M01-08

Question

Which of the following expressions has the greatest value?

A.  1^{999}  
B.  2^{300}  
C.  3^{200}  
D.  4^{100}  
E.  16^{50}

Bunuel · Accepted Answer

Official Solution:

Which of the following expressions has the greatest value?

A.  1^{999}  
B.  2^{300}  
C.  3^{200}  
D.  4^{100}  
E.  16^{50}

To compare the given expressions effectively, consider a common base or power. Observe that all expressions can be expressed as some power of 100:
 
A.  1^{999} . Taking 1 to any power is still 1. If the base were a different number, then we could approximate the answer by using a power of 1,000.
 
B.  2^{300} = 2^{3*100}=(2^3)^{100} = 8^{100} .
 
C.  3^{200} =3^{2*100} = (3^2)^{100} = 9^{100} .
 
D.  4^{100} = 4^{100} .
 
E.  16^{50} = (4^2)^{50} = 4^{100} .
 
Therefore, option C,  3^{200} , has the greatest value.

Answer: C

bb · Answer

You mean to make it easier for you to answer the question? Good try.... :lol:

P.S. On the GMAT if a question asks for the largest/smallest value, the answer choices do NOT follow a pattern.

iamgregmaicher · Answer

I think this is a  high-quality  question and I agree with explanation. Fantastic solution. So simple!

CircleOfLife · Answer

Since this is a PS question. shouldn't the answer choices be either ascending or descending?

PrayasT · Answer

I think this is a  high-quality  question and I agree with explanation. A good question with a little trick to follow.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

tbafupcf · Answer

How I solved it:

1^9^9^9  = 1

When looking at the remaining values, notice that all of the exponents share a GCF: 50. Raise each of these remaining values to the  \frac{1}{50}  power

You're now left with  2^6 ,  3^4 ,  4^2 , and  16^1 . From here, it's really simple to find each of these values and realize the largest value is  3^4  = 81.

ameerassan · Answer

I think this is a  high-quality  question and I agree with explanation.

maurizio_raina · Answer

I think this is a  high-quality  question and I agree with explanation.

sssdd1234 · Answer

I think this is a  high-quality  question and I agree with explanation.

satish_sahoo · Answer

I think this is a  high-quality  question and I agree with explanation.

AMan02 · Answer