Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 19 May 2013, 10:07

# Confusing MGMAT quant problem on Number Properties

Author Message
TAGS:
Intern
Joined: 18 May 2011
Posts: 5
Followers: 0

Kudos [?]: 0 [0], given: 0

Confusing MGMAT quant problem on Number Properties [#permalink]  28 Jul 2011, 17:29
HI everyone. I'm very very very new to this forum. I am studying for the GMAT and started with the MGMAT books. I'm doing Number Properties right now. There's a question in their first chapter that goes like this:

Is x divisible by 120?
(1) x is divisible by 12
(2) x is divisible by 30

So I drew the prime boxes for 12 and 30, and obtained, correctly that 12's prime factors are 2,2,3 and 30's prime factors are 2, 3, 5. Then, I constructed the prime box for x as 2, 2, 5.... Notice that I did not include another 2 because it is redundant. I applied the same logic to not including the 3, since it appeared in both prime boxes. I did get the right answer, i.e., (E) cannot be determined, but apparently for the wrong reasons, which frighten me.

According to the MGMAT answer key, the prime box for x SHOULD contain the 3. In other words, the prime box for x should be: 2, 2, 3, 5.

My question is, if a 2 is considered redundant (as the MGMAT answer key reminds you), then why wouldn't this apply to other numbers that appear in both prime boxes as well, i.e., the number 3 appears as a factor of both 12 and 30.

Thank you very much for your time.
Dors
 Manhattan GMAT Discount Codes Kaplan GMAT Prep Discount Codes GMAT Pill GMAT Discount Codes
Senior Manager
Joined: 08 Jan 2009
Posts: 337
GMAT 1: 770 Q50 V46
Followers: 16

Kudos [?]: 58 [0], given: 7

Re: Confusing MGMAT quant problem on Number Properties [#permalink]  28 Jul 2011, 19:31
dorsvenabili wrote:

So I drew the prime boxes for 12 and 30, and obtained, correctly that 12's prime factors are 2,2,3 and 30's prime factors are 2, 3, 5. Then, I constructed the prime box for x as 2, 2, 5.... Notice that I did not include another 2 because it is redundant. I applied the same logic to not including the 3, since it appeared in both prime boxes. I did get the right answer, i.e., (E) cannot be determined, but apparently for the wrong reasons, which frighten me.

According to the MGMAT answer key, the prime box for x SHOULD contain the 3. In other words, the prime box for x should be: 2, 2, 3, 5.

It is not redundant. Think of it like this.

Is x divisible by 4?

x = 2 <---- no
x = 2*2 <---- yes

Clearly we need to know the number of twos to answer this question.

To know that x is divisible by 120, it must have 2,2,2,3,5 as its prime factors (at a minimum). If it has only one 2, then it will not be divisible by 120.

Now on the other hand, we are told through 1) and 2) that x is divisible by 12 and 30. The most information we can glean from this is that

x = 2,2,3,5

Note that when we do THIS, we don't just lump all factors from 1) and 2) and get

x = 2,2,2,3,3,5

This is because we could have 'seen' the some number twice. Consider

x = 60 = 2*3*5*2

This is divisible by 1) and 2), yet is not divisible by 120...
_________________
Intern
Joined: 20 Apr 2011
Posts: 46
Location: United Kingdom
Followers: 0

Kudos [?]: 0 [0], given: 9

Re: Confusing MGMAT quant problem on Number Properties [#permalink]  29 Jul 2011, 03:02
good explanation, regards
Intern
Joined: 11 May 2011
Posts: 24
Followers: 0

Kudos [?]: 7 [0], given: 1

Re: Confusing MGMAT quant problem on Number Properties [#permalink]  01 Aug 2011, 00:47
Let us take A. first :
divisible by 12: numbers divisible by 12 are 12,24,36,48...... 120.....

hence A alone not sufficient. since we have numbers less than 120 divisible by 12

Let us take B.
divisible by 30: numbers divisible by 30 are 30,60,90,120....

Hence B alone is not sufficient. Since we have numbers less than 120 divisible by 30

Let us combine : We have number divisible by 12 and 30 :
to find combined divisibility we take LCM. LCM of 12 and 30 can be found by reducing each number to its prime factors

12 : 2*3*2
30: 2*3*5

Now LCM can be obtained by taking highest powers of each prime factor and multiplying them 2^2*3^1*5^1 i.e 2*2*3*5 = 60

This number is also not divisible by 120.

Hence option E. We need more data and both together are in sufficient.
Intern
Joined: 18 May 2011
Posts: 5
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: Confusing MGMAT quant problem on Number Properties [#permalink]  11 Aug 2011, 15:29
Dear pike and raghava747: THANK YOU SO MUCH for your explanations. I am SO SORRY it took me so long to respond, but I'm living in an island in the Caribbean with haphazard electricity AND spotty internet service. I finally understood that the 3 could have been seen twice and hence; the option is E. Thank you very very much again. I really really appreciate it.
Re: Confusing MGMAT quant problem on Number Properties   [#permalink] 11 Aug 2011, 15:29
Similar topics Replies Last post
Similar
Topics:
Help with Number Properties.. (quant) 0 14 Jul 2007, 04:45
2 MGMAT's Number Properties (4th Edition) - OG 12 Problems? 2 30 Jul 2010, 07:23
3 Number Properties Problem 11 22 Aug 2010, 20:14
Quant question. Number properties 7 13 Nov 2011, 14:53
Is a*b*c divisible by 24? (1) a,b, and c are consecutive 3 28 May 2012, 05:06
Display posts from previous: Sort by