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 500,000 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:

Re: If n is an integer greater than 50, then the expression (n^2 [#permalink]

Show Tags

12 May 2014, 20:12

2

This post received KUDOS

(n^2-2n)(n^2-1) = (n-1)n(n+1)(n^2-2)

ii. Product of 3 consecutive integers is always divisible by 3 and since one of n-1,n,n+1 is even => The product is divisible by 6

i. n= odd => n-1 and n+1 are even, so the product is divisible by 4 n= even => n and n^2-2 are even, so the product is divisible by 4

iii. for the expression to be divisible by 18, the product should have 3,3,2 lets consider n = 100 and n= 101 n=100, 99*100*101*9998 => 99 has two threes and overall expression has plenty of 2's n=101, 100*101*102*10199 => plenty of 2's but no 3 (sum of digits of 10199 = 20; not divisible by 3; hence 10199 not divisible by 3)

Therefore, i & ii, Hence C
_________________

Do not hesitate to share appreciation, hit Kudos!!

Re: If n is an integer greater than 50, then the expression (n^2 [#permalink]

Show Tags

13 May 2014, 03:35

1

This post received KUDOS

(n^2-2n)(n^2-1) = n(n-2)(n-1)(n+1) or (n-2)(n-1)n(n+1) this represents product of 4 consecutive integers.

Out of these 4 integers, two will be even and two will be odd.

If the first term is divisible by 3 then the last term will also divisible by 3. (check by taking 4 consecutive integers as 54,55,56,57) If the first term is not divisible by 3 then out of 4 consecutive integers, only one will be divisible by 3. (check by taking 4 consecutive integers as 52,53,54,55)

Hence 4 consecutive expressions may contain minimum 1 and maximum two integers divisible by 3.

Divisibility by 4: Product of two even number is always divisible by 4. hence expression is divisible by 4. Divisibility by 6: Product of an even number and a number divisible by 3 will be divisible by 6. Divisibility by 18: Product of an even number and two numbers divisible by 3 will be divisible by 18. However, if first number is not divisible by 3, there will be only 1 (not 2) number divisible by 3. Therefore we can't be sure that there will be 2 numbers divisible by 3. Hence divisibility by 18 is not sure.

The expression is divisible by 4 and 6 only . Hence C _________________

Please click on Kudos, if you think the post is helpful

Re: If n is an integer greater than 50, then the expression (n^2 [#permalink]

Show Tags

25 Nov 2016, 16:27

Hi,

Can you help me clarify something. if the stem says that n is greater than 50, should not I use 51=n as the smallest test number. if so, i get.... 49*50*51*52?

Your insight is appreciated. I got the wrong answer of E, but if you can help me close the gap. I got stuck in the words "if n is an integer greater than 50"

Can you help me clarify something. if the stem says that n is greater than 50, should not I use 51=n as the smallest test number. if so, i get.... 49*50*51*52?

Your insight is appreciated. I got the wrong answer of E, but if you can help me close the gap. I got stuck in the words "if n is an integer greater than 50"

Dear lalania1,

I'm the author of this question and I am happy to respond.

My friend, with all due respect, it is a HUGE mistake to approach this a plug in problem. One would get absurdly large numbers if one used that method. Plugging-in numbers is not at all the best way to approach this problem. See the OE on this blog article.

Re: If n is an integer greater than 50, then the expression (n^2 [#permalink]

Show Tags

25 Nov 2016, 17:15

Hi Mike,

Yes, I see your point. In essence, the question says "when will the condition MUST apply" for all numbers. Using the logic of consecutive integers and the solution steps you suggest I can clearly see how it works.

thanks Mike. I am about to finish your videos on Number Properties and then ready to take the 5 question quiz.

\((n^2 - 2n)(n^2 - 1)\) =n(n-2)(n-1)(n+1) =(n-2)(n-1)n(n+1) So, its a multiple for 4 consecutive integers, which means there are two even numbers and two odd numbers. So it must be divisible by 4. Also among the 4 consecutive numbers, there must be atleast one multiple of 3. So, it must be divisible by 6. Now the number may or may not be divisible by 18 = 3*3*2.

Lets check for a value of n = 51 So number = 49*50*51*52

Bingo this no is not divisible by 18. hence (I) & (II) only . Answer C _________________

Version 8.1 of the WordPress for Android app is now available, with some great enhancements to publishing: background media uploading. Adding images to a post or page? Now...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...