ramannjit wrote:If a = 5^20-5^19+5^18, what is the length of a? (The length of an integer is the number of prime numbers, not necessarily distinct, in the prime factoriztion of the integer.)

Answer I got is correct, I am confused between when simply "length" is stated vs "maximum possible length". Help is needed in understanding the concept.

OA 20

Maximum possible length will be discussed only when the value of the integer is unknown. For example:

What is the maximum possible length of a positive integer less than 10?
Answer = 3, because 2*2*2 = 8, giving us 3 prime factors. If we add another prime factor, the product will become larger than 10.

In the problem above, the value of the integer is known, so all we have to do is count the number of prime factors:
5^20-5^19+5^18 = 5^18(5^2 - 5 + 1) = 5^18(21) = 5^18*3*7, giving us 18+1+1=20 prime factors. Thus, the length is 20.

GMATGuruNY wrote:

ramannjit wrote:If a = 5^20-5^19+5^18, what is the length of a? (The length of an integer is the number of prime numbers, not necessarily distinct, in the prime factoriztion of the integer.)

Answer I got is correct, I am confused between when simply "length" is stated vs "maximum possible length". Help is needed in understanding the concept.

OA 20

Maximum possible length will be discussed only when the value of the integer is unknown. For example:

What is the maximum possible length of a positive integer less than 10?
Answer = 3, because 2*2*2 = 8, giving us 3 prime factors. If we add another prime factor, the product will become larger than 10.

In the problem above, the value of the integer is known, so all we have to do is count the number of prime factors:
5^20-5^19+5^18 = 5^18(5^2 - 5 + 1) = 5^18(21) = 5^18*3*7, giving us 18+1+1=20 prime factors. Thus, the length is 20.

So when the integer is known = this will translate into "how many total factors the integer has?" If unknow, will go ahead with starting with only 2 and making it count.

Am I correct?

ramannjit wrote:

GMATGuruNY wrote:

ramannjit wrote:If a = 5^20-5^19+5^18, what is the length of a? (The length of an integer is the number of prime numbers, not necessarily distinct, in the prime factoriztion of the integer.)

Answer I got is correct, I am confused between when simply "length" is stated vs "maximum possible length". Help is needed in understanding the concept.

OA 20

Maximum possible length will be discussed only when the value of the integer is unknown. For example:

What is the maximum possible length of a positive integer less than 10?
Answer = 3, because 2*2*2 = 8, giving us 3 prime factors. If we add another prime factor, the product will become larger than 10.

In the problem above, the value of the integer is known, so all we have to do is count the number of prime factors:
5^20-5^19+5^18 = 5^18(5^2 - 5 + 1) = 5^18(21) = 5^18*3*7, giving us 18+1+1=20 prime factors. Thus, the length is 20.

So when the integer is known = this will translate into "how many total factors the integer has?" If unknow, will go ahead with starting with only 2 and making it count.

Am I correct?

Yes, if you're asked for the length of a known integer, just count the number of prime factors.
If you're asked for the maximum possible length of an unknown integer, use as many 2's as possible. However, the problem could be restricted in such a way that you can't use all 2's:

What is the maximum possible length of a positive multiple of 7 less than 100?
7*2*2*2 = 56. The correct answer is 4. If we add another 2, the product will be greater than 100.

Please note that you don't have to memorize the definition of length. if the GMAT asks about the length of an integer, you'll be given the definition.

GMATGuruNY wrote:

ramannjit wrote:

GMATGuruNY wrote:

ramannjit wrote:If a = 5^20-5^19+5^18, what is the length of a? (The length of an integer is the number of prime numbers, not necessarily distinct, in the prime factoriztion of the integer.)

Answer I got is correct, I am confused between when simply "length" is stated vs "maximum possible length". Help is needed in understanding the concept.

OA 20

Maximum possible length will be discussed only when the value of the integer is unknown. For example:

What is the maximum possible length of a positive integer less than 10?
Answer = 3, because 2*2*2 = 8, giving us 3 prime factors. If we add another prime factor, the product will become larger than 10.

In the problem above, the value of the integer is known, so all we have to do is count the number of prime factors:
5^20-5^19+5^18 = 5^18(5^2 - 5 + 1) = 5^18(21) = 5^18*3*7, giving us 18+1+1=20 prime factors. Thus, the length is 20.

So when the integer is known = this will translate into "how many total factors the integer has?" If unknow, will go ahead with starting with only 2 and making it count.

Am I correct?

Yes, if you're asked for the length of a known integer, just count the number of prime factors.
If you're asked for the maximum possible length of an unknown integer, use as many 2's as possible. However, the problem could be restricted in such a way that you can't use all 2's:

What is the maximum possible length of a positive multiple of 7 less than 100?
7*2*2*2 = 56. The correct answer is 4. If we add another 2, the product will be greater than 100.

Please note that you don't have to memorize the definition of length. if the GMAT asks about the length of an integer, you'll be given the definition.

Thanks for clarification and adding another restricted case !