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Suppose a is a three-digit number that has 3 prime factors and b is a
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06 Mar 2024, 02:00
06 Mar 2024, 02:00
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Suppose a is a three-digit number that has 3 prime factors and b is a two-digit number that has 3 prime factors. What is the smallest integer ob that has 4 prime factors?
A. 360
B. 420
C. 1360
D. 3060
E. There is not enough information to determine the answer.
A. 360
B. 420
C. 1360
D. 3060
E. There is not enough information to determine the answer.
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Free Materials for the GRE General Exam - Where to get it!!
GRE Geometry Formulas
GRE - Math Book
Re: Suppose a is a three-digit number that has 3 prime factors and b is a
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07 Apr 2024, 01:36
07 Apr 2024, 01:36
Expert Reply
D.
This number t4eory problem tests your understanding of prime factors and number composition.The first step is to find the smallest 3-digit number which has 3 prime factors. Choose the two smallest possible primes: 2 and 3. Find the smallest prime which, when multiplied with 2 and 3, is a 3-digit number.This happens to be 17: 2(3)(17) = 102.
101 is a prime number, so with 102 you have found the smallest 3-digit number with 3 prime factors. Call this a.
Now find the smallest 2-digit number with 3 prime factors. The three smallest prime factors are 2, 3, and 5:2(3) (5) = 30, which is a 2-digit number. Call this b.
This gives you: ab = (2 • 3 • 17) • (2 • 3 • 5) = 22 • 32 • 5 • 17 = 3060. As you can see, 3060 has exactly 4 prime factors: 2, 3, 5, 17.
The correct answer choice is D.
This number t4eory problem tests your understanding of prime factors and number composition.The first step is to find the smallest 3-digit number which has 3 prime factors. Choose the two smallest possible primes: 2 and 3. Find the smallest prime which, when multiplied with 2 and 3, is a 3-digit number.This happens to be 17: 2(3)(17) = 102.
101 is a prime number, so with 102 you have found the smallest 3-digit number with 3 prime factors. Call this a.
Now find the smallest 2-digit number with 3 prime factors. The three smallest prime factors are 2, 3, and 5:2(3) (5) = 30, which is a 2-digit number. Call this b.
This gives you: ab = (2 • 3 • 17) • (2 • 3 • 5) = 22 • 32 • 5 • 17 = 3060. As you can see, 3060 has exactly 4 prime factors: 2, 3, 5, 17.
The correct answer choice is D.
gmatclubot
Re: Suppose a is a three-digit number that has 3 prime factors and b is a [#permalink]
07 Apr 2024, 01:36
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