hard calculation....

Expert replies

Previous Topic Next Topic

willbeatthegmat: Senior | Next Rank: 100 Posts; Posts: 71; Joined: Sat Sep 20, 2008 5:48 am; Thanked: 5 times

by willbeatthegmat » Wed Feb 04, 2009 5:57 am

Q-List the following in increasing order from left to right:
2^1/3, 5^1/6, 10^1/10, 30^1/15

Like this post

Source: Beat The GMAT — Problem Solving | Wed Feb 04, 2009 5:57 am

jail: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Tue Jan 27, 2009 6:37 am; Thanked: 3 times

by jail » Wed Feb 04, 2009 7:18 am

The order is:

10^(1/10) ; 2^(1/3) ; 5^(1/6) ; 30^(1/5)

The easiest way to solve this is to find the lcm between 10 3 6 5 = 30

Then apply 30 as power for all the numbers:

10^(30/10) ; 2^(30/3) ; 5^(30/6) ; 30^(30/5) =

10^(3) ; 2^(10) ; 5^(5) ; 30^(6) =

Now we can check easily that

10^(3) < 2^(10) < 5^(5) ; 30^(6)

Like this post

willbeatthegmat: Senior | Next Rank: 100 Posts; Posts: 71; Joined: Sat Sep 20, 2008 5:48 am; Thanked: 5 times

by willbeatthegmat » Thu Feb 05, 2009 2:52 am

that's a wrong answer jail...

OA is 30^1/15,10^1/10, 2^1/3, 5^1/6

wher have all the gurus gone??

Like this post

maihuna: Legendary Member; Posts: 1578; Joined: Sun Dec 28, 2008 1:49 amFollowed by: 9 members; Thanked: 82 times; GMAT Score:720

by maihuna » Thu Feb 05, 2009 3:54 am

I think approach in jail(r u in oval's) is fine.

after multiplying with 30 we get:

2x10, 5x5 10x3 30x2

1024 3125 1000 900

so u can rearrang it like:

30^2, 10^3 2^10 5^5

Like this post

GMAT/MBA Expert

Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Thu Feb 05, 2009 10:06 am

jail wrote:The order is:

10^(1/10) ; 2^(1/3) ; 5^(1/6) ; 30^(1/5)

jail's approach is very good here, and it was just a small typo that made the answer incorrect. jail must have miscopied the question - the exponent on the 30 is 1/15, not 1/5, in the original question. Otherwise, the math is perfect. maihuna's post above fixes that error.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

Like this post

sjd00d: Senior | Next Rank: 100 Posts; Posts: 97; Joined: Mon Jan 05, 2009 11:04 pm; Thanked: 2 times

by sjd00d » Fri Feb 06, 2009 5:41 pm

Ian Stewart wrote:
jail wrote:The order is:

10^(1/10) ; 2^(1/3) ; 5^(1/6) ; 30^(1/5)
jail's approach is very good here, and it was just a small typo that made the answer incorrect. jail must have miscopied the question - the exponent on the 30 is 1/15, not 1/5, in the original question. Otherwise, the math is perfect. maihuna's post above fixes that error.

Is it really the right way to solve this? You are multiplying each of the numbers by a different number in order to restructure the powers, is that ok?

I mean from 2^1/3 -> 2^10, you are multiplying 2^29/3 to 2^1/3
from 5^1/6 -> 5^30/3, you are multiplying 5^59/6

now, 5^59/6 != 2^29/3, I don't think you can do that.

Like this post

sureshbala: Master | Next Rank: 500 Posts; Posts: 319; Joined: Wed Feb 04, 2009 10:32 amFollowed by: 9 members; Location: Delhi; Thanked: 84 times

by sureshbala » Fri Feb 06, 2009 10:17 pm

Hi, there is nothing wrong with jail's aprroach...

In order to solve questions like these quickly, all we have to do is take the LCM of the denominators of powers.

In this case it is LCM (3,6,10,15) = 30.

Let's look at the logic here to avoid the confusion.

2^1/3 = 2^10/30
5^1/6 = 5^5/30
10^1/10 = 10^3/30
30^1/15 = 30^2/30

Now if we observe the above numbers the denominators of the powers are all same which is 30.

So you now eliminate the denominator and quickly conclude the ascending order of these numbers.

Thus we consider 2^10, 5^5, 10^3 and 30^2 instead of the original numbers.

Hence the ascending order is 30^2, 10^3, 2^10 and 5^5

i.e 30^1/15 < 10^1/10 < 2^1/3 < 5^1/6

Like this post

jail: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Tue Jan 27, 2009 6:37 am; Thanked: 3 times

by jail » Sat Feb 07, 2009 9:43 am

lol, sorry I just miscopied the statement...(that teaches me that I cannot solve this problems in my work time).

Anyway the procedure to solve this kind of problems is good.

My regards to all the members in this post.

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review