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

 It is currently 20 Oct 2019, 17:06

### 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

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 all even integers n, h(n) is defined to be the sum of the even

Author Message
TAGS:

### Hide Tags

Manager
Joined: 30 Oct 2012
Posts: 58
Location: India
WE: Marketing (Manufacturing)
For all even integers n, h(n) is defined to be the sum of the even  [#permalink]

### Show Tags

Updated on: 31 Aug 2016, 02:18
1
12
00:00

Difficulty:

35% (medium)

Question Stats:

71% (01:46) correct 29% (01:47) wrong based on 290 sessions

### HideShow timer Statistics

For all even integers n, h(n) is defined to be the sum of the even integers between 2 and n, inclusive. What is the value of h(18)/h(10) ?

(A) 1.8
(B) 3
(C) 6
(D) 18
(E) 60

_________________
i am the master of my fate, I am the captain of my soul

Originally posted by mystiquethinker on 31 Aug 2016, 01:56.
Last edited by Bunuel on 31 Aug 2016, 02:18, edited 1 time in total.
RENAMED THE TOPIC.
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: For all even integers n, h(n) is defined to be the sum of the even  [#permalink]

### Show Tags

31 Aug 2016, 05:13
3
6
mystiquethinker wrote:
For all even integers n, h(n) is defined to be the sum of the even integers between 2 and n, inclusive. What is the value of h(18)/h(10) ?

(A) 1.8
(B) 3
(C) 6
(D) 18
(E) 60

CONCEPT: When terms are in Arithmetic Progression (A.P.) i.e. terms are equally spaced then

Mean = Median =(First+Last)/2

and Sum = Mean*Number of terms

h(18) = [(2+18)/2]*9 = 90

h(10) = (2+10)/2]*5 = 30

h(18)/h(10) = (90) / (30) = 3
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
##### General Discussion
Senior Manager
Joined: 24 Nov 2015
Posts: 490
Location: United States (LA)
Re: What is the value of h(18)/h(10) ?  [#permalink]

### Show Tags

31 Aug 2016, 02:38
2
sum of n terms can be represented by the formula = $$\frac{n*(n+1)}{2}$$

h(10) :- 2+4+6+8+10 = 2(1+2+3+4+5) = 2 * $$\frac{5*6}{2}$$ = 30

h(18) :- 2+4+6+8+10+12+14+16+18 = 2(1+2+3+4+5+6+7+8+9) = $$\frac{2 * 9 *10}{2}$$ = 90

$$\frac{h(18)}{h(10)}$$ = $$\frac{90}{30}$$ =3

correct answer -$$B$$
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4015
Re: For all even integers n, h(n) is defined to be the sum of the even  [#permalink]

### Show Tags

31 Aug 2016, 07:48
1
Top Contributor
1
mystiquethinker wrote:
For all even integers n, h(n) is defined to be the sum of the even integers between 2 and n, inclusive. What is the value of h(18)/h(10) ?

(A) 1.8
(B) 3
(C) 6
(D) 18
(E) 60

We can also apply a nice rule that says (a + b)/c = a/c + b/c AND use some estimation, since the answer choices are nicely spread apart.

h(18)/h(10) = (2+4+6+8+10+12+14+16+18)/(2+4+6+8+10)
= (2+4+6+8+10)/(2+4+6+8+10) + (12+14+16+18)/(2+4+6+8+10)
= 1 + (12+14+16+18)/(2+4+6+8+10)
= 1 + some value around 2 [yes, I'm aware that the fraction evaluates to be exactly 2, but we could actually be quite aggressive in our estimation and still reach the correct answer]
≈ 3

RELATED VIDEO

_________________
Test confidently with gmatprepnow.com
Intern
Joined: 26 May 2015
Posts: 7
For all even integers n, h(n) is defined to be the sum of the even  [#permalink]

### Show Tags

20 Jul 2017, 13:48
Hi,
Could I apply the following?

$$h(18)/h(10)$$ simplified is $$h(9)/h(5)$$, so the even numbers are $$(2+4+6+8)/(2+4)$$ = 3

Thanks
Intern
Joined: 18 Aug 2017
Posts: 30
GMAT 1: 670 Q49 V33
For all even integers n, h(n) is defined to be the sum of the even  [#permalink]

### Show Tags

22 Aug 2017, 09:05
Esguitar wrote:
Hi,
Could I apply the following?

$$h(18)/h(10)$$ simplified is $$h(9)/h(5)$$, so the even numbers are $$(2+4+6+8)/(2+4)$$ = 3

Thanks

h(10) = 2+4+6+8+10 = 30
h(5) = 2+4 =6
so h(10) can't = 2 x h(5), you can't simplify like that.
Director
Joined: 14 Nov 2014
Posts: 598
Location: India
GMAT 1: 700 Q50 V34
GPA: 3.76
Re: For all even integers n, h(n) is defined to be the sum of the even  [#permalink]

### Show Tags

22 Aug 2017, 10:46
The number are in AP
we can use n/2(2a + (n-1)d)
we will get sum of n even terms ---( a = 2 , d = 2) =n(n+1)
Now 2 to 18 we have 9 terms
2 to 10 we have 5 terms
9*10 / 5*6
we will get 3
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8117
Location: United States (CA)
Re: For all even integers n, h(n) is defined to be the sum of the even  [#permalink]

### Show Tags

24 Aug 2017, 16:05
mystiquethinker wrote:
For all even integers n, h(n) is defined to be the sum of the even integers between 2 and n, inclusive. What is the value of h(18)/h(10) ?

(A) 1.8
(B) 3
(C) 6
(D) 18
(E) 60

First, notice that h(18) will be the sum of the even integers between 2 and 18 inclusive. We can thus calculate h(18) using the formula sum = avg x quantity.

First, find the average of this evenly spaced set of numbers:

avg = (18 + 2)/2 = 10

Now calculate how many numbers are in this set:

quantity = (18 - 2)/2 + 1 = 9

Now we use the formula sum = avg x quantity:

sum = (10)(9)

sum = 90 = h(18)

Next we can determine h(10) using the same procedure we used to calculate h(18):

avg = (10 + 2)/2 = 6

quantity = (10 - 2)/2 + 1 = 5

sum = 30

Thus, h(18)/h(10) = 90/30 = 3

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager
Status: Enjoying the Journey
Affiliations: ND
Joined: 26 Sep 2017
Posts: 114
Schools: Rotman '21
WE: Marketing (Consulting)
Re: For all even integers n, h(n) is defined to be the sum of the even  [#permalink]

### Show Tags

22 Mar 2018, 03:31
Hi Everyone,

I used a different way here

A modified version of $$\frac{(n*(n+1))}{2}$$ would be $$\frac{(n*(n+2))}{4}$$

$$h(18)=\frac{(18)(20)}{4} = \frac{360}{4}= 90$$

$$h(10)= \frac{(10)(12)}{4} = \frac{120}{4}= 30$$

$$\frac{h(18)}{h(10)}= \frac{90}{30}= 3$$ ===> B
_________________
"it takes more time to fix a mistake than to avoid one"
"Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anything

High achievement always takes place in the framework of high expectation Charles Kettering
If we chase perfection we can catch excellence Vince Lombardi

GMAT Club Live: 5 Principles for Fast Math: https://gmatclub.com/forum/gmat-club-live-5-principles-for-fast-math-251028.html#p1940045
The Best SC strategies - Amazing 4 videos by Veritas: https://gmatclub.com/forum/the-best-sc-strategies-amazing-4-videos-by-veritas-250377.html#p1934575
Non-Human User
Joined: 09 Sep 2013
Posts: 13317
Re: For all even integers n, h(n) is defined to be the sum of the even  [#permalink]

### Show Tags

12 Aug 2019, 12:33
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.
_________________
Re: For all even integers n, h(n) is defined to be the sum of the even   [#permalink] 12 Aug 2019, 12:33
Display posts from previous: Sort by