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

It is currently 19 Aug 2018, 08:24

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: 47983
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:

  45% (medium)

Question Stats:

69% (00:58) correct 31% (01:47) wrong based on 89 sessions

HideShow timer Statistics

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

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Senior Manager
Senior Manager
User avatar
P
Joined: 02 Jul 2017
Posts: 294
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.
SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 1908
Premium Member CAT Tests
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
1
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.
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"


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.
BSchool Forum Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3044
Location: India
GPA: 3.12
Premium Member CAT Tests
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
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3176
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

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: If x ? y is defined for all x and y as the sum of all integers from x &nbs [#permalink] 07 Sep 2017, 16:48
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  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.