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If x is equal to the sum of the integers from 30 to 50

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If x is equal to the sum of the integers from 30 to 50 [#permalink] New post 08 Feb 2012, 14:31
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If x is equal to the sum of the integers from 30 to 50, inclusive, and y is the number of EVEN integers from 30 to 50, inclusive, what is the value of x+y ?

A. 810
B. 811
C. 830
D. 850
E. 851

[Reveal] Spoiler:
I started solving like this .....

Sum of integers = (Mean x No of Terms)

So for X - {30 to 50} , No. of terms = 21, Mean = 50+30 / 2 = 40
So Sum of X = No of terms x Mean = 21 x 40 = 840
----------------------------------------------------------------------------------------------------------------
Now for Y - {30, 32,34,36,38,40,42,44,46,48,50} Now since these have already been added before.....what am i supposed to do?......i am lost here..

Sum = x + y = ????
[Reveal] Spoiler: OA

Last edited by Bunuel on 10 Feb 2013, 08:50, edited 3 times in total.
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Re: Consecutive Numbers (Number Properties) [#permalink] New post 08 Feb 2012, 14:37
Expert's post
nimc2012 wrote:
If x is equal to the sum of the integers from 30 to 50, inclusive, and y is the number of EVEN integers from 30 to 50, inclusive,
what is the value of x+y ?

a) 810
b) 811
c) 830
d)850
e)851

---------------------------------------------

I started solving like this .....

Sum of integers = (Mean x No of Terms)

So for X - {30 to 50} , No. of terms = 21, Mean = 50+30 / 2 = 40
So Sum of X = No of terms x Mean = 21 x 40 = 840
----------------------------------------------------------------------------------------------------------------
Now for Y - {30, 32,34,36,38,40,42,44,46,48,50} Now since these have already been added before.....what am i supposed to do?......i am lost here..

Sum = x + y = ????


The sum of the integers from 30 to 50, inclusive is \(x=\frac{first \ term+ last \ term}{2}*# \ of \ terms=\frac{30+50}{2}*21=40*21=840\);

The number of even integers from 30 to 50 is \(y=\frac{50-30}{2}+1=11\) (check this: totally-basic-94862.html);

x+y=840+11=851.

Answer: E.

As for your question: x and y are two different numbers: x is a sum of the integers from 30 to 50, inclusive and y is the number of EVEN integers from 30 to 50, inclusive.

Hope it's clear.
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Re: If x is equal to the sum of the integers from 30 to 50 [#permalink] New post 10 Feb 2013, 07:58
The correct answer to this question is E not D. You put D as the correct answer, so you could change it to E. It is confusing at first look.
Thanks!
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Re: If x is equal to the sum of the integers from 30 to 50 [#permalink] New post 11 Feb 2013, 19:09
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Since the integers from 30-50 are consecutive we can use the "median x # of terms formula" to determine x. There are 21 terms and the median is 40. This gives a total of 21x40 = 840. There are 11 even integers from 30-50 = y. Therefore, x+y = 851. Answer: E
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If x is equal to the sum of the integers from 30 to 50, [#permalink] New post 06 Mar 2013, 13:34
If x is equal to the sum of the integers from 30 to 50, inclusive, and y is the number of even integers from 30 to 50, inclusive, what is the value of x+y ?

(A) 810
(B) 811
(C) 830
(D) 850
(E) 851

I know this is pretty easy. However, I always get the sum of even (or some multiple) integers wrong, I use the formula: (last-first)/2+1). Also hoping @GyanOne can show his mad Quant skills with some genius shortcut :)
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Re: If x is equal to the sum of the integers from 30 to 50, [#permalink] New post 06 Mar 2013, 13:37
Expert's post
megafan wrote:
If x is equal to the sum of the integers from 30 to 50, inclusive, and y is the number of even integers from 30 to 50, inclusive, what is the value of x+y ?

(A) 810
(B) 811
(C) 830
(D) 850
(E) 851

I know this is pretty easy. However, I always get the sum of even (or some multiple) integers wrong, I use the formula: (last-first)/2+1). Also hoping @GyanOne can show his mad Quant skills with some genius shortcut :)


Merging similar topics.
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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

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Re: If x is equal to the sum of the integers from 30 to 50 [#permalink] New post 17 Feb 2015, 18:14
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Re: If x is equal to the sum of the integers from 30 to 50 [#permalink] New post 18 Feb 2015, 00:45
If x is equal to the sum of the integers from 30 to 50, inclusive, and y is the number of EVEN integers from 30 to 50, inclusive, what is the value of x+y ?

A. 810
B. 811
C. 830
D. 850
E. 851


For X,
Series is - 30,31,32,33,.......,48,49,50 (21 terms (50-30+1) with common difference 1)
Sum = (21/2)*((2*30)+(20)) = 21*40 = 840

For Y,
Series is - 30,32,34,....48,50 (11 terms (((50-30)/2)+1) with common difference 2)
Y=11

X+Y = 840+11 = 851

E
Re: If x is equal to the sum of the integers from 30 to 50   [#permalink] 18 Feb 2015, 00:45
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