GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Jul 2018, 18:01

### 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

# STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION.

Author Message
TAGS:

### Hide Tags

SC Moderator
Joined: 13 Apr 2015
Posts: 1712
Location: India
Concentration: Strategy, General Management
GMAT 1: 200 Q1 V1
GPA: 4
WE: Analyst (Retail)
Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION. [#permalink]

### Show Tags

12 Jan 2017, 23:05
1
St1: k = 13t + 13
t = 0 --> k is prime
t = any other integer --> k is not prime
Not Sufficient

St2: k = 17! + 13 --> 13(Some number + 1) --> k is not prime
Sufficient

BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2646
GRE 1: 323 Q169 V154
Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION. [#permalink]

### Show Tags

13 Jan 2017, 01:13
If x,y,z are positive integers,is the product x*y*z divisibly by 21?
(1) The greatest common factor of x, y, and z is 3.
(2) The lowest common multiple of x, y, and z is 63.

_________________

MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2646
GRE 1: 323 Q169 V154
Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION. [#permalink]

### Show Tags

13 Jan 2017, 03:25
If a positive integer $$n$$ is given by $$n=26*p$$ where $$p$$ is a prime number greater than 2,how many even divisors does n have ?

A)4
B)3
C)2
D)1
E)cannot be determined.

_________________

MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2646
GRE 1: 323 Q169 V154
Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION. [#permalink]

### Show Tags

13 Jan 2017, 05:47
Here is what i did in this Question.
We are asked about the number of factors of a Positive integer N.

Statement 1->
The only way 27*N^3 =3^3*N^3 will have 16 factors is if N is a prime number.
Hence N must be a prime number => 2 factors only.
Hence Sufficient.

Statement 2->
Since N is an integer => N^3 must be a perfect Cube.
The only perfect cube between 90 and 200 is 125.
Hence N^3 must be 125 => N must be 5 => Two factors only.
Hence sufficient.

Hence D.

_________________

MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2646
GRE 1: 323 Q169 V154
Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION. [#permalink]

### Show Tags

13 Jan 2017, 05:55
If $$N$$ is a positive integer,what is the value of $$N$$?
(1) $$N$$ is divisible by 31.
(2) $$\frac{N}{100}$$ is a prime number.

_________________

MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

Director
Joined: 05 Mar 2015
Posts: 980
Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION. [#permalink]

### Show Tags

13 Jan 2017, 07:43
stonecold wrote:
If a positive integer $$n$$ is given by $$n=26*p$$ where $$p$$ is a prime number greater than 2,how many even divisors does n have ?

A)4
B)3
C)2
D)1
E)cannot be determined.

n=26p
=2*13*p
where p is odd(prime >2 is odd)
thus no. of even factors are
2 , 2*13 , 2*p , 2*13*p
=4

Ans A
BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2646
GRE 1: 323 Q169 V154
Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION. [#permalink]

### Show Tags

13 Jan 2017, 07:47
rohit8865 wrote:
stonecold wrote:
If a positive integer $$n$$ is given by $$n=26*p$$ where $$p$$ is a prime number greater than 2,how many even divisors does n have ?

A)4
B)3
C)2
D)1
E)cannot be determined.

n=26p
=2*13*p
where p is odd(prime >2 is odd)
thus no. of even factors are
2 , 2*13 , 2*p , 2*13*p
=4

Ans A

Counter Question->
What if p=13?

_________________

MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

Director
Joined: 05 Mar 2015
Posts: 980
Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION. [#permalink]

### Show Tags

13 Jan 2017, 08:04
stonecold wrote:
rohit8865 wrote:
stonecold wrote:
If a positive integer $$n$$ is given by $$n=26*p$$ where $$p$$ is a prime number greater than 2,how many even divisors does n have ?

A)4
B)3
C)2
D)1
E)cannot be determined.

n=26p
=2*13*p
where p is odd(prime >2 is odd)
thus no. of even factors are
2 , 2*13 , 2*p , 2*13*p
=4

Ans A

Counter Question->
What if p=13?

sure
p may be 13
then this is debatable one
on my side it will better be a DS question
BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2646
GRE 1: 323 Q169 V154
Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION. [#permalink]

### Show Tags

13 Jan 2017, 08:19
rohit8865 wrote:
stonecold wrote:
rohit8865 wrote:

Counter Question->
What if p=13?

sure
p may be 13
then this is debatable one
on my side it will better be a DS question

We may not agree on that.
Since two values of the number of factors are possible => The answer cannot be determined.
Hence E.

_________________

MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

Director
Joined: 05 Mar 2015
Posts: 980
Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION. [#permalink]

### Show Tags

13 Jan 2017, 08:26
stonecold wrote:

sure
p may be 13
then this is debatable one
on my side it will better be a DS question
[/quote]

We may not agree on that.
Since two values of the number of factors are possible => The answer cannot be determined.
Hence E.
[/quote]

well i have not considered the last option
Ans will be E
BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2646
GRE 1: 323 Q169 V154
Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION. [#permalink]

### Show Tags

13 Jan 2017, 08:29
A number is said to be prime saturated if the product of all the different positive prime factors of n is less than the square root of n.
If p is a prime saturated,what is the value of p?

A)p is a perfect cube.
B)2≤p≤15

_________________

MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

Director
Joined: 05 Mar 2015
Posts: 980
Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION. [#permalink]

### Show Tags

13 Jan 2017, 08:31
stonecold wrote:
If $$N$$ is a positive integer,what is the value of $$N$$?
(1) $$N$$ is divisible by 31.
(2) $$\frac{N}{100}$$ is a prime number.

(1) n could be 31 or 62
not suff

(2) n can be 200 or 300
not suff

combining n=31p from (1)
& 31p/100 is prime From (2)
thus n must be 3100

Ans C
SC Moderator
Joined: 13 Apr 2015
Posts: 1712
Location: India
Concentration: Strategy, General Management
GMAT 1: 200 Q1 V1
GPA: 4
WE: Analyst (Retail)
Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION. [#permalink]

### Show Tags

13 Jan 2017, 08:55
St1: x = y = z = 3 --> x * y * z is not divisible by 3*7
x = 3, y = z = 21 --> x * y * z is divisible by 3*7
Not Sufficient.

St2: LCM(x, y, z) = 63
x * y * z is a multiple of 63 and hence divisible by 21
Sufficient.

Senior CR Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1392
Location: Viet Nam
Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION. [#permalink]

### Show Tags

13 Jan 2017, 09:17
1
stonecold wrote:
A number is said to be prime saturated if the product of all the different positive prime factors of n is less than the square root of n.
If p is a prime saturated,what is the value of p?

A)p is a perfect cube.
B)2≤p≤15

A) $$p$$ is a perfect cube. Then $$p$$ could be $$3^3=27$$ or $$2^3=8$$. Insufficient.

B) $$2 \leq p \leq 15$$

First, $$p$$ can't be a prime. Out 2, 3, 5, 7, 11, 13, left 4, 6, 8, 9, 10, 12, 14, 15
Second, $$p$$ can't be in prime factorization of $$a \times b$$ where $$a$$ and $$b$$ are prime. Out 6, 10, 14, 15. Left 4, 8, 9, 12.
Third, $$p$$ can't be in form of $$a^2$$ where $$a$$ is prime. Out 4, 9. Left 8, 12.

8 is a cube, so 8 is prime saturated.
$$12=2^2 \times 3$$. We have $$2 \times 3 = 6 > \sqrt{12}=2\sqrt{3}$$ so 12 is not prime saturated.

Hence, $$p=8$$. Sufficient.

_________________
BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2646
GRE 1: 323 Q169 V154
Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION. [#permalink]

### Show Tags

13 Jan 2017, 10:33
If $$a = b^3*c^2*d$$,how many positive factors does a have?

(1)$$b$$, $$c$$ and $$d$$ are prime numbers.
(2)$$b$$,$$c$$,$$d$$ are distinct integers.

_________________

MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

Senior Manager
Joined: 21 Aug 2016
Posts: 282
Location: India
GPA: 3.9
WE: Information Technology (Computer Software)
Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION. [#permalink]

### Show Tags

14 Jan 2017, 05:07
stonecold wrote:
If $$a = b^3*c^2*d$$,how many positive factors does a have?

(1)$$b$$, $$c$$ and $$d$$ are prime numbers.
(2)$$b$$,$$c$$,$$d$$ are distinct integers.

BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2646
GRE 1: 323 Q169 V154
Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION. [#permalink]

### Show Tags

14 Jan 2017, 09:18
1
Director
Joined: 05 Mar 2015
Posts: 980
Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION. [#permalink]

### Show Tags

14 Jan 2017, 11:11
stonecold wrote:
How many positive even divisors does 96 have ?

A. 12
B. 10
C. 8
D. 6
E. Cannot be determined

96= 2^5*3
thus no. of even factors = 5*2=10

Ans B
BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2646
GRE 1: 323 Q169 V154
Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION. [#permalink]

### Show Tags

15 Jan 2017, 14:17
BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2646
GRE 1: 323 Q169 V154
Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION. [#permalink]

### Show Tags

16 Jan 2017, 11:51
Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION.   [#permalink] 16 Jan 2017, 11:51

Go to page   Previous    1   2   3   4    Next  [ 71 posts ]

Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.