Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Re: How many positive integers less than 1000 have a 5th root? [#permalink]
11 Apr 2018, 03:01

1) We need to find the numbers with 5th root and are less than or equal to 1000. So let's say the number is x. It can be written as n^5 where n is a natural number. So, n^5 <= 1000 gives n=1, 2, 3 as 1^5 = 5, 2^5 = 32, 3^5 = 243. But 4^5 = 1024 which is greater than 1000.

Hence the answer is 3. The numbers are 1, 32 and 243

2) We need to find the numbers with square root and cube root and are less than or equal to 1000. Again let's say the number is x. x can be written as: ((n)^2)^3. Square of any natural number and then the cube of that number, since we have to take a cube root and a square root. So, it becomes effectively n^6 <= 1000. We can now solve it. The total number of such numbers is 3 again. 1^6 = 1 2^6 = 64 3^6 = 729

greprepclubot

Re: How many positive integers less than 1000 have a 5th root?
[#permalink]
11 Apr 2018, 03:01