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

It is currently 16 Jun 2019, 22:31

Close

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If x ? y is defined for all x and y as the sum of all integers from x

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55618
If x ? y is defined for all x and y as the sum of all integers from x  [#permalink]

Show Tags

New post 05 Sep 2017, 01:10
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

74% (01:33) correct 26% (02:01) wrong based on 143 sessions

HideShow timer Statistics

Current Student
User avatar
P
Joined: 02 Jul 2017
Posts: 294
Concentration: Entrepreneurship, Technology
GMAT 1: 730 Q50 V38
GMAT ToolKit User
If x ? y is defined for all x and y as the sum of all integers from x  [#permalink]

Show Tags

New post Updated on: 12 Nov 2017, 04:59
1
x ? y = the sum of all integers from x to y, inclusive
Find : 5 ? 150

5 ? 150 = 5+6+7...+150

Sum of Continues series a+(a+1)+(a+2)+.... L = S = \(\frac{n}{2} *(a+L)\)
where n is number of terms, a is first term, L is last term

Here number of terms = (150-5)+1 = 146 ( Here +1 as 150 and 5 both are included)

Sum=\(\frac{146}{2}* (5+150) = \frac{146}{2} *(155)\)

= 11315

Answer: C

Originally posted by Nikkb on 05 Sep 2017, 01:18.
Last edited by Nikkb on 12 Nov 2017, 04:59, edited 1 time in total.
Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 2892
If x ? y is defined for all x and y as the sum of all integers from x  [#permalink]

Show Tags

New post Updated on: 05 Sep 2017, 14:02
Bunuel wrote:
If x ? y is defined for all x and y as the sum of all integers from x to y, inclusive, what is the value of 5 ? 150?

A. 22,630
B. 22,475
C. 11,315
D. 11,238
E. 5,658

The ? strange symbol just gives the rule that, in this problem, the task is to find the sum of an arithmetic series of integers, from 5 to 150 inclusive.

Sum = (Average) * (Number of terms)

Average = \(\frac{First Term + Last Term}{2}\)

Average = \(\frac{150 + 5}{2}\) = \(\frac{155}{2}\) Leave it.*

Number of terms = (Last Term - First term + 1)

Number of terms = (150 - 5) + 1 = 146

Sum of series: \(\frac{155}{2}\) * (146) = 155 * 73

If you do the arithmetic fully, 155 * 73 = 11,315

ANSWER C

To simplify the arithmetic:

Three answers, A, D,and E, can be eliminated immediately because the units' digit of the answer must be five (3*5 = 15).

Between B and C: Answers B and C are far enough apart that you can round numbers to speed the arithmetic.

150 * 70 = 10,500. That's close to C. To get close to Answer B, the number of terms would have to double.

Either way:

Answer C

*If the average of consecutive integers is not an integer because the sum of the first and last terms is odd (odd/2 = not integer), the number of terms will be even, and the 2 in the denominator will be factored out. So write the two factors, average and number of terms, before calculating; that way it is clear that dividing by 2 will lead to an integer.
_________________
SC Butler has resumed!
Get two SC questions to practice, whose links you can find by date, here.


Tell me, what is it you plan to do with your one wild and precious life? -- Mary Oliver

Originally posted by generis on 05 Sep 2017, 12:25.
Last edited by generis on 05 Sep 2017, 14:02, edited 1 time in total.
Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3385
Location: India
GPA: 3.12
Re: If x ? y is defined for all x and y as the sum of all integers from x  [#permalink]

Show Tags

New post 05 Sep 2017, 12:37
1
Since x ? y is defined for all x and y as the sum of all integers from x to y, inclusive and
we have been asked to find the value of 5 ? 150, one easy way is to find the sum of the
first 150 numbers and subtract 1+2+3+4(10)

The sum of first n numbers is \(\frac{n(n+1)}{2} = \frac{150*151}{2} = 75*151 = 11325\)

Therefore 5 ? 150 = 11325 - 10 = 11315(Option C)
_________________
You've got what it takes, but it will take everything you've got
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6521
Location: United States (CA)
Re: If x ? y is defined for all x and y as the sum of all integers from x  [#permalink]

Show Tags

New post 07 Sep 2017, 16:48
Bunuel wrote:
If x ? y is defined for all x and y as the sum of all integers from x to y, inclusive, what is the value of 5 ? 150?

A. 22,630
B. 22,475
C. 11,315
D. 11,238
E. 5,658


We can use the formula sum = (avg)(quantity).

Let’s first get the average of the integers from 5 to 150 inclusive:

average = (5 + 150)/2 = 155/2

quantity = 150 - 5 + 1 = 146

sum = 155/2 x 146 = 11,315

Answer: C
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
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.

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 11369
Re: If x ? y is defined for all x and y as the sum of all integers from x  [#permalink]

Show Tags

New post 27 Oct 2018, 04:49
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.
_________________
GMAT Club Bot
Re: If x ? y is defined for all x and y as the sum of all integers from x   [#permalink] 27 Oct 2018, 04:49
Display posts from previous: Sort by

If x ? y is defined for all x and y as the sum of all integers from x

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


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