Big numbers

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

Big numbers

by Brent@GMATPrepNow » Sun Dec 28, 2008 11:54 am

If n = 2×3×5×7×11×13×17, then which of the following statements are true?
I. n^2 is divisible by 600
II. n+19 is divisible by 19
III. (n+4)/2 is even

A) I only
B) II only
C) III only
D) I and III
E) None of the above

Brent Hanneson - Creator of GMATPrepNow.com

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Source: Beat The GMAT — Problem Solving | Sun Dec 28, 2008 11:54 am

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pm; Thanked: 331 times; Followed by:11 members

by cramya » Sun Dec 28, 2008 11:57 am

Are true meaning must be true??

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Sun Dec 28, 2008 11:59 am

Since n is a set value (constant value), "must be true," "could be true" and "are true" all have the same meaning.

Brent Hanneson - Creator of GMATPrepNow.com

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pm; Thanked: 331 times; Followed by:11 members

by cramya » Sun Dec 28, 2008 12:00 pm

I would say III only.

N IS EVEN N+4 IS ALSO EVEN THEREFORE MUST BE DIVISIBLE BY 2

n^2 is not divisible by 600 since n^2 will be missing a 2

n^2+19 will not be divisible by 19 since n^2 is not

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Sun Dec 28, 2008 12:04 pm

n^2+19 will not be divisible by 19 since n^2 is not

Be careful. The question refers to n+19, not n^2+19

Brent Hanneson - Creator of GMATPrepNow.com

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vivek.kapoor83: Legendary Member; Posts: 833; Joined: Mon Aug 04, 2008 1:56 am; Thanked: 13 times

by vivek.kapoor83 » Sun Dec 28, 2008 12:05 pm

i think C.
coz...divic=nd by n^2 , 2 remains in Denom.
in 3...
n +4 = even
n = even -even =even
so...true
1 is wrong , 3 is true
no need to cal 2.as only option left with this is C

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parallel_chase: Legendary Member; Posts: 1153; Joined: Wed Jun 20, 2007 6:21 am; Thanked: 146 times; Followed by:2 members

Re: Big numbers

by parallel_chase » Sun Dec 28, 2008 12:20 pm

Brent Hanneson wrote:If n = 2×3×5×7×11×13×17, then which of the following statements are true?
I. n^2 is divisible by 600
II. n+19 is divisible by 19
III. (n+4)/2 is even

A) I only
B) II only
C) III only
D) I and III
E) None of the above

I - 600 = 2^3 * 5^2 * 3

therefore n^2 is not divisible by 600, coz in denominator we would be left with one 2.

Eliminate - A and D.

II - n+19 is divisible by 19
Only way this could be possible is when n is a multiple of 19 i.e. prime number
Eliminate - B

III
(n+4)/2 = even

Since we have all prime numbers here, we can do a test with only 2 prime numbers

let n=2*3 = 6

(6+4)/2 = 5

hence eliminate C

Therefore, E.

OA?

No rest for the Wicked....

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Sun Dec 28, 2008 12:32 pm

Nice work, Parallel Chase

I might add the full explanation for III here:

If n = 2×3×5×7×11×13×17, then n+4 = n = 2×3×5×7×11×13×17+4
We can factor out a 2 to get: n+4 = 2(3×5×7×11×13×17 + 2)

So, (n+4)/2 = 2(3×5×7×11×13×17 + 2)/2
= 3×5×7×11×13×17 + 2
= odd + even
= odd

Last edited by Brent@GMATPrepNow on Sun Dec 28, 2008 12:41 pm, edited 1 time in total.

Brent Hanneson - Creator of GMATPrepNow.com

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pm; Thanked: 331 times; Followed by:11 members

by cramya » Sun Dec 28, 2008 12:35 pm

Be careful. The question refers to n+19, not n^2+19

Thanks that was a typo.

If n was divisible by 19 then n+19 is divisible by 19

If n^2 is divisible by 19 then n^2+19 is divisible by 19

In the problem above neither n nor n^2 is divisible by 19 (If n was divisible by 19 then n^2 is also divisible by 19)

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pm; Thanked: 331 times; Followed by:11 members

by cramya » Sun Dec 28, 2008 12:42 pm

Rushing does not help! sure to make mistakes like I did :roll:

2*3*5*7*11*13*17 + 4 /2

2 (3*5*7*11*13*17 + 2) /2

= 1 * (odd+even)

= 1 * odd
=odd

Hence E)

Good solution PC and a good problem Brent!