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

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If x is equal to the sum of the integers from 30 to 50, incl [#permalink]

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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: OA

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New post 19 Dec 2010, 16:31
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MasterGMAT12 wrote:
Please help with the approach for the below question:

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


The sum of the integers from 30 to 50 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.


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Re: If x is equal to the sum of the integers from 30 to 50, incl [#permalink]

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Re: If x is equal to the sum of the integers from 30 to 50, incl [#permalink]

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New post 28 Aug 2014, 09:54
I will use AP:

Sum = n/2[2a+(n-1)d) = 21/2[2*30+20*1] = 840 = sum from 30- 50
Number of even terms from 30 -50 are 11.
so total = 240+11 =251
Hope this helps :)
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If x is equal to the sum of the integers from 30 to 50, incl [#permalink]

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New post 16 Dec 2015, 03:36
21 integers from 30 to 50 inclusive

so 11th integer is mean, it is 40

21*40=840

from 21 integers 11 ones is even

840+11=851

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Re: If x is equal to the sum of the integers from 30 to 50, incl [#permalink]

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New post 16 Dec 2015, 09:13
Bunuel wrote:
MasterGMAT12 wrote:
Please help with the approach for the below question:

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


The sum of the integers from 30 to 50 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.


!
Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/
Please post DS questions in the DS subforum: gmat-data-sufficiency-ds-141/

No posting of PS/DS questions is allowed in the main Math forum.

Hi Bunuel how do you calculate no. of terms(i.e 21). By counting or is there any method. Counting no. of terms in given range or no. of hours have always been a problem for me. i always count which consumes a lot of time.
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Re: If x is equal to the sum of the integers from 30 to 50, incl [#permalink]

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New post 17 Dec 2015, 09:43
Expert's post
sharma123 wrote:
Bunuel wrote:
MasterGMAT12 wrote:
Please help with the approach for the below question:

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


The sum of the integers from 30 to 50 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.


!
Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/
Please post DS questions in the DS subforum: gmat-data-sufficiency-ds-141/

No posting of PS/DS questions is allowed in the main Math forum.

Hi Bunuel how do you calculate no. of terms(i.e 21). By counting or is there any method. Counting no. of terms in given range or no. of hours have always been a problem for me. i always count which consumes a lot of time.


How many integers are from x to y inclusive? y - x + 1.
For example, how many integers are from 2 to 7 inclusive? 7 - 2 + 1 = 6. Namely, 2, 3, 4, 5, 6 and 7.

How many integers are from x to y NOT inclusive? y - x - 1.
For example, how many integers are from 2 to 7 NOT inclusive? 7 - 2 - 1 = 4. Namely, 3, 4, 5, and 6.
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New to the Math Forum?
Please read this: 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?
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Re: If x is equal to the sum of the integers from 30 to 50, incl   [#permalink] 17 Dec 2015, 09:43
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