Manhattan GMAT-Hey-Im a little confused here

Expert replies

dddanny2006: Master | Next Rank: 500 Posts; Posts: 209; Joined: Thu Jan 12, 2012 12:59 pm

by dddanny2006 » Mon Nov 11, 2013 3:49 am

Answer the questions with a Yes,No or Cannot be determined.
1.If a is divided by 7 or by 18,an integer results.Is (a/42) an integer?

2.If j is divisible by 12 and 10,is j divisible by 24?

These problems are from Manhattan Number Properties guide.What I fail to understand is the difference between the 2 problems.They have been solved by the PrimeBox method.Why in the 2nd answer we see three boxes drawn?,in comparison to the one thats drawn in the 1st problem solution?I have attached the way they have drawn their boxes.

Thanks

Attachments

Like this post

Source: Beat The GMAT — Problem Solving | Mon Nov 11, 2013 3:49 am

ganeshrkamath: Master | Next Rank: 500 Posts; Posts: 283; Joined: Sun Jun 23, 2013 11:56 pmFollowed by: 26 members; Location: Bangalore, India; Thanked: 97 times; GMAT Score:750

by ganeshrkamath » Mon Nov 11, 2013 6:53 am

dddanny2006 wrote:Answer the questions with a Yes,No or Cannot be determined.
1.If a is divided by 7 or by 18,an integer results.Is (a/42) an integer?

2.If j is divisible by 12 and 10,is j divisible by 24?

These problems are from Manhattan Number Properties guide.What I fail to understand is the difference between the 2 problems.They have been solved by the PrimeBox method.Why in the 2nd answer we see three boxes drawn?,in comparison to the one thats drawn in the 1st problem solution?I have attached the way they have drawn their boxes.

Thanks

I don't know the PrimeBox method, but here's my solution:

1. a is a multiple of LCM(7,18)
a = k * 126 _____________(k is an integer)
a/42 = k*126/42 = 3k (also an integer)
Yes.

2. j is a multiple of LCM(12,10)
j = m * 60 ______________(m is an integer)
j/24 = m*60/24 = 5m/2
This may or may not result in an integer.
Cannot be determined.

Cheers

Every job is a self-portrait of the person who did it. Autograph your work with excellence.

Kelley School of Business (Class of 2016)
GMAT Score: 750 V40 Q51 AWA 5 IR 8
https://www.beatthegmat.com/first-attemp ... tml#688494

Like this post

Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

by Abhishek009 » Mon Nov 11, 2013 7:05 am

dddanny2006 wrote:Answer the questions with a Yes,No or Cannot be determined.
1.If a is divided by 7 or by 18,an integer results.Is (a/42) an integer?

2.If j is divisible by 12 and 10,is j divisible by 24?

These problems are from Manhattan Number Properties guide.What I fail to understand is the difference between the 2 problems.They have been solved by the PrimeBox method.Why in the 2nd answer we see three boxes drawn?,in comparison to the one thats drawn in the 1st problem solution?I have attached the way they have drawn their boxes.

Thanks

Really in love with these kind of problems , post more if U have such..

1.If a is divided by 7 or by 18,an integer results.Is (a/42) an integer?

The green highlighted part simply means that the number A is completely divisible by both 7 and 18

The question states that the number A is divisible by 7 as well as 18

We can write A as -

A = 7 M * 18 N

Now the question here ask - Is (a/42) an integer?

Find out the factors of the denominator -

42 = 2*3*7

The part (a/42) can be re stated as -

A = 7 M * 18 N / 42 = 2*3*7

Which in every possible case will yield an integer...

2.If j is divisible by 12 and 10,is j divisible by 24?

Going to solve this one with the help of LCM

Since J is divisible by 12 and 10 , the least number possible is LCM ( 12 and 10 ) 60

So the number series of this pattern will be -

60 , 120 , 180 .......

Test each one individually

60/24 = Not completely divisible

120/24 = 5 Completely divisible

180 / 24 = Not completely divisible

So , we can't predict this one...

Abhishek

Like this post

dddanny2006: Master | Next Rank: 500 Posts; Posts: 209; Joined: Thu Jan 12, 2012 12:59 pm

by dddanny2006 » Mon Nov 11, 2013 7:48 am

Thanks your your inputs guys.I'd prefer if someone explains the box method to me.

Like this post

Mathsbuddy: Master | Next Rank: 500 Posts; Posts: 447; Joined: Fri Nov 08, 2013 7:25 amFollowed by: 1 member; Thanked: 25 times

by Mathsbuddy » Tue Nov 12, 2013 9:18 am

I don't know what the box method is, but maybe this will simplify the algebra:

Question 1)

a is a multiple of both 7 and 18, therefore a is a multiple of 7 x 18 = 126 (LCM)
As 126 is a multiple of 42 (because 126/42 = 3) then it is TRUE.

Question 2)

j is a multiple of both 12 and 10, therefore j is a multiple of 60 (LCM, divisible by both 12 and 10)
60/24 = 2.5 which is not an integer
Odd multiples of 2.5 produce a non-integer
Even multiples of 2.5 produce an integer
Therefore the answer is TRUE 50% of the time and NOT TRUE 50% of the time
Conclusion: Cannot be determined without more information.

Like this post

GMAT/MBA Expert

ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » Wed Nov 13, 2013 3:00 pm

The primary difference between these two questions is that 7 and 18 do not SHARE FACTORS, but 12 and 10 do.

"Prime boxes" are handy ways of visualizing the prime factors of a given number - the component pieces. If a number is divisible by 18, for example, we can say that it has a 2, 3, and 3 in its "prime box." It might also have other factors, but those are the ones we know about. So we can say that it has AT LEAST a 2 and two 3's.

1) a is a multiple of both 7 and 18
Translate this as: "a has in its prime box at least one 7, and at least one 2 and two 3's." Since 42 is composed of one 2, one 3, and one 7, then a definitely has all of the component pieces of 42, so it's divisible.

2) j is a multiple of both 12 and 10
Translate this as: "j has in its prime box at least two 2's and one 3 (the factors of 12), and at least one 2 and one 5 (the factors of 10)."
If we say that j has "at least two 2's" and "at least one 2", can we then conclude that it has three 2's? No, because one of those 2's might be overlapping. All we can conclude is that it has at least two 2's in its prime box.

Since 24 has three factors of 2, it might go into j, but it might not. Inconclusive.

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 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