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

Question

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

firas92 · Accepted Answer

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)

Bunuel · Answer

Similar questions: https://gmatclub.com/forum/if-s-is-the- ... 51326.html https://gmatclub.com/forum/if-x-is-equa ... 97544.html

Shorub · Answer

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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Archit3110 · Answer

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

Arro44 · Answer

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.

firas92 · Answer

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!

kanak2016 · Answer

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.

Farina · Answer

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.

tomloveless · Answer

Yup, fell for the basic trap on this one........ read very carefully. Got 25 immediately and went for it.

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

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

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