Test Prep2

moneyman wrote:M=(4)^1/2+(4)1/3+(4)1/2 what is the value of M??

Greater than 3
Equal to 3
Between 3 and 4
Equal to 4
Greater than 4

The answer is E

Look, M=(4)^1/2+(4)1/3+(4)1/2
or M = 2 + 4/3 + 2 = 4 + 4/3
So M > 4
So go for E.

camitava wrote:

moneyman wrote:M=(4)^1/2+(4)1/3+(4)1/2 what is the value of M??

Greater than 3
Equal to 3
Between 3 and 4
Equal to 4
Greater than 4

The answer is E

Look, M=(4)^1/2+(4)1/3+(4)1/2
or M = 2 + 4/3 + 2 = 4 + 4/3
So M > 4
So go for E.

Sorry to disagree with you Amitava, here is my dig at it :

M=(4)^1/2+(4)1/3+(4)1/2

Now, (4)^1/2 = +2 or -2

if it is +2 then your solution is correct,

if it is -2, then

M= 4/3 = 1.33

this choice is not provided. Thus the question is ambiguous

Hey musicdaemon, what a catch man! Good catch, indeed! But I would like to say here that generally this type of ambiguous Qs are not asked in GMAT. I agree I missed the issue mentioned by u ...

Hey guys,

Just a quick comment. Original question was like, see the link, please.

https://www.beatthegmat.com/gmatprep-ps-t9183.html#36723

smushkas wrote:Hey guys,

Just a quick comment. Original question was like, see the link, please.

https://www.beatthegmat.com/gmatprep-ps-t9183.html#36723

Smushkas,

even then squrt(4)= +2 or -2
and the answer choices are ambiguous. Isn't it?

musicdaemon wrote:

smushkas wrote:Hey guys,

Just a quick comment. Original question was like, see the link, please.

https://www.beatthegmat.com/gmatprep-ps-t9183.html#36723

Smushkas,

even then squrt(4)= +2 or -2
and the answer choices are ambiguous. Isn't it?

Actually musicdaemon, sqrt(x) is always positive and it can not be negative.

Amitava,
I guess My basics in quant are still in place.

Sqrt of any number will have two values one -ve and one +ve

apply the reverse logic:

(-2)^2 = 4 & (2)^2 =4

Take sqrt on both sides now,

-2=sqrt(4) & 2 = sqrt(4)

Thus, sqrt(4) = +2 and -2


Prove me wrong!!!

musicdaemon wrote:Amitava,
I guess My basics in quant are still in place.

Sqrt of any number will have two values one -ve and one +ve

apply the reverse logic:

(-2)^2 = 4 & (2)^2 =4

Take sqrt on both sides now,

-2=sqrt(4) & 2 = sqrt(4)

Thus, sqrt(4) = +2 and -2


Prove me wrong!!!

Musicdaemon,
I agree with ur point partially. I said sqrt(x) should always be positive. But \/-x can be both positive and negative. Got me, MusicDaemon? If you search this PS forum, u will find that this issue has already been discussed. And still if u r having any doubt, u can ask Stuart to help.

Amitava,
I don't have an iota of doubt on this.

The answer choices for this question are ambiguous.

Actually Amitava is right, the sqrt of a number until unless mentioned should be considered positive. While you are right that any integer has 2 roots, we consider only the positive root (the principal root) for solving problems such as these. So Amitava's answer is right i.e m>4. There is no ambiguity in the answer choices.

Do a google search on "principal square root" and you will find articles on why this is so.

Regards

FIrst, all you guys are great at catching such subtle details. I am a bit confused now, I see Mr. Daemon's point but see moderators point also. For the sake of the exam, are we considering all roots positive? I believe this is what is taught in the manhattan gmat book also.

AS for the original question, I think the original poster is hurting from understanding that all fractional exponents are treated as roots. I had to make a flash card on this to commit it to memory. Recommendations to you also.

Enginpasa1 wrote:FIrst, all you guys are great at catching such subtle details. I am a bit confused now, I see Mr. Daemon's point but see moderators point also. For the sake of the exam, are we considering all roots positive? I believe this is what is taught in the manhattan gmat book also.

AS for the original question, I think the original poster is hurting from understanding that all fractional exponents are treated as roots. I had to make a flash card on this to commit it to memory. Recommendations to you also.

It is not just for GMAT, but for math in general we consider only the principal roots that is the positive roots of any real number. There are many reasons for this e.g. use of square roots in the Pythagoras theorem.

Regards

Gabriel,
For discreet values given as choices, of simple functions, we can use the principle sq root. But, when the range of values is required then you may have to use both the values. And that is what is the case in the given problem.

i guess we have to get it by heart - to use +ve root for GMAT unless required specifically.

Yes by convention, sqrt(x) is always positive. Because of this, the answer must be greater than 4.