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What is the sum of first 10 non-negative even integers? A) 40 B) 60 C

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What is the sum of first 10 non-negative even integers? A) 40 B) 60 C  [#permalink]

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New post 18 Jun 2017, 20:30
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What is the sum of first 10 non-negative even integers?

A) 40
B) 90
C) 100
D) 110
E) 200

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What is the sum of first 10 non-negative even integers? A) 40 B) 60 C  [#permalink]

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New post 18 Jun 2017, 20:47
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GMATinsight wrote:
What is the sum of first 10 non-negative even integers?

A) 40
B) 90
C) 100
D) 110
E) 200

Source: http://www.GMATinsight.com


First 10 Non - negative numbers \(= 0,1,2,3,4,5,6,7,8,9\)

First 10 Non - negative even numbers \(= 0,2,4,6,8,10,12,14,16,18\)

Properties of zero :

1) Zero is even

2) Zero is neither positive nor negative.

Sum of first n positive even numbers \(= n (n + 1)\)

Sum of first 9 positive even numbers \(= 9 (9 + 1) = 9 * 10 = 90.\)

Therefore sum of first 10 non-negative even integers \(= 90 + 0 = 90.\) Answer (B)...
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Re: What is the sum of first 10 non-negative even integers? A) 40 B) 60 C  [#permalink]

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New post 18 Jun 2017, 21:31
GMATinsight wrote:
What is the sum of first 10 non-negative even integers?

A) 40
B) 90
C) 100
D) 110
E) 200

Source: http://www.GMATinsight.com



Hi,
A method to calculate if you do not know the formula n(n+1) is ...
First number=0..
Tenth number = 0+(10-1)*2=18, 10 is total numbers and 2 is the difference between consecutive integers.

So mean = \(\frac{0+18}{2}=9\)..
Sum = 9*10=90
B
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Re: What is the sum of first 10 non-negative even integers? A) 40 B) 60 C  [#permalink]

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New post 19 Jun 2017, 05:03
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GMATinsight wrote:
What is the sum of first 10 non-negative even integers?

A) 40
B) 90
C) 100
D) 110
E) 200

Source: http://www.GMATinsight.com


Another approach....

We want: 0 + 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18

Let's add the 10 values in PAIRS, starting with the two outermost values and working inwards.
Notice that 0 + 18 = 18
And 2 + 16 = 18
And 4 + 14 = 18
In fact, when we add the values like this, every pair adds to 18

There are 10 values, so there are 5 pairs (all of which add to 18)
So, the sum = 5 x 18 = 90

Answer:

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Re: What is the sum of first 10 non-negative even integers? A) 40 B) 60 C  [#permalink]

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New post 20 Jun 2017, 18:01
GMATinsight wrote:
What is the sum of first 10 non-negative even integers?

A) 40
B) 90
C) 100
D) 110
E) 200


The first 10 non-negative even integers are from 0 to 18.

The average of those integers is (0 + 18)/2 = 18/2 = 9.

Thus, the sum of those integers is 9 x 10 = 90.

Answer: B
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Re: What is the sum of first 10 non-negative even integers? A) 40 B) 60 C  [#permalink]

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New post 20 Jun 2017, 22:28
imo b
this is a tricky question as we are asked sum of first 10 non negative even integers , so we have to include 0 .
our numbers will be 0 2 4 6 8 10 12 14 16 18
sum =10/2(0+18)=90
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Re: What is the sum of first 10 non-negative even integers? A) 40 B) 60 C  [#permalink]

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New post 20 Jun 2017, 23:35
GMATinsight wrote:
What is the sum of first 10 non-negative even integers?

A) 40
B) 90
C) 100
D) 110
E) 200

Source: http://www.GMATinsight.com


First 10 non-ve even integers area : 0, 2, 4,6, 8, .... 18
Sum = 0+2+4+6+8+....+18
=2(0+1+2+3+4......+9)
90
Answer B.

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Re: What is the sum of first 10 non-negative even integers? A) 40 B) 60 C  [#permalink]

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New post 01 Jul 2017, 10:57
Adding pairs we get 18*5=90
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Re: What is the sum of first 10 non-negative even integers? A) 40 B) 60 C  [#permalink]

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New post 01 Jul 2017, 11:45
The sum of the first 10 even integers is given by formula \(n(n+1)\)

Since we have been asked the sum of the first non-negative even integers, it includes 0 as well.
So in essence, we need to find the sum of the first 9 even integers, which is \(9(9+1)\) = 90(Option B)
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Re: What is the sum of first 10 non-negative even integers? A) 40 B) 60 C  [#permalink]

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