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Marshall & McDonough Moderator D
Joined: 13 Apr 2015
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Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION.  [#permalink]

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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

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GRE 1: Q169 V154 Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION.  [#permalink]

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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.

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GRE 1: Q169 V154 Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION.  [#permalink]

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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.

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GRE 1: Q169 V154 Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION.  [#permalink]

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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.

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GRE 1: Q169 V154 Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION.  [#permalink]

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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.

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

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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
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GRE 1: Q169 V154 Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION.  [#permalink]

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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?

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Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION.  [#permalink]

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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
Current Student D
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GRE 1: Q169 V154 Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION.  [#permalink]

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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.

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Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION.  [#permalink]

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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
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GRE 1: Q169 V154 Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION.  [#permalink]

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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

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Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION.  [#permalink]

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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
Marshall & McDonough Moderator D
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Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION.  [#permalink]

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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.

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Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION.  [#permalink]

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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.

The answer is B.
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GRE 1: Q169 V154 Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION.  [#permalink]

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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.

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Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION.  [#permalink]

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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.

Clearly, the answer is A
Current Student D
Joined: 12 Aug 2015
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GRE 1: Q169 V154 Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION.  [#permalink]

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1
If $$x$$ is an integer, is $$x^3$$ divisible by 7 ?
(1) $$x^{12}$$ is divisible by 7.
(2) $$x^4$$ is divisible by 7.

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Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION.  [#permalink]

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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
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GRE 1: Q169 V154 Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION.  [#permalink]

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Mock Test 1(600-700) Updated.

stonecold-s-mock-test-217160.html#p1676182
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GRE 1: Q169 V154 Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION.  [#permalink]

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Mock Test 2 (700+) Updated.

stonecold-s-mock-test-217160.html#p1676182
_________________ Re: STONECOLD'S MATH CHALLENGE - PS AND DS QUESTION COLLECTION.   [#permalink] 16 Jan 2017, 11:51

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