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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

the next step is to choose all possibilities for which n>77:

one prime number: 2, 4, 5, 25, 7- 0 possibilities for n two prime numbers: 2*5, 2*25, 4*5, 4*25, 2*7, 4*7, 5*7, 25*7 - 2 possibilities for n three prime numbers: 2*5*7, 4*5*7, 2*25*7, 4*25*7- 3 possibilities for n

So, we have 5 possible values of n: 4*25, 25*7, 4*5*7, 2*25*7, 4*25*7

the next step is to choose all possibilities for which n>77:

one prime number: 2, 4, 5, 25, 7- 0 possibilities for n two prime numbers: 2*5, 2*25, 4*5, 4*25, 2*7, 4*7, 5*7, 25*7 - 2 possibilities for n three prime numbers: 2*5*7, 4*5*7, 2*25*7, 4*25*7- 3 possibilities for n

So, we have 5 possible values of n: 4*25, 25*7, 4*5*7, 2*25*7, 4*25*7

I meant to post the actual explanation that came with the question.. and which is still confusing to me.. If anybody can evaluate the latter, it will be great (bolded part..):

If the remainder is 77, then n must logically be greater than 77. Also, there must be a positive integer q such that 777= nq + 77. i.e. nq = 700.

Therefore, the factors of 700 greater than 77 comprise the possible values of n. Instead of counting the factors of 700 that are greater than 77, let’s count the ones that are less than or equal to 700/77. As 700 = 50 × 2 × 7, we can see that there are 5 factors of 700 that are less than or equal to 7: 1 , 2 , 4 , 5 , and 7. Thus there are 5 possible values of n (i.e. factors of 700) greater than 77. We don’t need to know these values, but for the curious, they are 700, 350, 175, 140 and 100.

Instead of counting the factors of 700 that are greater than 77, let’s count the ones that are less than or equal to 700/77. As 700 = 50 × 2 × 7, we can see that there are 5 factors of 700 that are less than or equal to 7: 1 , 2 , 4 , 5 , and 7. Thus there are 5 possible values of n (i.e. factors of 700) greater than 77. We don’t need to know these values, but for the curious, they are 700, 350, 175, 140 and 100.

Excellent!

700=(factor >77)*(factor <700/77)

OE say that for each factor >70 we have one factor <700/77 in order to have 700 as a product of those factors. So, we can count only all factors <700/77

Instead of counting the factors of 700 that are greater than 77, let’s count the ones that are less than or equal to 700/77. As 700 = 50 × 2 × 7, we can see that there are 5 factors of 700 that are less than or equal to 7: 1 , 2 , 4 , 5 , and 7. Thus there are 5 possible values of n (i.e. factors of 700) greater than 77. We don’t need to know these values, but for the curious, they are 700, 350, 175, 140 and 100.

Excellent!

700=(factor >77)*(factor <700/77)

OE say that for each factor >70 we have one factor <700/77 in order to have 700 as a product of those factors. So, we can count only all factors <700/77