A simple one

Expert replies

knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pmFollowed by: 11 members; Thanked: 114 times

by knight247 » Thu Aug 04, 2011 11:52 am

A teacher was trying to arrange the students of her class in rows with an equal number of students in each row. First, she tried to arrange 4 students in a row. Later, she tried to arrange 6 students in a two. In either case, she was left with one extra student. However, when she tried to arrange 7 students in a row, she was not left with any extra student. What is the minimum number of students in the class?

I don't have answer options or an OA. The answer is 49 as per my calculations. Detailed explanations would be appreciated. Thanks

Like this post

Source: Beat The GMAT — Problem Solving | Thu Aug 04, 2011 11:52 am

gmatboost: Master | Next Rank: 500 Posts; Posts: 312; Joined: Tue Aug 02, 2011 3:16 pmFollowed by: 33 members; Location: New York City; Thanked: 130 times; GMAT Score:780

by gmatboost » Thu Aug 04, 2011 12:00 pm

If there was 1 student left over when she tried both 4 and 6 per row, that means that the number of students is both
A) 1 more than a multiple of 4
A) 1 more than a multiple of 6

What do we call a number that is both a multiple of 4 and a multiple of 6?
Well, 4 = 2*2 and 6 = 2*3
To be a multiple of both, a number would need to have both 2*2 and 2*3 in its prime factorization, which means it would need to have 2*2*3 as part of its prime factorization. Which means it would need to be a multiple of 2*2*3 = 12.

Another way of looking at that step is that we need the LCM of 4 and 6, which is 12.

So, the number of students is 1 more than multiple of 12.
Also, it is a multiple of 7.

Start checking numbers that are 1 more than a multiple of 12 to see if each is or is not a multiple of 7.

12 -> 13 -> NO
[spoiler]24 -> 25 -> NO
36 -> 37 -> NO
48 -> 49 -> YES[/spoiler]

Last edited by gmatboost on Thu Aug 04, 2011 12:15 pm, edited 1 time in total.

Greg Michnikov, Founder of GMAT Boost

GMAT Boost offers 250+ challenging GMAT Math practice questions, each with a thorough video explanation, and 100+ GMAT Math video tips, each 90 seconds or less.
It's a total of 20+ hours of expert instruction for an introductory price of just $10.
View sample questions and tips without signing up, or sign up now for full access.

Also, check out the most useful GMAT Math blog on the internet here.

Like this post

knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pmFollowed by: 11 members; Thanked: 114 times

by knight247 » Thu Aug 04, 2011 12:14 pm

Thanks Greg. I didn't wanna rack my brain too much so I did it by a simple formula substitution method.

Let N be the number of students
N-1=4j (Coz 1 subtracted from the Dividend would make it perfectly divisible by 4)
N-1=6k (Coz 1 subtracted from the Dividend would make it perfectly divisible by 6)

4j=6k
2^2j=3*2k

So, N-1 has both 2^2 and 3 among its prime factors
N-1=(2^2)(3)x
N-1=12x
N=12x+1

Only x=48 fits the requirement. So, N=49. I'm guessing this method was pretty accurate

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review