Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 22 Jul 2019, 17:53

### GMAT Club Daily Prep

#### 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

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

# IF P = 9^{1/2} - 9^{1/3} - 9^{1/4}, then P is:

Author Message
TAGS:

### Hide Tags

Senior Manager
Status: Manager
Joined: 27 Oct 2018
Posts: 480
Location: Egypt
GPA: 3.67
WE: Pharmaceuticals (Health Care)
IF P = 9^{1/2} - 9^{1/3} - 9^{1/4}, then P is:  [#permalink]

### Show Tags

09 Jun 2019, 19:42
1
00:00

Difficulty:

65% (hard)

Question Stats:

52% (01:31) correct 48% (01:16) wrong based on 104 sessions

### HideShow timer Statistics

If $$P = 9^{1/2} - 9^{1/3} - 9^{1/4}$$, then P is:

A) Less than 0

B) Equal to 0

C) Between 0 and 2

D) Between 2 and 3

E) Greater than 3

_________________
Senior Manager
Joined: 22 Nov 2018
Posts: 491
Location: India
GMAT 1: 640 Q45 V35
GMAT 2: 660 Q48 V33
Re: IF P = 9^{1/2} - 9^{1/3} - 9^{1/4}, then P is:  [#permalink]

### Show Tags

09 Jun 2019, 22:04
2
1
I solved it by estimating the numbers like

9^1/2=3
9^1/3 must be greater 2 as 2*2*2 is 8.
9^1/4 is 1.7 as root 3 as it can be simplified.

Therefore 3-3.7 must be less than 0 IMO option A.

But would like to know the official solution (or a more elegant/template one)

Posted from my mobile device
_________________
Give +1 kudos if this answer helps..!!
Intern
Joined: 20 Aug 2017
Posts: 18
Re: IF P = 9^{1/2} - 9^{1/3} - 9^{1/4}, then P is:  [#permalink]

### Show Tags

15 Jun 2019, 04:36
something is wrong with the answer to this question.

using calculator:

9^1/2=3
-
9^1/3 = 1.12983
-
9^1/4 = 1.16652
=
0.70365,

Hence C.
Senior Manager
Joined: 22 Nov 2018
Posts: 491
Location: India
GMAT 1: 640 Q45 V35
GMAT 2: 660 Q48 V33
Re: IF P = 9^{1/2} - 9^{1/3} - 9^{1/4}, then P is:  [#permalink]

### Show Tags

15 Jun 2019, 04:55
omavsp wrote:
something is wrong with the answer to this question.

using calculator:

9^1/2=3
-
9^1/3 = 1.12983
-
9^1/4 = 1.16652
=
0.70365,

Hence C.

You must have made some error with the calculations cause 2*2*2=8 so 9^1/3 must be greater than 2 (2.08 to be precise, checked with calculator)
9^1/4=3^1/2=1.732. Root 3 is a standard term which is 1.7

Posted from my mobile device
_________________
Give +1 kudos if this answer helps..!!
Director
Joined: 19 Oct 2018
Posts: 712
Location: India
Re: IF P = 9^{1/2} - 9^{1/3} - 9^{1/4}, then P is:  [#permalink]

### Show Tags

15 Jun 2019, 05:10
$$P= 9^{1/4}[9^{1/4}-9^{1/12}-1]$$
$$1<9^{1/4}<2$$
$$9^{1/12}>1$$
Hence
$$[9^{1/4}-9^{1/12}-1]<0$$
or
$$P= 9^{1/4}[9^{1/4}-9^{1/12}-1]$$<0

Mahmoudfawzy83 wrote:
If $$P = 9^{1/2} - 9^{1/3} - 9^{1/4}$$, then P is:

A) Less than 0

B) Equal to 0

C) Between 0 and 2

D) Between 2 and 3

E) Greater than 3
Intern
Joined: 27 Feb 2019
Posts: 5
Concentration: General Management, Marketing
Re: IF P = 9^{1/2} - 9^{1/3} - 9^{1/4}, then P is:  [#permalink]

### Show Tags

16 Jun 2019, 10:17
nick1816 wrote:
$$P= 9^{1/4}[9^{1/4}-9^{1/12}-1]$$
$$1<9^{1/4}<2$$
$$9^{1/12}>1$$
Hence
$$[9^{1/4}-9^{1/12}-1]<0$$
or
$$P= 9^{1/4}[9^{1/4}-9^{1/12}-1]$$<0

Mahmoudfawzy83 wrote:
If $$P = 9^{1/2} - 9^{1/3} - 9^{1/4}$$, then P is:

A) Less than 0

B) Equal to 0

C) Between 0 and 2

D) Between 2 and 3

E) Greater than 3

Did not understand
Intern
Joined: 11 Feb 2019
Posts: 3
Re: IF P = 9^{1/2} - 9^{1/3} - 9^{1/4}, then P is:  [#permalink]

### Show Tags

16 Jun 2019, 12:08
9^1/2 = 3
9^ 1/4= 1.732
Let 9^1/3 will have min value as 1.732 ( assumption) , no need for exact value
together 9^1/3 and 9^1/4 is more than 3 ( Considering min value)
so 9^1/2 - ( 9^1/3 +9^1/4) = value will always be less than zero.
Intern
Joined: 27 Feb 2019
Posts: 5
Concentration: General Management, Marketing
IF P = 9^{1/2} - 9^{1/3} - 9^{1/4}, then P is:  [#permalink]

### Show Tags

16 Jun 2019, 18:50
msali1983 wrote:
9^1/2 = 3
9^ 1/4= 1.732
Let 9^1/3 will have min value as 1.732 ( assumption) , no need for exact value
together 9^1/3 and 9^1/4 is more than 3 ( Considering min value)
so 9^1/2 - ( 9^1/3 +9^1/4) = value will always be less than zero.

But then what if you dont know the value of 9^1/3 and 9^1/4. I dont think that you can rely on this approach
Intern
Joined: 28 Apr 2013
Posts: 8
Location: India
Re: IF P = 9^{1/2} - 9^{1/3} - 9^{1/4}, then P is:  [#permalink]

### Show Tags

16 Jun 2019, 19:02
I did it like this:
take 9^1/4 common ,
P= 9 ^1/4 *( 9^1/4 -9^1/12 - 1)
P= 9^1/4 *( 1.~ - 1.~ - 1)
P= 9^1/4* ( overall a negative )
P= negative
hence A.
Manager
Joined: 29 Nov 2018
Posts: 120
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.99
WE: Engineering (Computer Hardware)
Re: IF P = 9^{1/2} - 9^{1/3} - 9^{1/4}, then P is:  [#permalink]

### Show Tags

18 Jun 2019, 21:43
amitcpotnis wrote:
msali1983 wrote:
9^1/2 = 3
9^ 1/4= 1.732
Let 9^1/3 will have min value as 1.732 ( assumption) , no need for exact value
together 9^1/3 and 9^1/4 is more than 3 ( Considering min value)
so 9^1/2 - ( 9^1/3 +9^1/4) = value will always be less than zero.

But then what if you dont know the value of 9^1/3 and 9^1/4. I dont think that you can rely on this approach

Here is how i solved it:
Square root, cube root, fourth root are increasing function. for eg x^(1/2) greater the value of X greater is the value of square root, cube root, fourth root.
Lets use this info in this question.

square root of 9 is 3
Cube root of 8 is 2. 9 is greater than 8 so the cube root of 9 will be greater than 2 at-least.
Fourth root of 1 is 1. 9 is greater than 1. so the fourth root of 9 will be greater than 1.
Now lets combine the above three information.
You have 3 - (something greater than 2) - (something greater than 1)

hence the answer will be less than 0.

hope the explanation helped.

Please give kudos if you like the explanation.
Manager
Joined: 07 May 2018
Posts: 68
IF P = 9^{1/2} - 9^{1/3} - 9^{1/4}, then P is:  [#permalink]

### Show Tags

27 Jun 2019, 12:58
Mahmoudfawzy83 wrote:
If $$P = 9^{1/2} - 9^{1/3} - 9^{1/4}$$, then P is:

A) Less than 0

B) Equal to 0

C) Between 0 and 2

D) Between 2 and 3

E) Greater than 3

Hi All,

I don't seem to understand why there is so much confusion regarding this question:

$$P = 9^{1/2} - 9^{1/3} - 9^{1/4}$$,

then you should square both sides

$$P^2 = {9^{1/2}}^{2} - {9^{1/3}}^{2} - {9^{1/4}}^{2}$$,

$$P^2 = 9 - {9^{2}}^{1/3} - 9^{1/2}$$,

$$P^2 = 9 - 3 - 3$$

Therefore $$p = 3^{1/2}$$
IF P = 9^{1/2} - 9^{1/3} - 9^{1/4}, then P is:   [#permalink] 27 Jun 2019, 12:58
Display posts from previous: Sort by