When the number 777 is divided by the integer N. . . .

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

When the number 777 is divided by the integer N. . . .

by Vincen » Tue Dec 26, 2017 5:16 am

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When the number 777 is divided by the integer N, the remainder is 77. How many integer possibilities are there for N?

A. 2
B. 3
C. 4
D. 5
E. 6

The OA is the option D.

What are these numbers and how I find them? I am confused here. Experts, may you clarify this for me? Thanks in advanced.

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Source: Beat The GMAT — Problem Solving | Tue Dec 26, 2017 5:16 am

elias.latour.apex: Master | Next Rank: 500 Posts; Posts: 228; Joined: Thu Apr 20, 2017 1:02 am; Location: Global; Thanked: 32 times; Followed by:3 members; GMAT Score:770

by elias.latour.apex » Tue Dec 26, 2017 6:07 am

Upon reading this problem, we know that the factor must be greater than 77 to give that as a remainder. We also know that the number must divide 700 evenly. So how many numbers are there that divide 700 evenly and that are greater than 77?

700 can be prime factored to 10*10*7, which further reduces to 1*2*2*5*5*7. With these numbers in mind, we can determine how many factors there are:

700 / 1 = 700 is one possible factor.
700 / 2 = 350 is another.
700 / 2 /2 = 175 is another.
700 / 5 = 140 is another factor.
700 / 7 = 100 is the final factor.

So there are 5 possible factors. That's answer choice (D)

Elias Latour
Verbal Specialist @ ApexGMAT
blog.apexgmat.com
+1 (646) 736-7622

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 am; Location: New York, NY; Thanked: 39 times; Followed by:22 members

by Jeff@TargetTestPrep » Mon May 07, 2018 10:02 am

Vincen wrote:When the number 777 is divided by the integer N, the remainder is 77. How many integer possibilities are there for N?

A. 2
B. 3
C. 4
D. 5
E. 6

We can create the equation:

777/N = Q + 77/N

When N = 700, the remainder is 77.

Thus, all factors of 700 that are greater than 77, will also leave a remainder of 77 when divided into 777.

Breaking 700 into primes, we have:

700 = 100 x 7 = 2^2 x 5^2 x 7^1

So factors of 700 that are greater than 77 are:

100, 7 x 25 = 175, 7 x 25 x 2 = 350, 7 x 4 x 5 = 140, and lastly, 700.

So there are 5 possibilities of N.

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]