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rakeshd347: Master | Next Rank: 500 Posts; Posts: 391; Joined: Sat Mar 02, 2013 5:13 amFollowed by: 4 members; Thanked: 50 times

by rakeshd347 » Sun Oct 13, 2013 1:49 am

If Â¡5! = (1)(2)(3)(4)(5)(5)(4)(3)(2)(1), then Â¡17! - !16! =

A) Â¡1!

B) (Â¡16!)(Â¡4!)(2)

C) (Â¡16!)(12)(2)

D) 17^2

E) (Â¡16!)(12^2)(2)

Last edited by rakeshd347 on Sun Oct 13, 2013 2:21 am, edited 1 time in total.

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Source: Beat The GMAT — Problem Solving | Sun Oct 13, 2013 1:49 am

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

by theCodeToGMAT » Sun Oct 13, 2013 2:08 am

I tried but got a very different Answer

i17! - i16!

(17!)^2 - (16!)^2

(17!+16!)(17!-16!)

= 16!(17+1)16!(17-1)

= (16!)^2 (18)(16)

= (i16!) * 288

R A H U L

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rakeshd347: Master | Next Rank: 500 Posts; Posts: 391; Joined: Sat Mar 02, 2013 5:13 amFollowed by: 4 members; Thanked: 50 times

by rakeshd347 » Sun Oct 13, 2013 2:22 am

theCodeToGMAT wrote:I tried but got a very different Answer

i17! - i16!

(17!)^2 - (16!)^2

(17!+16!)(17!-16!)

= 16!(17+1)16!(17-1)

= (16!)^2 (18)(16)

= (i16!) * 288

This is the correct answer indeed. Sorry there was some edit problem and square sign in E didn't come properly but your solution is perfect.
Thanks

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vipulgoyal: Master | Next Rank: 500 Posts; Posts: 468; Joined: Mon Jul 25, 2011 10:20 pmFollowed by: 4 members; Thanked: 29 times

by vipulgoyal » Mon Oct 14, 2013 12:36 am

I have a little query here "i" should be Precisely defined as function else i could also be 5! and in that case entire solution will be differ

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » Tue Oct 15, 2013 5:03 pm

vipulgoyal wrote:I have a little query here "i" should be Precisely defined as function else i could also be 5! and in that case entire solution will be differ

I'm not sure exactly what you're asking, but I think you're wondering if the language of "i" signifies a function generally.

In this question, it's not actually a lowercase "i" but rather an upside-down exclamation point (!). Funny story... this question actually stemmed from a dream I had! I dreamed that I was doing factorial problems, and came across a "Spanish factorial" (in Spanish, an exclamation begins with an inverted exclamation point, and ends with a rightside-up one). In my dream, I wasn't sure how to solve the problem... because "Spanish factorials" don't actually exist! I told my coworkers about the dream, we all laughed about it, and this problem was the result.

I don't know if that actually helps to answer your question, but the larger idea is that whenever we're given function language, we want to apply the same definition given to the new circumstance.

In this case, Â¡n! = 1*2*...*(n - 1)*n*n*(n - 1)*...*1. We just need to follow that definition for 17 and 16, as TheCode did correctly.

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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vipulgoyal: Master | Next Rank: 500 Posts; Posts: 468; Joined: Mon Jul 25, 2011 10:20 pmFollowed by: 4 members; Thanked: 29 times

by vipulgoyal » Tue Oct 15, 2013 10:16 pm

quant in dreams too

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