source Kaplan
How many positive factors does the positive integer x have?
(1) x is the product of 3 distinct prime numbers.
(2) x and (3^7) have the same number of positive factors.
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How many positive factors does the positive integer x have?
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conquistador
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Last edited by conquistador on Sat Dec 26, 2015 9:01 am, edited 1 time in total.
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GMATGuruNY
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Statement 2 indicates that x is PRIME, while statement 1 indicates that x is NOT prime.Mechmeera wrote:source Kaplan
How many positive factors does the positive integer x have?
(1) x is the product of 3 distinct prime numbers.
(2) x and 37 have the same number of positive factors.
Since it is guaranteed on the GMAT that the two statements will not contradict each other, this DS seems invalid.
I would ignore this problem.
I explain how to count positive factors here:
https://www.beatthegmat.com/all-factors- ... 15019.html
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conquistador
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3^7 is mistyped as 37. Sorry for the typo.GMATGuruNY wrote:Statement 2 indicates that x is PRIME, while statement 1 indicates that x is NOT prime.Mechmeera wrote:source Kaplan
How many positive factors does the positive integer x have?
(1) x is the product of 3 distinct prime numbers.
(2) x and 37 have the same number of positive factors.
Since it is guaranteed on the GMAT that the two statements will not contradict each other, this DS seems invalid.
I would ignore this problem.
I explain how to count positive factors here:
https://www.beatthegmat.com/all-factors- ... 15019.html
Please look into this once again.
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GMATGuruNY
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To count the number of positive factors of an integer:
1) Prime-factorize the integer
2) Add 1 to each exponent
3) Multiply
For example:
72 = 2³ * 3².
Adding 1 to each exponent and multiplying, we get (3+1)*(2+1) = 12 positive factors.
Here's why:
To determine how many factors can be created from 72 = 2³ * 3², we need to determine the number of choices we have of each prime factor and to count the number of ways these choices can be combined:
For 2, we can use 2�, 2¹, 2², or 2³, giving us 4 choices.
For 3, we can use 3�, 3¹, or 3², giving us 3 choices.
Multiplying the number of choices we have of each factor, we get 4*3 = 12 positive factors.
x = a¹b¹c¹, where a, b and c are distinct prime numbers.
Adding 1 to each exponent and multiplying, we get:
(1+1)(1+1)(1+1) = 8 positive factors.
SUFFICIENT.
Statement 2:
Since we can count the number of positive factors for 3�, the number of positive factors for x can be determined.
SUFFICIENT.
The correct answer is D.
To determine the number of positive factors for 3�, we simply add 1 to the exponent:
7+1 = 8 positive factors.
1) Prime-factorize the integer
2) Add 1 to each exponent
3) Multiply
For example:
72 = 2³ * 3².
Adding 1 to each exponent and multiplying, we get (3+1)*(2+1) = 12 positive factors.
Here's why:
To determine how many factors can be created from 72 = 2³ * 3², we need to determine the number of choices we have of each prime factor and to count the number of ways these choices can be combined:
For 2, we can use 2�, 2¹, 2², or 2³, giving us 4 choices.
For 3, we can use 3�, 3¹, or 3², giving us 3 choices.
Multiplying the number of choices we have of each factor, we get 4*3 = 12 positive factors.
Statement 1:Mechmeera wrote:source Kaplan
How many positive factors does the positive integer x have?
(1) x is the product of 3 distinct prime numbers.
(2) x and 3� have the same number of positive factors.
x = a¹b¹c¹, where a, b and c are distinct prime numbers.
Adding 1 to each exponent and multiplying, we get:
(1+1)(1+1)(1+1) = 8 positive factors.
SUFFICIENT.
Statement 2:
Since we can count the number of positive factors for 3�, the number of positive factors for x can be determined.
SUFFICIENT.
The correct answer is D.
To determine the number of positive factors for 3�, we simply add 1 to the exponent:
7+1 = 8 positive factors.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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Matt@VeritasPrep
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S1::
x = p * q * r, where p, r, and q are distinct primes.
A number has three types of factors, broadly speaking:
Type I: 1 and itself
Type II: Its primes
Type III: The products of its primes
So our number has
1, itself, p, q, r, p*q, q*r, and p*r, for a total of 8 factors; SUFFICIENT.
S2::
This is definitely sufficient: we don't even need to know how to count the number of factors of 3�, so this is a freebie
x = p * q * r, where p, r, and q are distinct primes.
A number has three types of factors, broadly speaking:
Type I: 1 and itself
Type II: Its primes
Type III: The products of its primes
So our number has
1, itself, p, q, r, p*q, q*r, and p*r, for a total of 8 factors; SUFFICIENT.
S2::
This is definitely sufficient: we don't even need to know how to count the number of factors of 3�, so this is a freebie
