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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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19 Dec 2010, 16:14
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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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19 Dec 2010, 16:31
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MasterGMAT12 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

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.

 ! 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.

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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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01 Aug 2014, 19:23
Hello from the GMAT Club BumpBot!

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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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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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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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16 Dec 2015, 09:13
Bunuel wrote:
MasterGMAT12 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

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.

 ! 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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Kudos [?]: 99245 [0], given: 11010

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

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17 Dec 2015, 09:43
sharma123 wrote:
Bunuel wrote:
MasterGMAT12 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

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.

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

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10 Mar 2017, 10:42
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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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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18 Mar 2017, 10:37
21*(30+50)/2=840

(50-30)/2=10+1=11
Re: If x is equal to the sum of the integers from 30 to 50, incl   [#permalink] 18 Mar 2017, 10:37
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