Hi,
I encountered this surds related problem while writing the Test 1 of GMATPrep. During the test I got the answer by process of elimination but I'm sure there is a better and more accurate way of solving this. Here is the problem:
If M = (4^1/2) + (4^1/3) + (4^1/4) then the value of M is
a) less than 3
b) equal to 3
c) between 3 and 4
d) equal to 4
e) greater than 4
OA: e
Many thanks in advance.
-Anirban
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
GMATPrep Test 1 - Surds problem
This topic has expert replies
-
anirban_lax
- Junior | Next Rank: 30 Posts
- Posts: 27
- Joined: Tue Nov 10, 2009 2:29 pm
- Thanked: 1 times
GMAT/MBA Expert
-
Rahul@gurome
- GMAT Instructor
- Posts: 1179
- Joined: Sun Apr 11, 2010 9:07 pm
- Location: Milpitas, CA
- Thanked: 447 times
- Followed by:88 members
If M = (4^1/2) + (4^1/3) + (4^1/4) then the value of M is
a) less than 3
b) equal to 3
c) between 3 and 4
d) equal to 4
e) greater than 4
M = (4^1/2) + (4^1/3) + (4^1/4)
4^1/2 = √4 = 2
4^1/4 = (2^2)^1/4 = 2^(1/2) = √2 = 1.414
4^1/3 lies between 1 and 2.
So, (4^1/2) + (4^1/3) + (4^1/4) = 2 + value between 1 and 2 + 1.414 = 3.414 + value greater than 1, which means M will be a value greater than 4.
The correct answer is [spoiler](E)[/spoiler].
a) less than 3
b) equal to 3
c) between 3 and 4
d) equal to 4
e) greater than 4
M = (4^1/2) + (4^1/3) + (4^1/4)
4^1/2 = √4 = 2
4^1/4 = (2^2)^1/4 = 2^(1/2) = √2 = 1.414
4^1/3 lies between 1 and 2.
So, (4^1/2) + (4^1/3) + (4^1/4) = 2 + value between 1 and 2 + 1.414 = 3.414 + value greater than 1, which means M will be a value greater than 4.
The correct answer is [spoiler](E)[/spoiler].
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
-
anirban_lax
- Junior | Next Rank: 30 Posts
- Posts: 27
- Joined: Tue Nov 10, 2009 2:29 pm
- Thanked: 1 times
Thanks Rahul!
That's an elegant solution!
I was wondering if there is a way to solve this if I do not know the value of 2^1/3, or for that matter if we have a number whose cube root is not well known.
That's an elegant solution!
I was wondering if there is a way to solve this if I do not know the value of 2^1/3, or for that matter if we have a number whose cube root is not well known.
GMAT/MBA Expert
-
Rahul@gurome
- GMAT Instructor
- Posts: 1179
- Joined: Sun Apr 11, 2010 9:07 pm
- Location: Milpitas, CA
- Thanked: 447 times
- Followed by:88 members
We don't need to find the exact value if we don't know the cube root of a number. Just find the approximate value in that case as done in this question.anirban_lax wrote:Thanks Rahul!
That's an elegant solution!
I was wondering if there is a way to solve this if I do not know the value of 2^1/3, or for that matter if we have a number whose cube root is not well known.
1^(1/3) = 1 and 8^(1/3) = 2. So, definitely 2^(1/3) will have a value between 1 and 2.
Does that help?
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
-
anirban_lax
- Junior | Next Rank: 30 Posts
- Posts: 27
- Joined: Tue Nov 10, 2009 2:29 pm
- Thanked: 1 times
Ah! I see it now! Awesome!
Can't help but click the Thanks button twice for your 2 replies on this post
Thanks a lot!
Can't help but click the Thanks button twice for your 2 replies on this post
Thanks a lot!GMAT/MBA Expert
-
Rahul@gurome
- GMAT Instructor
- Posts: 1179
- Joined: Sun Apr 11, 2010 9:07 pm
- Location: Milpitas, CA
- Thanked: 447 times
- Followed by:88 members
U r welcome!anirban_lax wrote:Ah! I see it now! Awesome!
Can't help but click the Thanks button twice for your 2 replies on this post
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
