Data Sufficiency: Number Properties

Expert replies

saracuse: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Sun Jun 08, 2008 6:17 am; Location: New York, NY

by saracuse » Fri Sep 18, 2009 12:06 pm

Having issue with wording here. can someone help?

#132.

If the integer n>1, is n =2?

1) n has exactly two positive factors

2) the Difference of any two distinct positive factors of n is odd.

the Answer is B. #2 is sufficient
However .. see below

Answer:

1) n is a prime number, but n could be = to 2, 3, 5, etc. Not sufficient.

2) if n is 5.. factors are 5 and 1.. so difference is even. So could be 2. 2-1 = odd number

BUT, what about 6 -- 6-1. odd number. what about 3-2 = odd number. N and 1 are still factors.

Am i missing something in the language in Assumption #2? In #2, we stll dont know that N is a prime number. But the answer is B....

Like this post

Source: Beat The GMAT — Data Sufficiency | Fri Sep 18, 2009 12:06 pm

GMAT/MBA Expert

Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

Re: Data Sufficiency: Number Properties

by Ian Stewart » Fri Sep 18, 2009 4:57 pm

saracuse wrote:Having issue with wording here. can someone help?

#132.

If the integer n>1, is n =2?

1) n has exactly two positive factors

2) the Difference of any two distinct positive factors of n is odd.

the Answer is B. #2 is sufficient
However .. see below

Answer:

1) n is a prime number, but n could be = to 2, 3, 5, etc. Not sufficient.

2) if n is 5.. factors are 5 and 1.. so difference is even. So could be 2. 2-1 = odd number

BUT, what about 6 -- 6-1. odd number. what about 3-2 = odd number. N and 1 are still factors.

Am i missing something in the language in Assumption #2? In #2, we stll dont know that N is a prime number. But the answer is B....

There are four positive factors of 6: 1, 2, 3 and 6. From these numbers, we can make five different positive differences (we can get 1 in two different ways):

6 - 3 = 3
6 - 2 = 4
6 - 1 = 5
3 -2 = 1
3 -1 = 2
2 - 1 = 1

Some of these differences are odd, some even.

In general, if n is even, and n > 2, then n has itself and 2 as factors, and the difference n - 2 will certainly be even. If n is odd, and n > 1, then n has itself and 1 as factors, and n - 1 will be even. So the only possible value of n, given Statement 2, is n = 2.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

Like this post

jiteshch: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Tue Dec 16, 2008 12:42 am; Location: chennai

Can somebody help me with this

by jiteshch » Fri Sep 18, 2009 8:10 pm

DS question ::
Is |x|< 1?
(1) |x + 1| = 2|x - 1|
(2) |x - 3| â‰ 0

I am finding difficulties in inequalties and somebody suggest me how i can get extra pratice in these kinda sums...

Like this post

adamsmith2009: Senior | Next Rank: 100 Posts; Posts: 36; Joined: Fri Mar 27, 2009 6:53 pm

by adamsmith2009 » Sat Sep 19, 2009 5:05 pm

There are four positive factors of 6: 1, 2, 3 and 6. From these numbers, we can make five different positive differences (we can get 1 in two different ways):

6 - 3 = 3
6 - 2 = 4
6 - 1 = 5
3 -2 = 1
3 -1 = 2
2 - 1 = 1

Some of these differences are odd, some even.

In general, if n is even, and n > 2, then n has itself and 2 as factors, and the difference n - 2 will certainly be even. If n is odd, and n > 1, then n has itself and 1 as factors, and n - 1 will be even. So the only possible value of n, given Statement 2, is n = 2.

Ian,

Statement 2 says that the difference between any two distinct factors of n is odd. So taking 6 as an example, there are many ways for this to occur. E.g., 6 - 3 = 3, 6 - 1 = 5, 2 - 1 = 1. How/why did you choose 2 - 1 = 1 and know that would be sufficient to answer whether n = 2? I don't understand. Thanks.

Like this post

GMAT/MBA Expert

Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Sat Sep 19, 2009 7:12 pm

adamsmith2009 wrote: Ian,

Statement 2 says that the difference between any two distinct factors of n is odd. So taking 6 as an example, there are many ways for this to occur. E.g., 6 - 3 = 3, 6 - 1 = 5, 2 - 1 = 1. How/why did you choose 2 - 1 = 1 and know that would be sufficient to answer whether n = 2? I don't understand. Thanks.

You're only demonstrating that the difference between *some* pairs of factors of 6 is odd, not that the difference between *any* (or, if it's more clear, *every*) pair of factors of 6 is odd. Since 6 is divisible by itself and by 2, there is a pair of factors with an even difference: 6 -2 = 4. The same will be true for any even number larger than 2. Similarly, any odd number - 9, for example - will have itself and 1 as a factor, and therefore two factors with an even difference: 9-1 = 8.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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