Last visit was: 23 Apr 2026, 01:50 It is currently 23 Apr 2026, 01:50
Home
Messages
Tests
Schools
Events
Close
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
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
805+ (Hard)|   Algebra|   Roots|      
User avatar
Noshad
User avatar
Joined: 02 Nov 2018
Last visit: 30 Mar 2026
Posts: 207
Own Kudos:
1,029
 [22]
Given Kudos: 110
Status:Manager
Location: Bangladesh
Posts: 207
Kudos: 1,029
 [22]
For how many real values of x is p √(120 − √x) an integer? Updated on: 19 Mar 2019, 06:27
Originally posted by Noshad on 14 Mar 2019, 06:09.
Last edited by Noshad on 19 Mar 2019, 06:27, edited 1 time in total.
3
Kudos
Add Kudos
19
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

42% (02:00) correct 58% (02:17) wrong based on 282 sessions

History

Date
Time
Result
Not Attempted Yet
For how many real values of x is \(\sqrt{120 − √ x}\) an integer?

(A) 3

(B) 6

(C) 9

(D) 10

(E) 11
ShowHide Answer
Official Answer
E
avatar
razaaquib18
avatar
Joined: 19 Oct 2018
Last visit: 15 Mar 2021
Posts: 7
Own Kudos:
14
 [1]
Given Kudos: 30
Location: India
Concentration: Finance, Economics
Schools: IIMA PGPX"20 (D) XLRI"20
GPA: 4
WE:Human Resources (Consulting)
Products:
My Reviews
Schools: IIMA PGPX"20 (D) XLRI"20
Posts: 7
Kudos: 14
 [1]
For how many real values of x is p √(120 − √x) an integer? 19 Mar 2019, 04:34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
How to solve this? Me really confused about P.
User avatar
shuvodip04
User avatar
Joined: 05 Oct 2017
Last visit: 03 Mar 2022
Posts: 86
Own Kudos:
152
 [3]
Given Kudos: 103
Location: India
Concentration: Finance, International Business
Schools: IIMB IIMA ISB'22 (S) IIMA PGPX'22 (I)
GMAT 1: 660 Q48 V33
GMAT 2: 700 Q49 V35 (Online)
GPA: 4
WE:Analyst (Energy)
Schools: IIMB IIMA ISB'22 (S) IIMA PGPX'22 (I)
GMAT 2: 700 Q49 V35 (Online)
Posts: 86
Kudos: 152
 [3]
For how many real values of x is p √(120 − √x) an integer? 19 Mar 2019, 04:49
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Noshad
For how many real values of x is p \(\sqrt{120 − √ x}\) an integer?

(A) 3

(B) 6

(C) 9

(D) 10

(E) 11
Show more

Bunuel

is the question p=\(\sqrt{120 − √ x}\). Or it is correct as it is.I feel there is missing "=" sign.

My approach

For \(\sqrt{120 − √ x}\) to be an integer. The 120-√x must be a perfect square. Less than 120

So the value of the expression can be 100,81,64,49,36,25,16,9,4,1,0 total 11 values. For each of which there will be a corresponding value of x

x will have values √400,\(√39^2\),\(√56^2\) ..... \(√120^2\) . 11 values .Hence ans (E)
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 22 Apr 2026
Posts: 8,627
Own Kudos:
5,190
 [1]
Given Kudos: 243
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GMAT Focus 2: 645 Q83 V82 DI81
GPA: 4
WE:Marketing (Energy)
Products:
GMAT Club Tests Forum Quiz
GMAT Focus 2: 645 Q83 V82 DI81
Posts: 8,627
Kudos: 5,190
 [1]
For how many real values of x is p √(120 − √x) an integer? 19 Mar 2019, 11:38
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Noshad
For how many real values of x is \(\sqrt{120 − √ x}\) an integer?

(A) 3

(B) 6

(C) 9

(D) 10

(E) 11
Show more


total square values upto 120 ; 11 viz. 0,1,4,9,16,25,36,49,64,81,100
IMO E ; 11
User avatar
m1033512
User avatar
Joined: 25 Feb 2019
Last visit: 27 Oct 2019
Posts: 276
Own Kudos:
237
 [1]
Given Kudos: 32
Products:
My Reviews
Posts: 276
Kudos: 237
 [1]
For how many real values of x is p √(120 − √x) an integer? 08 Apr 2019, 08:44
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
but at x = 0 , this is not an integer


Am I missing something here ?

Posted from my mobile device
User avatar
mnav
User avatar
Joined: 22 May 2018
Last visit: 22 Aug 2019
Posts: 24
Own Kudos:
17
 [2]
Given Kudos: 46
WE:Project Management (Energy)
Posts: 24
Kudos: 17
 [2]
For how many real values of x is p √(120 − √x) an integer? 08 Apr 2019, 09:50
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
IMO D
At x=0, sqrt(120) is not an integer, so we have only 10 real values of X for P to be an integer

Sent from my Lenovo X3a40 using GMAT Club Forum mobile app
avatar
Dvaishnav
avatar
Joined: 25 Sep 2019
Last visit: 05 Aug 2021
Posts: 39
Own Kudos:
31
Given Kudos: 84
GMAT 1: 730 Q50 V40
GMAT 1: 730 Q50 V40
Posts: 39
Kudos: 31
For how many real values of x is p √(120 − √x) an integer? 05 Dec 2020, 09:37
Kudos
Add Kudos
Bookmarks
Bookmark this Post
shuvodip04
Noshad
For how many real values of x is p \(\sqrt{120 − √ x}\) an integer?

(A) 3

(B) 6

(C) 9

(D) 10

(E) 11

Bunuel

is the question p=\(\sqrt{120 − √ x}\). Or it is correct as it is.I feel there is missing "=" sign.

My approach

For \(\sqrt{120 − √ x}\) to be an integer. The 120-√x must be a perfect square. Less than 120

So the value of the expression can be 100,81,64,49,36,25,16,9,4,1,0 total 11 values. For each of which there will be a corresponding value of x

x will have values √400,\(√39^2\),\(√56^2\) ..... \(√120^2\) . 11 values .Hence ans (E)
Show more

I also selected E. However, the question only says that x has to be real, not positive. Hence, x can also be (-39)^2, (-56)^2 ... Hence, we will have 22 possible values. Isn't it?
User avatar
Banmeet
User avatar
Joined: 11 May 2024
Last visit: 16 Dec 2024
Posts: 6
Own Kudos:
5
Given Kudos: 123
Posts: 6
Kudos: 5
For how many real values of x is p √(120 − √x) an integer? 11 Jul 2024, 02:24
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi Guys,

 
At first, I also thought that there are only 10 values of X,
However, If we examine the the equation closely, there can be more possibilities. For eg, when X=-1

Which will then be, √120 -(√-1)= √120+1=√121= 11, an integer.

There are many such numbers that will satisfy the equation for example -2401, which √-2401= -49 which would result in √120+49=√169 = 13.

So all the possibilities are, -1, 1, 2, 3, 4, 5,6 ,7,8 9, 10, -2401 and there could be more.
But since in options 11 is the highest, So we will have to go with that.

Answer choice: E­
Moderators:
Bunuel
Math Expert
109763 posts
Krunaal
Tuck School Moderator
853 posts