?

Thank you for your help!

[cylverixxx]

@user1501

And how do we know that 2^1000 is not larger than 3^750?

2^{1000}= \left(2^{20}\right)^{50} = \left(2^4\right)^{250}

3^{750}= \left(3^{15}\right)^{50} = \left(3^3\right)^{250}

Then it’s fairly obvious to see that 3^3 > 2^4 thus 3^{750} > 2^{1000}

@user1501

I don’t get how we can come to the conclusion that 3^750 is larger than 5^400 by logic?

Why don’t you compare 5^{400} to 2^{1000}. The template should be exactly how i compared the two quantities above.

You’ll realize that 2^{1000} > 5^{400} and thus transitively 3^{750} > 5^{400}