Data Sufficiency Question - I can't find my error - The Beat The GMAT Forum

Data Sufficiency Question - I can't find my error

Expert replies

Captain_of_Industry 1984: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Tue Mar 05, 2013 11:59 am

by Captain_of_Industry 1984 » Tue Jan 07, 2014 2:05 pm

Hey guys,

I have a question on this D.S. problem, can someone explain why my solution is incorrect?

If k is a positive integer and n = k(k + 7), is n divisible by 6?

1. K is odd

Test cases:
K=1 n=1(1+7) = 8, is 8/6 NO
K=3 n=3(3+7)=30, is 30/6 YES
INSUFFICIENT

2. When k is divided by 3, the remainder is 2

Test Cases:
K=1 1/3=0 remainder 2, n=1(1+7) = 8, is 8/6 NO
K=5 5/3 =1 remainder 2, n=5(5+7) =60, is 60/6 YES
INSUFFICIENT

Combined:
K=1 overlaps - NO
K=5 overlaps - YES

OA - B

I've seen a complex math approach that seems to prove that B is sufficient but why would the test cases produce a different result? What am I missing here?

Thanks in advance.

Like this post

Source: Beat The GMAT — Data Sufficiency | Tue Jan 07, 2014 2:05 pm

theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Tue Jan 07, 2014 6:50 pm

Statement 2:
k/3 leaves remainder 2

that means "k" can be
2 ==> n = 2*9 YES
5 ==> n = 5*12 YES
8 ==> n = 8*15 YES
SUFFICIENT

The problem in your solution is that you assumed k = 1, which is incorrect as per the condition. 1/3 leaves remainder "1" and not "2"

R A H U L

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Jan 07, 2014 7:58 pm

Captain_of_Industry 1984 wrote: 2. When k is divided by 3, the remainder is 2

This means k is 2 more than a multiple of 3:
k = 3a + 2, where a is a nonnegative integer.
Thus:
k = 2, 5, 8, 11, 14, 17...

Given that n = k(k+7), we get:
If k=2, then n = 2*9.
If k=5, then n = 5*12.
If k=8, then n = 8*15.
In every case, n is divisible by 6.
SUFFICIENT.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Tue Jan 07, 2014 11:19 pm

Captain_of_Industry 1984 wrote:Hey guys,

I have a question on this D.S. problem, can someone explain why my solution is incorrect?

If k is a positive integer and n = k(k + 7), is n divisible by 6?

1. K is odd

Test cases:
K=1 n=1(1+7) = 8, is 8/6 NO
K=3 n=3(3+7)=30, is 30/6 YES
INSUFFICIENT

2. When k is divided by 3, the remainder is 2

Test Cases:
K=1 1/3=0 remainder 2, n=1(1+7) = 8, is 8/6 NO
K=5 5/3 =1 remainder 2, n=5(5+7) =60, is 60/6 YES
INSUFFICIENT

Combined:
K=1 overlaps - NO
K=5 overlaps - YES

OA - B

I've seen a complex math approach that seems to prove that B is sufficient but why would the test cases produce a different result? What am I missing here?

Thanks in advance.

2. When k is divided by 3, the remainder is 2

It means that k = 3p + 2 for any non-negative integer p. When p = 0, k = 2, and the remainder when 3 divides 2 is 2 only. So n = (3p + 2) (3p + 2 + 7) = (3p + 2) (3p + 9) = 3 (p + 3) (3p + 2). Now, if p is even, 3p + 2 is also even, which makes the expression 3 (p + 3) (3p + 2) divisible by 6. And, if p is odd, p + 3 is even, which makes the expression 3 (p + 3) (3p + 2) again divisible by 6. In other words, if k = 3p + 2, then n is always divisible by 6. Hence, sufficient

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.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