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

 It is currently 23 May 2019, 22:07

### 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

# If x is equal to the sum of the even integers from 40 to 60

Author Message
TAGS:

### Hide Tags

Director
Joined: 25 Oct 2008
Posts: 500
Location: Kolkata,India
If x is equal to the sum of the even integers from 40 to 60  [#permalink]

### Show Tags

03 Jul 2009, 20:07
20
00:00

Difficulty:

25% (medium)

Question Stats:

78% (01:45) correct 22% (02:29) wrong based on 646 sessions

### HideShow timer Statistics

If x is equal to the sum of the even integers from 40 to 60 inclusive, and y is the number of even integers from 40 to 60 inclusive, what is the value of x+y?

A. 550
B. 551
C. 560
D. 561
E. 572

_________________
http://gmatclub.com/forum/countdown-beginshas-ended-85483-40.html#p649902
Math Expert
Joined: 02 Sep 2009
Posts: 55275
Re: If x is equal to the sum of the even integers from 40 to 60  [#permalink]

### Show Tags

20 Jul 2010, 01:50
2
4
xmagedo wrote:
If x is equal to the sum of the even integers from 40 to 60 inclusive, and y is the number of even integers from 40 to 60 inclusive ,what is the value of x+y?
a 550
b 551
c 560
d 561
e 572

pleas, someone help me with this !

# of even integers from 40 to 60 inclusive is $$y=\frac{60-40}{2}+1=11$$ (check this: totally-basic-94862.html?hilit=multiple%20range);

Sum of the even integers from 40 to 60 inclusive is $$x=\frac{40+60}{2}*11=550$$. Even integers represent evenly spaced set, the sum of the terms in evenly spaced set is: mean, which is the average of the first and the last terms, multiplied by the # of terms;

So, $$x+y=11+550=561$$.

_________________
##### General Discussion
Senior Manager
Affiliations: ACA, CPA
Joined: 26 Apr 2009
Posts: 382
Location: Vagabond
Schools: BC
WE 1: Big4, Audit
WE 2: Banking
Re: If x is equal to the sum of the even integers from 40 to 60  [#permalink]

### Show Tags

03 Jul 2009, 20:47
2
1
Step 1 (y) - No of even numbers from 40-60 = 11

Step 2 (x) - Sum of those 11 nos is given by the formula - (F+L)*N/2
F= 40 L = 60 N =11 Therefore ==> 550

x+y = 550+11 = 561

tejal777 wrote:
if x is equal to the sum of the even integers from 40 to 60 inclusive and y is the number of even integers from 40 to 60 inclusive,what is the value of x+y?
550
551
560
561
572

Guys I applied the formula for "sum of consecutive evn nos." but i am going wrong somewhere.Pease help.
y=11
x=sum of consecutive even integers=n(n+1)
where n= 1st even+last even/2 -1

Therefore,here n=40+60/2-1=50-1=49
So,x=49 x 50 =2450
Hence, x+y=2450+11=2461??!??!

_________________
If you have made mistakes, there is always another chance for you. You may have a fresh start any moment you choose, for this thing we call "failure" is not the falling down, but the staying down.
Manager
Joined: 28 Jan 2004
Posts: 192
Location: India
Re: If x is equal to the sum of the even integers from 40 to 60  [#permalink]

### Show Tags

04 Jul 2009, 00:10
1
This is solved by using AP series.

40,42,44,46..........................60
This is a AP series with common difference of 2

Number of terms = A + (n-1)d
A = first term (40)
n = number of terms (need to be calculated)
d = common difference (2 in this case)

60 = 40 + (n-1)2
or n = 11

Sum of series = [2A + (n-1)d ] * n/2
Sum = 550

So ans = 550 + 11 = 561
Senior Manager
Joined: 25 Mar 2009
Posts: 282
Re: If x is equal to the sum of the even integers from 40 to 60  [#permalink]

### Show Tags

07 Jul 2009, 08:29
Intern
Joined: 15 May 2009
Posts: 12
Re: If x is equal to the sum of the even integers from 40 to 60  [#permalink]

### Show Tags

07 Jul 2009, 08:47
For me,

step1: find y 40, 42, 44, ... 60 therefore y=11

step2: since consecutive numbers/even/odd, find the mean (40+60)/2=50

step3: x = 50(11)=550

step4: 550+11=561
Intern
Joined: 30 May 2009
Posts: 6
Re: If x is equal to the sum of the even integers from 40 to 60  [#permalink]

### Show Tags

08 Jul 2009, 03:10
sum of even integers = even number ( x is even)

number of even integers =11 ( y is odd )
so x+y = odd

A, C, E out ( all even)

Left with B and D :551, 561

If you have ever added even numbers you see that the pattern is 0,2,4,6,8 and 2+4+6+8 =20

{ there are 11 integers 5 in the 40's , 5 in the 50's and 60 , so when u add the u get 200+250+20+20+60 = 550}

hence the sum is 550 ( x=550) or x+y cannot be 551 since x =550

Manager
Joined: 20 Jul 2010
Posts: 102
Re: If x is equal to the sum of the even integers from 40 to 60  [#permalink]

### Show Tags

20 Jul 2010, 06:38
IMO D

xmagedo wrote:
If x is equal to the sum of the even integers from 40 to 60 inclusive, and y is the number of even integers from 40 to 60 inclusive ,what is the value of x+y?
a 550
b 551
c 560
d 561
e 572

pleas, someone help me with this !

Solution:

The number of even integers from 40 to 60 inclusive = 11 (40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60)
Sum of integers = 550

Thus, total = 550 + 11 = 561
_________________
Gotta hit the 700 score this time... 3rd time lucky !
Give me some kudos... Like you, even I need them badly
Intern
Joined: 26 Mar 2010
Posts: 12
Re: If x is equal to the sum of the even integers from 40 to 60  [#permalink]

### Show Tags

21 Jul 2010, 00:15
xmagedo wrote:
If x is equal to the sum of the even integers from 40 to 60 inclusive, and y is the number of even integers from 40 to 60 inclusive ,what is the value of x+y?
a 550
b 551
c 560
d 561
e 572

pleas, someone help me with this !

Sum can be calculated using Arithmetic Progression

$$Sum = (n/2)(a+(n-1)*d)$$

In this case a(first term) = 40, d(difference) = 2(since nos are even)

$$n = ((60-40)/2)+1$$ = 11

Thus sum = 550 (substituting the values)

and the number of terms have already been calculated as 11

Thus x + y = 550+11 = 561

Hope it helps,
meshtrap
Senior Manager
Status: Happy to join ROSS!
Joined: 29 Sep 2010
Posts: 258
Concentration: General Management, Strategy
Schools: Ross '14 (M\$)
Re: If x is equal to the sum of the even integers from 40 to 60  [#permalink]

### Show Tags

29 Mar 2011, 07:41
2
Another approach ('sum of pairs'):
Step 1: 11 numbers
Step 2: 40+60 = 42+58 = 100 (total 5 pairs, with exception of number 55 that does not have a pair)
Step 3: 500 + 55 (the middle number with no pair)+ 11 = 561

Advantages: you don't need to know formulas nor you can make mistake in formulas
Retired Moderator
Joined: 16 Nov 2010
Posts: 1391
Location: United States (IN)
Concentration: Strategy, Technology
Re: If x is equal to the sum of the even integers from 40 to 60  [#permalink]

### Show Tags

29 Mar 2011, 19:38
1
x = (60 + 40)/2 * y

60 = 40 + (y-1)*2

=> y = 20/2 + 1 = 11

so 50 * 11 + 11 = 561

_________________
Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings
Manager
Joined: 09 Aug 2010
Posts: 89
Re: If x is equal to the sum of the even integers from 40 to 60  [#permalink]

### Show Tags

30 Mar 2011, 06:43
1
I used to take a long time solving these kinds of problem until I learned about this formula:

Average = Sum of integers / number of terms
Average = (first term + last term) / 2 ==> this works for both consecutive and even integers

SOLUTION:

x (SUM) = Average x number of terms

Average = 40 +60 /2 = 50
number of terms = ((60 -40)/2)+1 = 11
x (SUM) = 50 x 11 = 550

Therefore,
x + y = 550 + 11 = 561
Director
Joined: 01 Feb 2011
Posts: 646
Re: If x is equal to the sum of the even integers from 40 to 60  [#permalink]

### Show Tags

30 Mar 2011, 18:34
x = 40+42+....60 = (mean).N = (mean)y

=> x+y = = (51).11 = 561

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9234
Location: Pune, India
Re: If x is equal to the sum of the even integers from 40 to 60  [#permalink]

### Show Tags

30 Mar 2011, 19:36
This is a perfect example of why you should not use formulas without understanding them properly. If you understand them, you will not make a mistake and will save time.
The formula quoted by the original poster: n(n+1) is absolutely fine. But one needs to understand that n is the number of even terms starting from the first even term. (I discuss why this is so here:
sum-of-even-numbers-68732.html#p849905)

Sum of even numbers from 40 to 60 using this formula will be:
30*31 - 19*20 = 10(3*31 - 19*2) = 550
Since number of terms is 11, required sum is 561

But, I would not use this formula for this question and would do it the way many of you have done:
Average = 50 (it is the middle number), Number of terms = 11 (No formula again. Any 10 consecutive integers have 5 even and 5 odd numbers. 41 to 60 will have 10 even integers and 40 is the 11th one)
Sum = 50*11 + 11 = 561
_________________
Karishma
Veritas Prep GMAT Instructor

Intern
Joined: 31 Aug 2012
Posts: 6
Re: If x is equal to the sum of the even integers from 40 to 60  [#permalink]

### Show Tags

28 Sep 2012, 06:56
I agree with the answer responses above. I'd avoid fancy formulas and sequences if you're not familiar with them. Just step back and ask yourself " what is the total ("the sum"). Total is your average times your count. In this case, list out all the even numbers. Average is 50. There's 11 even integers (your count). 50 X 11 = 550. Add the 11. Boom. 561. I like this way too; list it out and split out the the numbers and do the math. Example: 40 + 0, 40 + 2, 40 + 4...and so forth. Count the number of 40's, which is 5, so 40 x 5 = 200, plus 2 + 4 + 6 + 8 = 20, totals 220. Do the same for the 50s. Remember to add the y. 561 is your total. Forced method is time consuming and causes errors.
Math Expert
Joined: 02 Sep 2009
Posts: 55275
Re: If x is equal to the sum of the even integers from 40 to 60  [#permalink]

### Show Tags

28 Sep 2012, 07:07
xmagedo wrote:
If x is equal to the sum of the even integers from 40 to 60 inclusive, and y is the number of even integers from 40 to 60 inclusive, what is the value of x+y?

A. 550
B. 551
C.560
D. 561
E. 572

Similar questions to practice:
if-x-is-equal-to-the-sum-of-the-integers-from-30-to-127276.html
if-m-equals-the-sum-of-the-even-integers-from-2-to-128426.html
_________________
Current Student
Joined: 12 Aug 2015
Posts: 2617
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: If x is equal to the sum of the even integers from 40 to 60  [#permalink]

### Show Tags

16 Dec 2016, 18:47
Using the properties of an evenly spaced set=>
Here y=60-40/2+1=11
x=11/2[100]=50*11

x+y=11(50+1)=11*51 = 561

Hence D

_________________
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4486
Location: India
GPA: 3.5
Re: If x is equal to the sum of the even integers from 40 to 60  [#permalink]

### Show Tags

17 Dec 2016, 09:22
tejal777 wrote:
If x is equal to the sum of the even integers from 40 to 60 inclusive, and y is the number of even integers from 40 to 60 inclusive, what is the value of x+y?

A. 550
B. 551
C. 560
D. 561
E. 572

Even integers from 40 to 60 inclusive = { 40 , 42 , 44 , 46 , 48 ........56 , 58 , 60 }

Sum will be 40 + 42 + 46 + .....56 + 58 + 60 = 2 ( 20 + 21 + 22..... 30 )

So, Sum will be 40 + 42 + 46 + .....56 + 58 + 60 = 2 *275 = 550

Number of even integers from 40 to 60 inclusive is ( 30 - 20 ) + 1 = 11

So, Value of x + y = 561

Answer will hence be (D) 561

_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Manager
Joined: 20 Jun 2017
Posts: 92
GMAT 1: 570 Q49 V19
If x is equal to the sum of the even integers from 40 to 60  [#permalink]

### Show Tags

15 Sep 2018, 01:54
x = sum of even integers from 40 to 60 inclusive
y = no. of even integers from 40 to 60 inclusive
x+y = ?

x = 40+42+44+46+.......+60

We need to find the no. of terms between 40 and 60 (both inclusive) which are even in nature.
As per arithmetic progression, the $$n^{th}$$ term of a sequence whose first term is 'a', common difference between 2 consecutive terms is 'd' and the no. of terms in sequence is 'n' is given by:

$$n^{th}$$ term = a+(n-1)d
in the context of this question, we have:

a = 40
n = need to determine
d = 2
$$n^{th}$$ term = 60

60 = 40+(n-1)2

n = 11 = y

now to calculate x, we need to apply the formula for sum of the terms of sequence which is in arithmetic progression.
The formula is given by:
Sum = $$\frac{n}{2}$$(a+last term)

Sum = $$\frac{11}{2}$$(40+60)
x = 550

x+y = 550+11 = 561
If x is equal to the sum of the even integers from 40 to 60   [#permalink] 15 Sep 2018, 01:54
Display posts from previous: Sort by