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Math Expert V
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What is the sum of odd integers from 35 to 85, inclusive?  [#permalink]

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What is the sum of odd integers from 35 to 85, inclusive?

A) 1,560
B) 1,500
C) 1,240
D) 1,120
E) 1,100

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What is the sum of odd integers from 35 to 85, inclusive?  [#permalink]

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Bunuel wrote:
What is the sum of odd integers from 35 to 85, inclusive?

A) 1,560
B) 1,500
C) 1,240
D) 1,120
E) 1,100

Different approach (for kicks )

We want: 35 + 37 + 39 + 41 + . . . . 79 + 81 + 83 + 85

Add the numbers in pairs, starting from the outside and working towards the middle, we get:
35 + 37 + 39 + 41 + . . . . 79 + 81 + 83 + 85 = (35 + 85) + (37 + 83) + (39 + 81) + . . .
= (120) + (120) + (120) + (120) + .....
= 120 times some integer

So, the desired sum must be DIVISIBLE by 120
Only one answer choice is divisible by 120

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Originally posted by GMATPrepNow on 01 Jul 2017, 13:20.
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Re: What is the sum of odd integers from 35 to 85, inclusive?  [#permalink]

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35
27
Bunuel wrote:
What is the sum of odd integers from 35 to 85, inclusive?

A) 1,560
B) 1,500
C) 1,240
D) 1,120
E) 1,100

Number of odd integers = (85-35)/2 + 1
= 50/2 + 1
= 26
Sum of odd integers = (35+85)/2 * 26
= 60 * 26
= 1560
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Re: What is the sum of odd integers from 35 to 85, inclusive?  [#permalink]

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2
A

take average and multiply by number of terms

here number of odd terms=26 and average is 60.

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GMAT 1: 410 Q18 V27 GMAT 2: 490 Q35 V23 Re: What is the sum of odd integers from 35 to 85, inclusive?  [#permalink]

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2
Skywalker18 wrote:
Bunuel wrote:
What is the sum of odd integers from 35 to 85, inclusive?

A) 1,560
B) 1,500
C) 1,240
D) 1,120
E) 1,100

Number of odd integers = (85-35)/2 + 1
= 50/2 + 1
= 26
Sum of odd integers = (35+85)/2 * 26
= 60 * 26
= 1560

Hi Skywalker18,

I do understand the following on this exercise:

1. We're dealing with consecutive integers so I can find the average by: $$\cfrac { First\quad Number+Last\quad Number }{ 2 }$$
2. To find the range in a set of numbers for which both end points are inclusive, we: $$\left( Hightest\quad Number-Lowest\quad Number \right) +1$$

I don't understand why you can simply divide the range by 2 in $$\cfrac { \left( Hightest\quad Number-Lowest\quad Number \right) }{ 2 } +1$$ to find the number of odd numbers. Would it be the same if I wanted to find the number of even numbers?

Thanks'
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Re: What is the sum of odd integers from 35 to 85, inclusive?  [#permalink]

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He has divided by2 as we need to find out the number of odd numbers.(85-35)+1 is total number which includes even and odd
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Re: What is the sum of odd integers from 35 to 85, inclusive?  [#permalink]

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Notice that by adding pairs of numbers we get a sum of 120. We need to find the number of integers between 35 and 85 inclusive.
The number of integers is $$\frac{(85-35)}{2}+1$$ = 26

So we add 120 , 26 times to get 120*26, dividing this by 2 , we get 1560.
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Re: What is the sum of odd integers from 35 to 85, inclusive?  [#permalink]

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Hi Skywalker18 niks18 gmatbusters

What is the sum of odd integers from 35 to 85, inclusive?

Quote:
Number of odd integers = (85-35)/2 + 1
= 50/2 + 1
= 26

Can you explain why did you divide by 2?
If I want to count no. of terms from 1 to 10,
I would perform (Last term - First term) + 1.
But is not above approach only valid for consecutive terms
and sequence starting with 1?

Quote:
Sum of odd integers = (35+85)/2 * 26
= 60 * 26
= 1560

I guess you used that for consecutive numbers, mean = median = (First term + last term) / 2.
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Re: What is the sum of odd integers from 35 to 85, inclusive?  [#permalink]

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1
2

let me try to provide reply to your queries,
Your query: Can you explain why did you divide by 2?
Actually we divide by 2 because the difference between the consecutive odd numbers = 2.

In fact we have to count the multiple of any number say 7, multiple of 7 between 7 and 98 both inclusive.
it will be (98-7)/7 +1

Always divide by common difference
( this is as per Arithmetic progression , AP)

As per you "If I want to count no. of terms from 1 to 10, I would perform (Last term - First term) + 1."

you are right here, the common difference = 1. so dividing by 1 is not necessary.

Your Query :I guess you used that for consecutive numbers, mean = median = (First term + last term) / 2.

yes you are right, in fact, it is true for any set of equally spaced numbers (AP)

Hi Skywalker18 niks18 gmatbusters

What is the sum of odd integers from 35 to 85, inclusive?

Quote:
Number of odd integers = (85-35)/2 + 1
= 50/2 + 1
= 26

Can you explain why did you divide by 2?
If I want to count no. of terms from 1 to 10,
I would perform (Last term - First term) + 1.
But is not above approach only valid for consecutive terms
and sequence starting with 1?

Quote:
Sum of odd integers = (35+85)/2 * 26
= 60 * 26
= 1560

I guess you used that for consecutive numbers, mean = median = (First term + last term) / 2.
Let me know if we are on same page _________________
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What is the sum of odd integers from 35 to 85, inclusive?  [#permalink]

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GMATPrepNow wrote:
Bunuel wrote:
What is the sum of odd integers from 35 to 85, inclusive?

A) 1,560
B) 1,500
C) 1,240
D) 1,120
E) 1,100

Quote:
Different approach (for kicks )

We want: 35 + 37 + 39 + 41 + . . . . 79 + 81 + 83 + 85

Add the numbers in pairs, starting from the outside and working towards the middle, we get:
35 + 37 + 39 + 41 + . . . . 79 + 81 + 83 + 85 = (35 + 85) + (37 + 83) + (39 + 81) + . . .
= (120) + (120) + (120) + (120) + .....
= 120 x some integer

So, the desired sum must be DIVISIBLE by 120
Only one answer choice is divisible by 120

This observation is interesting but I would take a separate approach after the first two steps:-

Add the numbers in pairs, starting from the outside and working towards the middle, we get:
35 + 37 + 39 + 41 + . . . . 79 + 81 + 83 + 85 = (35 + 85) + (37 + 83) + (39 + 81) + . . .
= (120) + (120) + (120) + (120) + .....
= 120 x some integer

Some integer is 13 because the average of extreme values is 60. So for every odd number from 35 to 60 there will be a pair for it from 60 to 85. Its easy to count that the number of pairs will be 13. therefore the answer is 120*13. [Only reason I mentioned this approach was because sometimes dividing 5 numbers could be time consuming. Counting the number of pairs to 13 was simple and straight forward)

Edit: Formating

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Re: What is the sum of odd integers from 35 to 85, inclusive?  [#permalink]

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Check this out hope it helps
https://gmatclub.com/forum/how-many-mul ... ml#p730075
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Re: What is the sum of odd integers from 35 to 85, inclusive?  [#permalink]

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gmatbusters wrote:

let me try to provide reply to your queries,
Your query: Can you explain why did you divide by 2?
Actually we divide by 2 because the difference between the consecutive odd numbers = 2.

In fact we have to count the multiple of any number say 7, multiple of 7 between 7 and 98 both inclusive.
it will be (98-7)/7 +1

Always divide by common difference
( this is as per Arithmetic progression , AP)

As per you "If I want to count no. of terms from 1 to 10, I would perform (Last term - First term) + 1."

you are right here, the common difference = 1. so dividing by 1 is not necessary.

Your Query :I guess you used that for consecutive numbers, mean = median = (First term + last term) / 2.

yes you are right, in fact, it is true for any set of equally spaced numbers (AP)

Hi Skywalker18 niks18 gmatbusters

What is the sum of odd integers from 35 to 85, inclusive?

Quote:
Number of odd integers = (85-35)/2 + 1
= 50/2 + 1
= 26

Can you explain why did you divide by 2?
If I want to count no. of terms from 1 to 10,
I would perform (Last term - First term) + 1.
But is not above approach only valid for consecutive terms
and sequence starting with 1?

Quote:
Sum of odd integers = (35+85)/2 * 26
= 60 * 26
= 1560

I guess you used that for consecutive numbers, mean = median = (First term + last term) / 2.
Let me know if we are on same page I think you are missing one point here
Always divide by common difference ( this is as per Arithmetic progression , AP)
this is not true we have to divide by common difference of first and last multiple of the integer whose multiples are being found out in this case 7 and 98 are by chance multiples of 7 lets say multiples b/w 7 and 99 even then we do 98-7
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Re: What is the sum of odd integers from 35 to 85, inclusive?  [#permalink]

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Bunuel wrote:
What is the sum of odd integers from 35 to 85, inclusive?

A) 1,560
B) 1,500
C) 1,240
D) 1,120
E) 1,100

Because the numbers are evenly spaced we can find the average.

85+ 35 = 120/2 = 60

# of terms = 85 - 35 = 50/2 = 25 + 1 = 26

26 * 60 = 1,560

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Re: What is the sum of odd integers from 35 to 85, inclusive?  [#permalink]

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No. of odd integers = (85-35)/2 + 1 = 26

Sum of odd integers = average * no. of integers
= ( 35 + 85 ) /2 * 26
= 60 * 26
= 1560
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Re: What is the sum of odd integers from 35 to 85, inclusive?  [#permalink]

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Number of odd integers = (85-35)/2 + 1
= 50/2 + 1
= 26
Sum of odd integers = (35+85)/2 * 26
= 60 * 26
= 1560
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Re: What is the sum of odd integers from 35 to 85, inclusive?  [#permalink]

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no. of odd integers= 85-35/2+1
=26
sum of odd integers= first odd int.+last odd integers/2*no. of odd integers.
35+85/2*26= 1560 ans
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Re: What is the sum of odd integers from 35 to 85, inclusive?  [#permalink]

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Why do you find the number of odd integers? Why then do you add one to it??
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Re: What is the sum of odd integers from 35 to 85, inclusive?  [#permalink]

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ironsheep wrote:
Why do you find the number of odd integers? Why then do you add one to it??

Hey ironsheep,

The question has been solved using the formula so that you can avoid the long calculations of adding each of the digits.
The reason 1 is added is that in the set 35 & 85 both are included, hence if we don't add 1 while calculating the number of terms we will be missing 1 term

Hope this helps.
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Re: What is the sum of odd integers from 35 to 85, inclusive?  [#permalink]

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Bunuel wrote:
What is the sum of odd integers from 35 to 85, inclusive?

A) 1,560
B) 1,500
C) 1,240
D) 1,120
E) 1,100

a slightly different way
sum of n consective odd integers ( n+1)^2/4
so sum of odd integers from 35 to 85
sum of integers 1 to 85 - sum of integers ( 1 to 33)
(86*86)/4 - ( 34*34)/4 = 1849-289 ; 1560
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Re: What is the sum of odd integers from 35 to 85, inclusive?  [#permalink]

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The numbers are 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85. There are 26 of these numbers that are odd. 85 minus 35 equals 50 and that 50 equals both odd and even integers. 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85. 26th place is the median of those 50 numbers, but I am still confused on why it is 26 and not 25?? 1/2 of 50 is 25 Re: What is the sum of odd integers from 35 to 85, inclusive?   [#permalink] 26 Jul 2019, 16:33

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