GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Jun 2019, 20:09

### GMAT Club Daily Prep

#### 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

# For every positive even integer n, the function h(n) is defined to be

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Manager
Joined: 05 Oct 2017
Posts: 66
Location: India
Schools: GWU '21, Isenberg'21
For every positive even integer n, the function h(n) is defined to be  [#permalink]

### Show Tags

14 Dec 2018, 08:55
4
00:00

Difficulty:

35% (medium)

Question Stats:

67% (01:41) correct 33% (02:00) wrong based on 74 sessions

### HideShow timer Statistics

For every positive even integer n, the function h(n) is defined to be the product of all even integers from 2 to n, inclusive. For instance, h(10)= 2x4x6x8x10. What is the greatest prime factor of h(94)+h(96)?

a) 89
b) 91
c) 93
d) 97
e) 99

_________________
Director
Joined: 18 Jul 2018
Posts: 938
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: For every positive even integer n, the function h(n) is defined to be  [#permalink]

### Show Tags

14 Dec 2018, 10:48
h(94) = 2*4*6*....*94 = 2(1*2*3*...*47) = 2*47!
h(96) = 2*4*6*.....*96 = 2(1*2*3*...*48) = 2*48!
h(94)+h(96) = 47!(2+96) = 47!(97)
Hence the largest prime factor is 97.

D is the answer.
_________________
Press +1 Kudo If my post helps!
Manager
Status: Quant Expert Q51
Joined: 02 Aug 2014
Posts: 106
Re: For every positive even integer n, the function h(n) is defined to be  [#permalink]

### Show Tags

15 Dec 2018, 03:42
For every positive even integer n, the function h(n) is defined to be the product of all even integers from 2 to n, inclusive.
For instance, h(10)= 2x4x6x8x10.

What is the greatest prime factor of h(94)+h(96)?

$$h(94)+h(96) = 2*4*.....*94+2*4*......94*96 = (2*4*.....94)(1+96) = (2*4*.....94)*97$$

97 is a prime number so it is the greatest prime factor

Answer D
_________________
Manager
Joined: 15 Aug 2018
Posts: 51
GMAT 1: 740 Q47 V45
GPA: 3.5
Re: For every positive even integer n, the function h(n) is defined to be  [#permalink]

### Show Tags

19 Dec 2018, 02:56
Afc0892 wrote:
h(94) = 2*4*6*....*94 = 2(1*2*3*...*47) = 2*47!
h(96) = 2*4*6*.....*96 = 2(1*2*3*...*48) = 2*48!
h(94)+h(96) = 47!(2+96) = 47!(97)
Hence the largest prime factor is 97.

D is the answer.

47! (2+96) is not equal to 47! (97). However, it is equal to 47! (98). But from this we can't sufficiently conclude that 97 is a factor of the two numbers. Liked the thinking though!!

Best, gota900
_________________
A kudo a day...
Director
Joined: 18 Jul 2018
Posts: 938
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: For every positive even integer n, the function h(n) is defined to be  [#permalink]

### Show Tags

19 Dec 2018, 02:59
gota900 wrote:
Afc0892 wrote:
h(94) = 2*4*6*....*94 = 2(1*2*3*...*47) = 2*47!
h(96) = 2*4*6*.....*96 = 2(1*2*3*...*48) = 2*48!
h(94)+h(96) = 47!(2+96) = 47!(97)
Hence the largest prime factor is 97.

D is the answer.

47! (2+96) is not equal to 47! (97). However, it is equal to 47! (98). But from this we can't sufficiently conclude that 97 is a factor of the two numbers. Liked the thinking though!!

Best, gota900

Hey gota900, yes its 97*47!. Made a silly mistake while typing the answer ?

Posted from my mobile device
_________________
Press +1 Kudo If my post helps!
Manager
Joined: 15 Aug 2018
Posts: 51
GMAT 1: 740 Q47 V45
GPA: 3.5
Re: For every positive even integer n, the function h(n) is defined to be  [#permalink]

### Show Tags

19 Dec 2018, 03:08
Afc0892 wrote:
gota900 wrote:
Afc0892 wrote:
h(94) = 2*4*6*....*94 = 2(1*2*3*...*47) = 2*47!
h(96) = 2*4*6*.....*96 = 2(1*2*3*...*48) = 2*48!
h(94)+h(96) = 47!(2+96) = 47!(97)
Hence the largest prime factor is 97.

D is the answer.

47! (2+96) is not equal to 47! (97). However, it is equal to 47! (98). But from this we can't sufficiently conclude that 97 is a factor of the two numbers. Liked the thinking though!!

Best, gota900

Hey gota900, yes its 97*47!. Made a silly mistake while typing the answer ?

Posted from my mobile device

I know that it is 47! (97). Thats why the OA is D. But a little mistake in the factoring yields 98 in your answer. Not 97, thats why I liked your thinking, but the very last step went wrong. Let me show you what I mean:

2*47! + 2*48! - so far, so good!

The factoring which would yield the desired outcome, however, should be this:

2*47! (1+2*48)
94! (1+96)
94! (97)
OA: D

Agreed?

Best, gota900
_________________
A kudo a day...
Senior Manager
Joined: 12 Sep 2017
Posts: 267
Re: For every positive even integer n, the function h(n) is defined to be  [#permalink]

### Show Tags

31 Dec 2018, 12:03
Hello!

Can someone please give an alternative solution instead of binomial theorem?

Thank you very much!
Manager
Joined: 22 May 2015
Posts: 110
Re: For every positive even integer n, the function h(n) is defined to be  [#permalink]

### Show Tags

31 Dec 2018, 21:15
1
1
jfranciscocuencag wrote:
Hello!

Can someone please give an alternative solution instead of binomial theorem?

Thank you very much!

H(94) = 2*4*6....*94
H(96) = 2*4*6....*94*96 = H(94)*96

H(94) + H(96) = H(94) + H(94)*96 = H(94) { 1 + 96 } = H(94) * 97 = 2*4*.....*94*97

Hence greatest prime factor is 97
_________________
Consistency is the Key
Manager
Joined: 05 Oct 2017
Posts: 66
Location: India
Schools: GWU '21, Isenberg'21
Re: For every positive even integer n, the function h(n) is defined to be  [#permalink]

### Show Tags

01 Jan 2019, 08:52
This is how i have solved.

h(94) = 2*4*6*8........94 = 2^47 ( 1 * 2 * 3 * 4 ......47) .........(i)

h(96) = 2*4*6*8........96 =2^48 ( 1 * 2 * 3 * 4 ......48 ) .........(ii)

adding above two equation and taking 2^47 ( 1 * 2 * 3 * 4 ......47) common , we get
-->2^47 ( 1 * 2 * 3 * 4 ......47) (1 + $$2*48$$)
--> 2^47 ( 1 * 2 * 3 * 4 ......47) (97)

Thus 97 is our answer.

Hope it helps.
_________________
Re: For every positive even integer n, the function h(n) is defined to be   [#permalink] 01 Jan 2019, 08:52
Display posts from previous: Sort by

# For every positive even integer n, the function h(n) is defined to be

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne