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If a is equal to the sum of the odd integers from 15 to 35, inclusive

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CAMANISHPARMAR
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If a is equal to the sum of the odd integers from 15 to 35, inclusive [#permalink] New post   10 Jun 2019, 22:42
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If a is equal to the sum of the odd integers from 15 to 35, inclusive, and b is the number of even integers from 15 to 35, inclusive, what is the value of a – b?

A) 25
B) 215
C) 264
D) 265
E) 266
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firas92
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If a is equal to the sum of the odd integers from 15 to 35, inclusive [#permalink] New post   11 Jun 2019, 01:18
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\(a\) = Sum of an arithmetic sequence with first term, 15 and last term, 35 and common difference 2

Number of odd numbers from 15 to 35, \(n = \frac{(35-15)}{2} + 1 = 11\)
\(a=\frac{11}{2}(15+35) = 275\)

\(b\)=Number of even integers from 16 to 34 inclusive = \(\frac{(34-16)}{2}+1 = 10\)
Therefore, \(a-b=265\)

Answer is (D)
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Re: If a is equal to the sum of the odd integers from 15 to 35, inclusive [#permalink] New post   10 Jun 2019, 23:00
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CAMANISHPARMAR wrote:
If a is equal to the sum of the odd integers from 15 to 35, inclusive, and b is the number of even integers from 15 to 35, inclusive, what is the value of a – b?

A) 25
B) 215
C) 264
D) 265
E) 266


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https://gmatclub.com/forum/if-s-is-the- ... 51326.html
https://gmatclub.com/forum/if-x-is-equa ... 97544.html
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Re: If a is equal to the sum of the odd integers from 15 to 35, inclusive [#permalink] New post   11 Jun 2019, 01:43
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a= 15+17+...+35
b= 16+18+...+34

a-b= (15-16)+(17-18)+...(33-34)+35

Number of terms before 35 is 10.

a-b= 10(-1)+35 = 25

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Re: If a is equal to the sum of the odd integers from 15 to 35, inclusive [#permalink] New post   11 Jun 2019, 09:46
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CAMANISHPARMAR wrote:
If a is equal to the sum of the odd integers from 15 to 35, inclusive, and b is the number of even integers from 15 to 35, inclusive, what is the value of a – b?

A) 25
B) 215
C) 264
D) 265
E) 266


total odd integers ; 35-15/2 +1 = 11
even = 10 = b
so sum of odd ; 15+35/2 * 11 = 275=a
a-b = 265
IMO D
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Re: If a is equal to the sum of the odd integers from 15 to 35, inclusive [#permalink] New post   23 Jun 2019, 06:20
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firas92 , Archit3110

I cannot tell you guys apart due to the "number names" as well as the Simpsons profile pictures.
However, both of you usually provide very helpful explanations for Quant questions.

Therefore, kudos to you both. :)
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Re: If a is equal to the sum of the odd integers from 15 to 35, inclusive [#permalink] New post   23 Jun 2019, 06:52
Arro44 wrote:
firas92 , Archit3110

I cannot tell you guys apart due to the "number names" as well as the Simpsons profile pictures.
However, both of you usually provide very helpful explanations for Quant questions.

Therefore, kudos to you both. :)


Hey Arro44

Thank you! That means a lot coming from a 700 pointer, diamond member! I have learnt a lot from Archit3110 's posts too and I hope I could do as well as you did in the GMAT!
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Re: If a is equal to the sum of the odd integers from 15 to 35, inclusive [#permalink] New post   07 Jul 2019, 14:39
No. of odd int.= 35-15/2+1=11
B) No. of even int. 34-16/2+1=10

A) Sum of odd int.= 35-15/2*no. of odd int.
=35-15/2*11=275
A-B= 275-10=265 Ans D.
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If a is equal to the sum of the odd integers from 15 to 35, inclusive [#permalink] New post   29 Jan 2020, 01:35
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1- Sum of consecutive odd Int inclusive: = (Last term + First Term)/2 * Num of consecutive Int

Num of consecutive int = (Last term - First term) / 2 = Answer + 1
35-15/2 = 20/2 = 10 + 1 = 11

so,
put in formula:
a=Sum of cons int = (35+15)/2 * 11 = 50/2 * 11 = 25 * 11 = 275

2) Num of cons even int: Last term - First term/2 = Answer + 1
consider 16-34
b= 34-16/2 = 18/2 = 9 + 1 = 10

a-b=275-10=265

Option D

PS: What common mistake majority of us must be making here is that we are considering Sum of Consecutive Odd Integer - Sum of Consecutive Even Integer, whereas question is asking for Sum of Consecutive Odd integer - Number of Consecutive Even Integer. This is a clear trap.
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Re: If a is equal to the sum of the odd integers from 15 to 35, inclusive [#permalink] New post   24 Jan 2024, 09:44
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Re: If a is equal to the sum of the odd integers from 15 to 35, inclusive [#permalink]
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