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

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If x is equal to the sum of the even integers from 40 to 60 [#permalink] New post 19 Jul 2010, 23:58
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 28 Sep 2012, 06:02, edited 1 time in total.
Renamed the topic and edited the question.
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Re: arthimtic relation help pleas [#permalink] New post 20 Jul 2010, 00:50
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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.

Answer: D.

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Re: arthimtic relation help pleas [#permalink] New post 20 Jul 2010, 05:38
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

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Re: arthimtic relation help pleas [#permalink] New post 20 Jul 2010, 23:15
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
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if x is equal to the sum of the even integers from 40 to 60 incl [#permalink] New post 30 Mar 2011, 18:36
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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

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Re: sum of the even integers from 40 to 60 inclusive [#permalink] New post 28 Sep 2012, 05:56
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.
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Re: If x is equal to the sum of the even integers from 40 to 60 [#permalink] New post 28 Sep 2012, 06:07
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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

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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.


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Re: If x is equal to the sum of the even integers from 40 to 60   [#permalink] 28 Sep 2012, 06:07
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