Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Ah, you are right. I have omitted one additional step.

Group the a's together and group the numbers together to get: ka + k(k-1)/2 Factor out a k. k(a+ (k-1)/2) For this to be divisible by k, (a + (k-1)/2) must be a integer. So therefore k must be odd, otherwise the (k-1)/2) term would be a fraction...

Is k2 odd? (1) k - 1 is divisible by 2. (2) The sum of k consecutive integers is divisible by k.

Question Is k^2 odd?

Stmt1: k-1 is divisible by 2.

(k-1)/2 = m where m is some integer k-1 = 2m k = 2m+1. Now this is the equation of any odd number

Hence k is odd. Therefore k^2 is odd. Sufficient.

Stmt2: The sum of k consecutive integers is divisible by k sum = k(k+1)/2 Sum/k = m where m is some integer k(k+1)/2k = m (k+1)/2 = m k=2m-1. This again represents odd number.

Hence k is odd. Therefore k^2 is odd. Sufficient.

OA D _________________

My dad once said to me: Son, nothing succeeds like success.

I would like to point out a small possible improvement in your analysis, which is otherwise on track.

The sum of k consecutive integers is not k(k+1)/2. This is the expression for the sum of the first k natural numbers. Example: The sum of three consecutive integers 50,51,and 52 is not 3(3+1)/2.

The expression for the sum of k consecutive integers is ak + k(k-1)/2, where a is the first number and k is the number of terms. In this question, you may have assumed that k consecutive integers can also be n consecutive natural numbers and so used the expression k(k+1)/2.

The OA is (D) as explained by cellydan _________________

Is k2 odd? (1) k - 1 is divisible by 2. (2) The sum of k consecutive integers is divisible by k.

Question Is k^2 odd?

Stmt1: k-1 is divisible by 2.

(k-1)/2 = m where m is some integer k-1 = 2m k = 2m+1. Now this is the equation of any odd number

Hence k is odd. Therefore k^2 is odd. Sufficient.

Stmt2: The sum of k consecutive integers is divisible by k sum = k(k+1)/2 Sum/k = m where m is some integer k(k+1)/2k = m (k+1)/2 = m k=2m-1. This again represents odd number.

Is k2 odd? (1) k - 1 is divisible by 2. (2) The sum of k consecutive integers is divisible by k.

Question Is k^2 odd?

Stmt1: k-1 is divisible by 2.

(k-1)/2 = m where m is some integer k-1 = 2m k = 2m+1. Now this is the equation of any odd number

Hence k is odd. Therefore k^2 is odd. Sufficient.

Stmt2: The sum of k consecutive integers is divisible by k sum = k(k+1)/2 Sum/k = m where m is some integer k(k+1)/2k = m (k+1)/2 = m k=2m-1. This again represents odd number.

Hence k is odd. Therefore k^2 is odd. Sufficient.

OA D

Both statements imply that k is an integer.

Is k^2 odd?

(1) k - 1 is divisible by 2 --> \(k-1=even\) --> \(k=even+1=odd=integer\) --> \(k^2=odd^2=odd\). Sufficient.

(2) The sum of k consecutive integers is divisible by k. Here k must be a positive integer because otherwise the statement does not make sense.

Properties of consecutive integers: • If n is odd, the sum of n consecutive integers is always divisible by n. Given \(\{9,10,11\}\), we have \(n=3=odd\) consecutive integers. The sum is 9+10+11=30, which is divisible by 3. • If n is even, the sum of n consecutive integers is never divisible by n. Given \(\{9,10,11,12\}\), we have \(n=4=even\) consecutive integers. The sum is 9+10+11+12=42, which is NOT divisible by 4.

The statement says that the sum of k consecutive integers is divisible by k, which, according to the above means that k is odd, therefore \(k^2=odd^2=odd\). Sufficient.

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Michigan Ross: Center for Social Impact : The Center for Social Impact provides leaders with practical skills and insight to tackle complex social challenges and catalyze a career in...

The Importance of Financial Regulation : Before immersing in the technical details of valuing stocks, bonds, derivatives and companies, I always told my students that the financial system is...

The following pictures perfectly describe what I’ve been up to these days. MBA is an extremely valuable tool in your career, no doubt, just that it is also...