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:

The problem defines a made-up symbol; this type of problem is essentially asking you to follow directions. The weird symbol means a sort of “double factorial”: take the factorial and then take it again! For example, ¡5! would be (5)(4)(3)(2)(1)(5)(4)(3)(2)(1).

¡17! and ¡16! would work the same way as ¡5!, but nobody would want to multiply those out without a calculator. Is there a shortcut? Glance at the form of the answers—most still use the weird upside-down-exclamation symbol. There must be a way, then, to rewrite ¡17! and ¡16! in another form.

There is! The two numbers are close to identical, but ¡17! contains two additional factors: 17 and 17. Factor out a ¡16! from the two terms: ¡17! - ¡16! = ¡16! (17×17 – 1)

Glance at the answers. ¡16! is in three of them. Do any match? First, simplify the (17×17 – 1) part. 172 = 289, and 289 – 1 = 288. Find something that matches ¡16! (288) (B) (¡16!)(¡4!)(2) (C) (¡16!)(12)(2) (E) (¡16!)(122)(2)

Answer (C) is too small. Answer (E) is easier to process than (B); start with (E). 122 = 144. (144)(2) = 288. Bingo!

The problem defines a made-up symbol; this type of problem is essentially asking you to follow directions. The weird symbol means a sort of “double factorial”: take the factorial and then take it again! For example, ¡5! would be (5)(4)(3)(2)(1)(5)(4)(3)(2)(1).

¡17! and ¡16! would work the same way as ¡5!, but nobody would want to multiply those out without a calculator. Is there a shortcut? Glance at the form of the answers—most still use the weird upside-down-exclamation symbol. There must be a way, then, to rewrite ¡17! and ¡16! in another form.

There is! The two numbers are close to identical, but ¡17! contains two additional factors: 17 and 17. Factor out a ¡16! from the two terms: ¡17! - ¡16! = ¡16! (17×17 – 1)

Glance at the answers. ¡16! is in three of them. Do any match? First, simplify the (17×17 – 1) part. 172 = 289, and 289 – 1 = 288. Find something that matches ¡16! (288) (B) (¡16!)(¡4!)(2) (C) (¡16!)(12)(2) (E) (¡16!)(12^2)(2)

Answer (C) is too small. Answer (E) is easier to process than (B); start with (E). 122 = 144. (144)(2) = 288. Bingo!

The correct answer is (E).

So you have basically \(17!^2-16!^2\), you can rewrite that as \(16!^2\)*(\(17^2\)-1) = \(16!^2\)*(289-1) = \(16!^2\)*(288)

now look at the answers, and what the stem tells you; you're told that ¡n!=n!^2, so \(16!^2\) = ¡16!, and 288 is just 12^2 [144]*2,

Re: If ¡n! = (n!)^2, then ¡17! - ¡16! = [#permalink]

Show Tags

11 Apr 2015, 13:37

Hello from the GMAT Club BumpBot!

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. _________________

MBA Admission Calculator Officially Launched After 2 years of effort and over 1,000 hours of work, I have finally launched my MBA Admission Calculator . The calculator uses the...

Final decisions are in: Berkeley: Denied with interview Tepper: Waitlisted with interview Rotman: Admitted with scholarship (withdrawn) Random French School: Admitted to MSc in Management with scholarship (...

The London Business School Admits Weekend officially kicked off on Saturday morning with registrations and breakfast. We received a carry bag, name tags, schedules and an MBA2018 tee at...