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What is the sum of 60 consecutive integers from -29 inclusive, in a in

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What is the sum of 60 consecutive integers from -29 inclusive, in a in  [#permalink]

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New post 19 Jun 2016, 17:55
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A
B
C
D
E

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What is the sum of 60 consecutive integers from -29 inclusive, in a increasing order?
A. -29
B. 29
C. -30
D. 30
E. 60

*An answer will be posted in 2 days.

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Re: What is the sum of 60 consecutive integers from -29 inclusive, in a in  [#permalink]

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New post 19 Jun 2016, 21:57
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MathRevolution wrote:
What is the sum of 60 consecutive integers from -29 inclusive, in a increasing order?
A. -29
B. 29
C. -30
D. 30
E. 60

*An answer will be posted in 2 days.


From -29 to -1 --> 29 nos.
zero --> 1 number
from +1 to +29 --> 29 nos.

When we add up nos. from -29 to +29 sum will be zero. Total 59 nos will be added.

60th number will be "30".

Sum of these 60 nos. = 30.

D is the answer.
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Re: What is the sum of 60 consecutive integers from -29 inclusive, in a in  [#permalink]

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New post 21 Jun 2016, 17:18
(-29)+(-28)+…….+(-1)+0+1+…….+28+29+30=30. Hence, the correct answer is D.
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Re: What is the sum of 60 consecutive integers from -29 inclusive, in a in  [#permalink]

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New post 08 Aug 2016, 12:09
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we can solve it by applying direct formula-
tn=a+(n-1)d
tn=-29+(60-1)1
tn=+30 hence answer is D
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Re: What is the sum of 60 consecutive integers from -29 inclusive, in a in  [#permalink]

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New post 08 Aug 2016, 14:39
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30 numbers from -29 is +30, including -29 and 30 themselves. A, C are wrong because the number cannot be negative. B is not the answer since -29+29+1 is 59.
IMO D


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Re: What is the sum of 60 consecutive integers from -29 inclusive, in a in  [#permalink]

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New post 27 Oct 2016, 12:27
For this problem it is useful to try to visualize the number line:

-29 to 0: how many numbers is that? --> 29-0+1 = 30...GREAT! we're half way there

30-1+1 = 30 --> 30+30 = 60

We know that on the left hand side of zero we have -29 as the smallest value and on the right hand side we have all of the same values except 30. -29 cancels out with 29 in addition to all other values greater than -29 and less than 30. Thus, we are left with 30.

D is the correct answer.
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Re: What is the sum of 60 consecutive integers from -29 inclusive, in a in  [#permalink]

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New post 12 Oct 2017, 14:01
1
Number of Integers (inclusive) = N = (Last Number - First Number) +1

Sum of Integers = (First Number + Last Number)*N))/2

1.

We know N is 60 because it tells us that there are 60 integers and the smallest is -29, so -29 is the first number.

N =60 ... So 60 = (Last Number -(-29)) + 1

59 = Last Number - (-29)

59 + (-29) = 30 = Last Number

... So the range of numbers is between -29 to 30

2. Sum of Integers = ((-29)+30))*60))/2 = 30 D
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Re: What is the sum of 60 consecutive integers from -29 inclusive, in a in  [#permalink]

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New post 13 Oct 2017, 12:09
Watching the symmetric pattern, and also including -29

we have -29 ....0 .... 29 both inclusive to be 59 numbers and its resultant sum comes out to be ZERO

So 60th number equal to the sum of the series = 30.
Re: What is the sum of 60 consecutive integers from -29 inclusive, in a in &nbs [#permalink] 13 Oct 2017, 12:09
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