D01-05

Question

Which of the following expressions has the greatest value?

A.  999^{12}  
B.  10^{30}  
C.  777^{10}  
D.  (-20)^{24}  
E.  (\sqrt{15})^{40}

Bunuel · Accepted Answer

Official Solution:

Which of the following expressions has the greatest value?

A.  999^{12}  
B.  10^{30}  
C.  777^{10}  
D.  (-20)^{24}  
E.  (\sqrt{15})^{40}

Let's compare the options:
 
Option C ( 777^{10} ) is less than Option B ( 10^{30}=1000^{10} ), because  777 < 1000 .
 
Option E ( (\sqrt{15})^{40} =15^{20} ) is less than Option D ( 20^{24} ), as both the base and the exponent in E are smaller than those in D.
 
Option B ( 10^{30}=(10^5)^6 ) is less than Option D ( 20^{24}=(20^4)^6=(16*10^4)^6 ), because  10^5 < 16*10^4 . 
 
Lastly, Option D ( 400^{12} ) is less than Option A ( 999^{12} ), because  400 < 999 .

Answer: A

Bunuel · Answer

(a^m)^n=a^{mn} 10^{30} = 10^{3*10}=(10^3)^{10}=1000^{10} . Theory on Exponents: math-number-theory-88376.html Tips on Exponents: exponents-and-roots-on-the-gmat-tips-and-hints-174993.html All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39 All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60 Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

redfield · Answer

I promise I'm typically quite good with the exponent rules but for some reason I can't wrap my head around this one; can someone please break the rule out on this one as to why it's to the 10th?

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.

BottomJee · Answer

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

hbelden97 · Answer

I don't get why 10^30 is not the same as 1,000^28? You have 30 tens, you use one (10*10=100) 100^29, then you use another (100*10= 1,000) 1,000^28

Bunuel · Answer

That's not how exponentiation works.

10^{30} = 10^{2*15} = (10^2)^{15}=100^{15} , which does not equal to  100^{29} .

10^{30} = 10^{3*10} = (10^3)^{10}=1,000^{10} , which does not equal to  1,000^{28} .

8. Exponents and Roots of Numbers 
     Theory   
 Exponents and Roots on the GMAT: Tips and hints 
 Cyclicity and the remainders on the GMAT 
     Questions   
 Units digits, exponents, remainders problems 
  Tough and tricky DS exponents and roots questions with detailed solutions 
 Tough and tricky PS exponents and roots questions with detailed solutions  
 Exponents DS Questions 
 Exponents PS Questions 
 Roots DS Questions 
 Roots PS Questions

Check below for more:
 ALL YOU NEED FOR QUANT ! ! ! 
 Ultimate GMAT Quantitative Megathread

Hope it helps.

iwant605 · Answer

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

wwcd · Answer

I approached this by rounding off quite a bit. Is this okay or will this land me in trouble with the exam on similar questions?

A :  999^{12} = 10^{36}

B :  10^{30}

C :  777^{10} = 7^{10} * 10^{20}

D :  (-20)^{24} = 1024 * 1024 * 16 * 10^{24} = 10^{30} * 16

E :  15^{20}

BelisariusTirto · Answer

How did you compute sqrt(15)^40 to sqrt(15)^20 ?

Bunuel · Answer

(\sqrt{15})^{40} =

=(15^{\frac{1}{2}})^{40} =

=15^{\frac{1}{2}*40} =

=15^{20}

8. Exponents and Roots of Numbers 
 
    Theory    
 
 Exponents and Roots on the GMAT: Tips and hints 
 Cyclicity and the remainders on the GMAT 
 
    Questions    
 
 Units digits, exponents, remainders problems 
 Tough and tricky DS exponents and roots questions with detailed solutions 
 Tough and tricky PS exponents and roots questions with detailed solutions 
 Exponents PS Questions 
 Roots DS Questions 
 Roots PS Questions

Check below for more:
 ALL YOU NEED FOR QUANT ! ! ! 
 Ultimate GMAT Quantitative Megathread

Hope this helps.

BelisariusTirto · Answer

Thank you for taking the time to get back to me. I will need to do some reviewing it seems.

Wingo_17 · Answer

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

saynchalk · Answer

I like the solution - it’s helpful.

saynchalk · Answer

Need help with expanding option D please

Bunuel · Answer

For Option D: (-20)^24, the negative sign disappears because 24 is an even exponent. So (-20)^24 = 20^24 = (20^2)^12 = 400^12. That's it!

Karan0721 · Answer

I like the solution - it’s helpful.

ayushm23 · Answer

This is a great question that’s helpful for learning.

yrao1000 · Answer

I like the solution - it’s helpful.

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