Last visit was: 15 Dec 2024, 04:28 It is currently 15 Dec 2024, 04:28
Home
GMAT
Messages
Tests
Schools
Reviews
Social
Chat
My Profile
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
 1   2   
User avatar
souvik101990
User avatar
Joined: 19 Mar 2012
Last visit: 09 Nov 2024
Posts: 4,327
Own Kudos:
52,172
 []
Given Kudos: 2,326
Location: United States (WA)
Concentration: Leadership, General Management
Schools: Ross '20 (M)
GMAT 1: 760 Q50 V42
GMAT 2: 740 Q49 V42 (Online)
GMAT 3: 760 Q50 V42 (Online)
GPA: 3.8
WE:Marketing (Non-Profit and Government)
Products:
My Reviews
Expert reply
Schools: Ross '20 (M)
GMAT 3: 760 Q50 V42 (Online)
Posts: 4,327
Kudos: 52,172
 []
Find the number of factors of the number p 21 Apr 2018, 00:05
Kudos
Add Kudos
5
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:

28% (02:18) correct 72% (02:06) wrong based on 168 sessions

History

Date
Time
Result
Not Attempted Yet

GST Week 2 Day 5 e-GMAT Question 5


Give your best shot at writing a top notch application and you will have the chance to win GMAT Club tests daily and e-GMAT Quant Online Course . See the GMAT Spring Training Thread for all details


Find the number of factors of the number p, if p is a positive integer less than 100.

1. The number p has odd number of factors.

2. The number p can be expressed as \(x^{2}\), \(y^{3}\) or \(z^{6}\) where x, y, and z are positive integers.

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D) EACH statement ALONE is sufficient.

E) Statements (1) and (2) TOGETHER are NOT sufficient.
ShowHide Answer
Official Answer
E
User avatar
RohitGoyal1123
User avatar
Joined: 05 Dec 2017
Last visit: 21 May 2020
Posts: 49
Own Kudos:
55
 []
Given Kudos: 107
Location: India
Concentration: Finance, International Business
WE:Analyst (Commercial Banking)
Posts: 49
Kudos: 55
 []
Find the number of factors of the number p 21 Apr 2018, 00:39
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
souvik101990

GST Week 2 Day 3 e-GMAT Question 1


Give your best shot at writing a top notch application and you will have the chance to win GMAT Club tests daily and e-GMAT Quant Online Course . See the GMAT Spring Training Thread for all details


Find the number of factors of the number p, if p is a positive integer less than 100.

1. The number p has odd number of factors.

2. The number p can be expressed as \(x^{12}\), \(y^{3}\) or \(z^{6}\) where x, y, and z are positive integers.

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D) EACH statement ALONE is sufficient.

E) Statements (1) and (2) TOGETHER are NOT sufficient.


St 1: The number of factors of p : odd.

This means the number p is a perfect square.

Thus p can be 1, 4 , 36.

No of factors are :

1 = one factor

4 = 2^2; no of factors are (2+1) =3

36 = 2^2 *3^2 ; no of factors are (2+1)*(2+1) = 9

Not sufficient.


St2: if p can be written as x^12, x has to be 1, because 2^12>100. So x = 1

Hence p = 1^12 = 1

No of factors = 1.

Sufficient.



Answer B
User avatar
SonalSinha803
User avatar
Joined: 14 Feb 2018
Last visit: 18 Feb 2019
Posts: 310
Own Kudos:
301
Given Kudos: 29
Posts: 310
Kudos: 301
Find the number of factors of the number p 21 Apr 2018, 00:46
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The answer should be E, because the second statement just says that x,y and z are positive integers. We do not know whether they are the prime factors of the integer p.

Even after combining, the two statements we cannot be sure, if x,y and z are prime factors or not.

This, IMO E.

Sent from my Lenovo K53a48 using GMAT Club Forum mobile app
User avatar
LevanKhukhunashvili
User avatar
Joined: 13 Feb 2018
Last visit: 23 Jan 2021
Posts: 376
Own Kudos:
406
Given Kudos: 50
GMAT 1: 640 Q48 V28
GMAT 1: 640 Q48 V28
Posts: 376
Kudos: 406
Find the number of factors of the number p 21 Apr 2018, 01:04
Kudos
Add Kudos
Bookmarks
Bookmark this Post
SonalSinha803

Note that P<100 and P=x^12
avatar
PPhoenix77
avatar
Joined: 09 Jun 2012
Last visit: 22 Apr 2018
Posts: 24
Own Kudos:
32
 []
Given Kudos: 46
Location: India
Products:
My Reviews
Posts: 24
Kudos: 32
 []
Find the number of factors of the number p 21 Apr 2018, 01:17
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Given: p<100

To calculate the number of factors of p, we need the prime factors of p and the exponents of the prime factors.

1. The number p has odd number of factors.

this implies that the number p is a perfect square. So, it can be 1,4,9,16,25,36,49,64,81
Not Sufficient

2. the number p can be expressed as x^12,y^3,z^6

As p is less than 100, so we can have only one value for p
1 ^12= 1^3 = 1^6
p= 1

Correct Answer = B
avatar
seed
avatar
Joined: 03 Oct 2016
Last visit: 09 Dec 2018
Posts: 96
Own Kudos:
161
Given Kudos: 64
Posts: 96
Kudos: 161
Find the number of factors of the number p 21 Apr 2018, 06:16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
souvik101990

GST Week 2 Day 3 e-GMAT Question 1


Give your best shot at writing a top notch application and you will have the chance to win GMAT Club tests daily and e-GMAT Quant Online Course . See the GMAT Spring Training Thread for all details


Find the number of factors of the number p, if p is a positive integer less than 100.

1. The number p has odd number of factors.
2. The number p can be expressed as \(x^{12}\), \(y^{3}\) or \(z^{6}\) where x, y, and z are positive integers.

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient.

1. The number p has odd number of factors. >>>> If a number has odd factors that means its a perfect square in this case P can be 4,16,25,36,49,64,81 all are <100 , so St1 Not Sufficient.
2. The number p can be expressed as \(x^{12}\), \(y^{3}\) or \(z^{6}\) where x, y, and z are positive integers. >>>>> This implies:

a. P = \(x^{12}\) < 100 then x can be only 1 because \(2^{12}\) > 100.
b. P = \(y^{3}\) < 100 then y can be 1,2,3 or 4.
c. P = \(z^{6}\) < 100 then z can be 1 or 2.

From a,b and c its clear that the only factor common among them is 1 and because P = \(1^{12}\) < 100 St2 is sufficient.

Answer: B.
User avatar
push12345
User avatar
Joined: 02 Oct 2017
Last visit: 10 Feb 2019
Posts: 548
Own Kudos:
513
Given Kudos: 14
Posts: 548
Kudos: 513
Find the number of factors of the number p 21 Apr 2018, 06:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I) for odd no of factors power of number has to even
Eg 2^4 gives me 5 factors
2^2 gives me 3 factors
Different answers so not sufficient

II)2^ 12 is not possible which is smallest integer so only value which satisfy this is 1.

So B gives definite answer.

Posted from my mobile device
avatar
pawanpoolla
avatar
Joined: 10 May 2016
Last visit: 21 Apr 2019
Posts: 14
Own Kudos:
9
Given Kudos: 54
Location: India
Schools: Booth '21 Darden '21 Kellogg '21
GMAT 1: 690 Q49 V35
GPA: 3.9
Products:
My Reviews
Schools: Booth '21 Darden '21 Kellogg '21
GMAT 1: 690 Q49 V35
Posts: 14
Kudos: 9
Find the number of factors of the number p 21 Apr 2018, 15:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
souvik101990

GST Week 2 Day 3 e-GMAT Question 1


Give your best shot at writing a top notch application and you will have the chance to win GMAT Club tests daily and e-GMAT Quant Online Course . See the GMAT Spring Training Thread for all details


Find the number of factors of the number p, if p is a positive integer less than 100.

1. The number p has odd number of factors.

2. The number p can be expressed as \(x^{12}\), \(y^{3}\) or \(z^{6}\) where x, y, and z are positive integers.

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D) EACH statement ALONE is sufficient.

E) Statements (1) and (2) TOGETHER are NOT sufficient.


The correct answer is option B

The solution is fairly straight forward - From the question p<100.
Consider Option 1 - It is clearly not helpful. (Advanced : This does help us understand that p is made up of even powers of prime factors)
Now Option 2 - The number can be expressed as \(x^{12}\), where x is a positive integer. Let's consider x=2. \(2^{12}\) = \(64^{2}\) , clearly >100. So x <2, hence the only option is 1.

Hence option B is the final answer.
avatar
AV678
avatar
Joined: 26 Aug 2015
Last visit: 25 Dec 2018
Posts: 6
Given Kudos: 3
Posts: 6
Kudos: 0
Find the number of factors of the number p 21 Apr 2018, 21:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
B is the correct answer.

S1: p=odd; this is not sufficient as there can be many numbers which are less than 100 and have many odd factors
S2: if P can be written in the form of x^12, y^3 or z^6 then supposing
x=2 will give 2^12>100;
x=1 will give 1^12<100; x can have value 1
y=1 will give 1^3<100
y=2 will give 2^3<100; this will hold true for y=3 & 4; so y can have values : 1, 2, 3, 4
Z=1 will give 1^6<100
Z=2 will give 2^6<100
Z=3 will give 3^6>100; thus z can have values 1,2

So combining x, y, z we get p=1 hence B is sufficient.
User avatar
prince00113
User avatar
Joined: 17 Mar 2015
Last visit: 23 Jun 2019
Posts: 70
Own Kudos:
247
Given Kudos: 64
Products:
My Reviews
Posts: 70
Kudos: 247
Find the number of factors of the number p 21 Apr 2018, 23:42
Kudos
Add Kudos
Bookmarks
Bookmark this Post
souvik101990

GST Week 2 Day 3 e-GMAT Question 1


Give your best shot at writing a top notch application and you will have the chance to win GMAT Club tests daily and e-GMAT Quant Online Course . See the GMAT Spring Training Thread for all details


Find the number of factors of the number p, if p is a positive integer less than 100.

1. The number p has odd number of factors.

2. The number p can be expressed as \(x^{12}\), \(y^{3}\) or \(z^{6}\) where x, y, and z are positive integers.

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D) EACH statement ALONE is sufficient.

E) Statements (1) and (2) TOGETHER are NOT sufficient.




For statement 1,
Only square number have odd number of factors.
9 can be written as 3^2. so 3 factors.
36 can be written as 2^2 * 3^2. so 3*3 factor.

But unique answer cannot be obtained.

For statement 2,
If we take the smallest number greater than 1 i.e. 2, we get 2^12 >100
So the number should be 1.

We can get a unique answer here so the B should be IMO.


Please give Kudos if the answer is correct or the solution is helpful to you!!!!!!
avatar
pawanpoolla
avatar
Joined: 10 May 2016
Last visit: 21 Apr 2019
Posts: 14
Own Kudos:
9
Given Kudos: 54
Location: India
Schools: Booth '21 Darden '21 Kellogg '21
GMAT 1: 690 Q49 V35
GPA: 3.9
Products:
My Reviews
Schools: Booth '21 Darden '21 Kellogg '21
GMAT 1: 690 Q49 V35
Posts: 14
Kudos: 9
Find the number of factors of the number p 22 Apr 2018, 02:03
Kudos
Add Kudos
Bookmarks
Bookmark this Post
SonalSinha803
The answer should be E, because the second statement just says that x,y and z are positive integers. We do not know whether they are the prime factors of the integer p.

Even after combining, the two statements we cannot be sure, if x,y and z are prime factors or not.

This, IMO E.

Sent from my Lenovo K53a48 using GMAT Club Forum mobile app

Though the question doesn't say if x, y, z are prime, we can arrive at x=1 as no other value satisfies the conditions p=\(x^12\) and p<100 simultaneously.
How is the answer E then.
User avatar
GMATBusters
User avatar
GMAT Tutor
Joined: 27 Oct 2017
Last visit: 10 Dec 2024
Posts: 1,930
Own Kudos:
6,047
Given Kudos: 240
WE:General Management (Education)
Expert reply
Posts: 1,930
Kudos: 6,047
Find the number of factors of the number p 22 Apr 2018, 17:58
Kudos
Add Kudos
Bookmarks
Bookmark this Post
egmat
Please recheck the OA, it should be B.

souvik101990

GST Week 2 Day 3 e-GMAT Question 1


Give your best shot at writing a top notch application and you will have the chance to win GMAT Club tests daily and e-GMAT Quant Online Course . See the GMAT Spring Training Thread for all details


Find the number of factors of the number p, if p is a positive integer less than 100.

1. The number p has odd number of factors.

2. The number p can be expressed as \(x^{12}\), \(y^{3}\) or \(z^{6}\) where x, y, and z are positive integers.

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D) EACH statement ALONE is sufficient.

E) Statements (1) and (2) TOGETHER are NOT sufficient.

Posted from my mobile device
avatar
sghoshgt
avatar
Joined: 20 Aug 2017
Last visit: 16 Aug 2020
Posts: 18
Own Kudos:
8
Given Kudos: 118
Posts: 18
Kudos: 8
Find the number of factors of the number p 23 Apr 2018, 03:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The OA should be B, we can easily confirm as X^12 is provided.
User avatar
souvik101990
User avatar
Joined: 19 Mar 2012
Last visit: 09 Nov 2024
Posts: 4,327
Own Kudos:
52,172
Given Kudos: 2,326
Location: United States (WA)
Concentration: Leadership, General Management
Schools: Ross '20 (M)
GMAT 1: 760 Q50 V42
GMAT 2: 740 Q49 V42 (Online)
GMAT 3: 760 Q50 V42 (Online)
GPA: 3.8
WE:Marketing (Non-Profit and Government)
Products:
My Reviews
Expert reply
Schools: Ross '20 (M)
GMAT 3: 760 Q50 V42 (Online)
Posts: 4,327
Kudos: 52,172
Find the number of factors of the number p 23 Apr 2018, 07:55
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Thanks for attempting this one, everybody. My apologies for a typo in the question. The correct question (edited in the main post) is


Find the number of factors of the number p, if p is a positive integer less than 100.

1. The number p has odd number of factors.

2. The number p can be expressed as \(x^{2}\), \(y^{3}\) or \(z^{6}\) where x, y, and z are positive integers.

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D) EACH statement ALONE is sufficient.

E) Statements (1) and (2) TOGETHER are NOT sufficient.
User avatar
souvik101990
User avatar
Joined: 19 Mar 2012
Last visit: 09 Nov 2024
Posts: 4,327
Own Kudos:
52,172
Given Kudos: 2,326
Location: United States (WA)
Concentration: Leadership, General Management
Schools: Ross '20 (M)
GMAT 1: 760 Q50 V42
GMAT 2: 740 Q49 V42 (Online)
GMAT 3: 760 Q50 V42 (Online)
GPA: 3.8
WE:Marketing (Non-Profit and Government)
Products:
My Reviews
Expert reply
Schools: Ross '20 (M)
GMAT 3: 760 Q50 V42 (Online)
Posts: 4,327
Kudos: 52,172
Find the number of factors of the number p 23 Apr 2018, 07:58
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Although there was a typo (apologies again), some great work by all of you. rkgstyle - Kudos for a great explanation! Please PM me to get your GMATClub tests!
avatar
Bryxz
avatar
Joined: 18 Feb 2018
Last visit: 06 Jul 2018
Posts: 1
Given Kudos: 1
Posts: 1
Kudos: 0
Find the number of factors of the number p 24 Apr 2018, 15:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Good day everyone,

I have a question concerning the answer being E. I understand that with statement 2 we might arrive to 2 answers which would be 1 or 64. But for me - as I am understanding the way the question is asked -, the answer ''1'' is not valid. Indeed, the statement 2 cleary says that x, y and z are positive integers in plural. That means, therefore, that the integers x, y and z are 3 different integers and only the answer ''64'' satisfy this condition.

Am I wrong for thinking like that?

Thx for your help
User avatar
amanvermagmat
User avatar
Retired Moderator
Joined: 22 Aug 2013
Last visit: 31 Mar 2021
Posts: 1,178
Own Kudos:
2,651
 []
Given Kudos: 459
Location: India
Posts: 1,178
Kudos: 2,651
 []
Find the number of factors of the number p 24 Apr 2018, 22:18
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bryxz
Good day everyone,

I have a question concerning the answer being E. I understand that with statement 2 we might arrive to 2 answers which would be 1 or 64. But for me - as I am understanding the way the question is asked -, the answer ''1'' is not valid. Indeed, the statement 2 cleary says that x, y and z are positive integers in plural. That means, therefore, that the integers x, y and z are 3 different integers and only the answer ''64'' satisfy this condition.

Am I wrong for thinking like that?

Thx for your help

Hello

The question just says: x, y, z are positive integers. That doesnt necessarily mean that they are distinct, because the word 'distinct' has not been used in the question.
avatar
Aswini03
avatar
Joined: 02 Apr 2016
Last visit: 16 Oct 2022
Posts: 3
Own Kudos:
5
Given Kudos: 46
Location: United States
Concentration: Entrepreneurship, International Business
GPA: 3.95
WE:Project Management (Computer Software)
Posts: 3
Kudos: 5
Find the number of factors of the number p 25 Apr 2018, 20:35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
From statement 2 x,y,z are positive integers and p can be expressed as x^2,y^3,z^6.The only integer 64 satisfies this condition.
Hence I suppose answer as B.
Please correct me
User avatar
GMATBusters
User avatar
GMAT Tutor
Joined: 27 Oct 2017
Last visit: 10 Dec 2024
Posts: 1,930
Own Kudos:
6,047
Given Kudos: 240
WE:General Management (Education)
Expert reply
Posts: 1,930
Kudos: 6,047
Find the number of factors of the number p 25 Apr 2018, 20:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
x =1,2 both satisfied statement 2 hence it is not sufficient.

See if x = 1, x^2,x^3,x^6 =1 which is less than 100.
If x =2, max value is x^6=64, less than 100.
Hence x can be 1 or 2, unique value can't be found. Hence it is not sufficient.

B is not right answer.

Answer shall be E.


Aswini03
From statement 2 x,y,z are positive integers and p can be expressed as x^2,y^3,z^6.The only integer 64 satisfies this condition.
Hence I suppose answer as B.
Please correct me

Posted from my mobile device
avatar
jk94
avatar
Joined: 31 Mar 2017
Last visit: 10 Mar 2021
Posts: 33
Own Kudos:
7
Given Kudos: 46
Location: India
Concentration: Strategy
Schools: Anderson '22 (A$) Tuck '22 (D) Ross '22 (WA$) Tepper '22 (A$) Kenan-Flagler '22 (A)
GMAT 1: 690 Q49 V35
GMAT 2: 740 Q49 V41
GPA: 4
Products:
My Reviews
Schools: Anderson '22 (A$) Tuck '22 (D) Ross '22 (WA$) Tepper '22 (A$) Kenan-Flagler '22 (A)
GMAT 2: 740 Q49 V41
Posts: 33
Kudos: 7
Find the number of factors of the number p 03 May 2018, 15:53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I feel if the terms are given as x, y and z , they are bound to be distinct terms.
This leads us to the fact that P != 1 , and P= 2 , can be the only solution.
IMO B is the correct choice here.

P.S. : I see some folks have used x^12 , while I see x^2 in the question. Can anyone clarify?
 1   2   
Moderator:
Bunuel
Math Expert
97881 posts