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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # For every positive odd integer n, the function g(n) is defined to be t

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Intern  Joined: 15 Aug 2013
Posts: 12
WE: Marketing (Energy and Utilities)
For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

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26 00:00

Difficulty:   45% (medium)

Question Stats: 70% (01:46) correct 30% (01:39) wrong based on 326 sessions

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I came across this question on gmatpill. Now i have seen a similar question for even integer product...how do we approach this one...?

For every positive odd integer n, the function g(n) is defined to be the product of all the odd integers from 1 to n, inclusive. If t is the smallest prime factor of g(99) +1, then t is?

(A) between 2 and 19
(B) between 20 and 39
(C) between 40 and 59
(D) between 60 and 79
(E) 80 or greater

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Someday, everything will make perfect sense Math Expert V
Joined: 02 Sep 2009
Posts: 59674
Re: For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

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TheDelhiDude wrote:
I came across this question on gmatpill. Now i have seen a similar question for even integer product...how do we approach this one...?

For every positive odd integer n, the function g(n) is defined to be the product of all the odd integers from 1 to n, inclusive. If t is the smallest prime factor of g(99) +1, then t is?

(A) between 2 and 19
(B) between 20 and 39
(C) between 40 and 59
(D) between 60 and 79
(E) 80 or greater

g(99) = 1*3*5*..*99 = odd.

g(99) + 1 = odd + 1 = even. The smallest prime factor of any even number is 2 --> t = 2.

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Manager  Joined: 21 Jul 2014
Posts: 119
Re: For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

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1
TheDelhiDude wrote:
I came across this question on gmatpill. Now i have seen a similar question for even integer product...how do we approach this one...?

For every positive odd integer n, the function g(n) is defined to be the product of all the odd integers from 1 to n, inclusive. If t is the smallest prime factor of g(99) +1, then t is?

(A) between 2 and 19
(B) between 20 and 39
(C) between 40 and 59
(D) between 60 and 79
(E) 80 or greater

This question tries to trick you into thinking that you have to find the prime factorization of a very huge number. In fact, you won't have to do that at all.

Consider what g(99) means:
g(99) = 1 * 3 * 5 * 7 * 9 * ... * 97 * 99 = some huge number.

You can already establish that the smallest prime factor of that huge number is 3, since it is defined within what g(x) means.

Since t = smallest prime factor (which will always be 3 when n > 1) + 1, we can conclude that t = 4.

Math Expert V
Joined: 02 Sep 2009
Posts: 59674
Re: For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

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1
4
Bunuel wrote:
TheDelhiDude wrote:
I came across this question on gmatpill. Now i have seen a similar question for even integer product...how do we approach this one...?

For every positive odd integer n, the function g(n) is defined to be the product of all the odd integers from 1 to n, inclusive. If t is the smallest prime factor of g(99) +1, then t is?

(A) between 2 and 19
(B) between 20 and 39
(C) between 40 and 59
(D) between 60 and 79
(E) 80 or greater

g(99) = 1*3*5*..*99 = odd.

g(99) + 1 = odd + 1 = even. The smallest prime factor of any even number is 2 --> t = 2.

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Intern  Joined: 15 Aug 2013
Posts: 12
WE: Marketing (Energy and Utilities)
Re: For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

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Thanks Bunuel so its safe to assume if the question involves a product of consecutive odd integers (from any odd no. till any odd no.) and adds 1 to the product, it can be said that the smallest prime factor is 2.

Say if its g(n)=[5x7x9x...any no.]+1 , the smallest prime factor is 2?
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Re: For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

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TheDelhiDude wrote:
Thanks Bunuel so its safe to assume if the question involves a product of consecutive odd integers (from any odd no. till any odd no.) and adds 1 to the product, it can be said that the smallest prime factor is 2.

Say if its g(n)=[5x7x9x...any no.]+1 , the smallest prime factor is 2?

Well, yes. How else?

The product of odd numbers (consecutive or not) is odd. ODD + 1 = EVEN. The smallest prime factor of any even number is 2.
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Manager  Joined: 21 Jul 2014
Posts: 119
Re: For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

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Thanks for the clarification Bunuel, but maybe there could be two interpretations of the question?

My understanding was that the question was defining t = [smallest prime factor of g(99)] + 1, rather than t = smallest prime factor of (g(99)+1).

I thought that because answer choice A did not clarify "between 2 and 19 INCLUSIVE" (which the GMAT typically does, right?).

Either way, the answer choice is A.
Senior Manager  Joined: 20 Aug 2015
Posts: 384
Location: India
GMAT 1: 760 Q50 V44 Re: For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

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2
1
TheDelhiDude wrote:
For every positive odd integer n, the function g(n) is defined to be the product of all the odd integers from 1 to n, inclusive. If t is the smallest prime factor of g(99) +1, then t is?

(A) between 2 and 19
(B) between 20 and 39
(C) between 40 and 59
(D) between 60 and 79
(E) 80 or greater

The key here is not to get intimidated by the huge number g(99)

g(99) = 1*3*5* ...*97*99
We need to find the smallest prime factor of g(99) + 1

We know that:
Odd*Odd = Odd
Odd*Even = Even
Even*Even = Even

Hence g(99) = 1*3*5* ...*97*99 will always be an odd number

We also know that
Odd + Odd = Even
Even + Even = Even
Odd + Even = Odd

Therefore g(99) + 1 has to be an even number
The smallest prime factor of any even number = 2
Hence Option A
Manager  Joined: 10 Feb 2014
Posts: 81
GMAT 1: 690 Q50 V33 Re: For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

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TheDelhiDude wrote:
I came across this question on gmatpill. Now i have seen a similar question for even integer product...how do we approach this one...?

For every positive odd integer n, the function g(n) is defined to be the product of all the odd integers from 1 to n, inclusive. If t is the smallest prime factor of g(99) +1, then t is?

(A) between 2 and 19
(B) between 20 and 39
(C) between 40 and 59
(D) between 60 and 79
(E) 80 or greater

Bunuel: One doubt?

What if the question were reworded to find the largest prime number of g(99)+1?
Math Expert V
Joined: 02 Sep 2009
Posts: 59674
Re: For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

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itzmyzone911 wrote:
TheDelhiDude wrote:
I came across this question on gmatpill. Now i have seen a similar question for even integer product...how do we approach this one...?

For every positive odd integer n, the function g(n) is defined to be the product of all the odd integers from 1 to n, inclusive. If t is the smallest prime factor of g(99) +1, then t is?

(A) between 2 and 19
(B) between 20 and 39
(C) between 40 and 59
(D) between 60 and 79
(E) 80 or greater

Bunuel: One doubt?

What if the question were reworded to find the largest prime number of g(99)+1?

GMAT would never ask such question because the largest prime of g(99) +1 is 7728802419974390867942174885150693176068821337346448420812666105479729917, which is not that easy to find.
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GMAT 1: 690 Q50 V33 For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

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Bunuel wrote:
itzmyzone911 wrote:
TheDelhiDude wrote:
I came across this question on gmatpill. Now i have seen a similar question for even integer product...how do we approach this one...?

For every positive odd integer n, the function g(n) is defined to be the product of all the odd integers from 1 to n, inclusive. If t is the smallest prime factor of g(99) +1, then t is?

(A) between 2 and 19
(B) between 20 and 39
(C) between 40 and 59
(D) between 60 and 79
(E) 80 or greater

Bunuel: One doubt?

What if the question were reworded to find the largest prime number of g(99)+1?

GMAT would never ask such question because the largest prime of g(99) +1 is 7728802419974390867942174885150693176068821337346448420812666105479729917, which is not that easy to find.

Wow what a number! Just for curiosity, Bunuel is this a symbolic representation (fictitious) of the prime factor or you actually calculated it. Can you explain how you arrived at this no?...and in any case if the options were kept the same, option E would have been the correct answer?
Math Expert V
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Posts: 59674
Re: For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

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itzmyzone911 wrote:
Bunuel wrote:
itzmyzone911 wrote:
GMAT would never ask such question because the largest prime of g(99) +1 is 7728802419974390867942174885150693176068821337346448420812666105479729917, which is not that easy to find.

Wow what a number! Just for curiosity, Bunuel is this a symbolic representation (fictitious) of the prime factor or you actually calculated it. Can you explain how you arrived at this no?...and in any case if the options were kept the same, option E would have been the correct answer?

This is the largest prime of g(99) + 1. I used special calculator to get it.
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GMAT 1: 690 Q50 V33 Re: For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

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Ok...thanks Bunuel Intern  Joined: 03 Jul 2015
Posts: 5
Re: For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

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I agree that t=2, but the answer choice A reads: 2 < t < 19. Doesn't that make t=2 the wrong answer, since t={3,4,...,18}?
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Re: For every positive odd integer n, the function g(n) is defined to be t  [#permalink]

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_________________ Re: For every positive odd integer n, the function g(n) is defined to be t   [#permalink] 05 Oct 2019, 05:51
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