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# What is the range of 30 consecutive even numbers?

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Math Revolution GMAT Instructor
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What is the range of 30 consecutive even numbers?  [#permalink]

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14 Feb 2017, 00:17
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Difficulty:

5% (low)

Question Stats:

82% (00:50) correct 18% (01:10) wrong based on 88 sessions

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What is the range of 30 consecutive even numbers?

A. 54
B. 56
C. 58
D. 60
E. 62

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Re: What is the range of 30 consecutive even numbers?  [#permalink]

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14 Feb 2017, 01:17
It should be (n-1)d;
i.e. (30-1)*2 = 58;
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Re: What is the range of 30 consecutive even numbers?  [#permalink]

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14 Feb 2017, 05:04
let 2 be the first number
nth number is = a+(n-1)d = 2 +(30-1)2 = 60

Range = lasst number - first number = 60 - 2 = 58
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Re: What is the range of 30 consecutive even numbers?  [#permalink]

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14 Feb 2017, 05:09
Top Contributor
1
MathRevolution wrote:
What is the range of 30 consecutive even numbers?

A. 54
B. 56
C. 58
D. 60
E. 62

We can also solve this question without using a formula.
Instead, we'll look for a pattern.

Let 2 be the first even number and go from there.

1st even number = 2 = 2(1)
2nd even number = 4 = 2(2)
3rd even number = 6 = 2(3)
4th even number = 8 = 2(4)
.
.
.
30th even # = 2(30) = 60

Range = 60 - 2 = 58

Cheers,
Brent
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Re: What is the range of 30 consecutive even numbers?  [#permalink]

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14 Feb 2017, 07:12
MathRevolution wrote:
What is the range of 30 consecutive even numbers?

A. 54
B. 56
C. 58
D. 60
E. 62

The range of the 30 consecutive even numbers will be - { 2 , 4 , 6........... 54, 56 , 58 , 60 }

Thus we have a series range will be 60 - 2 = 58

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Re: What is the range of 30 consecutive even numbers?  [#permalink]

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18 Feb 2017, 07:03
==> The number of consecutive numbers become (last-first/2)+1=(range/2)+1. In other words, from (range/2)+1=30, you get range/2=29, range=2(29)=58.

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Re: What is the range of 30 consecutive even numbers?  [#permalink]

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02 Mar 2017, 03:57
option C should be the answer
it does not affect the result whatever no. we choose the range will be same for the consecutive even integers
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Re: What is the range of 30 consecutive even numbers?  [#permalink]

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06 Mar 2017, 17:12
MathRevolution wrote:
What is the range of 30 consecutive even numbers?

A. 54
B. 56
C. 58
D. 60
E. 62

If the first even number is n, then the second is n + 2 = n + 2(1), the third is n + 4 = n + 2(2), the fourth is n + 6 = n + 2(3), etc. As we can see, the 30th even number will be n + 2(29). Thus the range is n + 2(29) - n = 2(29) = 58.

Alternate Solution:

Let’s create a simple sequence of consecutive even numbers by letting 2 be the first number. Let’s use the formula for the nth term of an arithmetic sequence: a_n = a_1 + (n-1)d, in which n = 30 and the common difference d = 2. Thus, the 30th consecutive even number will be a_30 = 2 + (29)(2) = 60. (Note that if you can’t quickly recall the formula for the nth term of an arithmetic sequence, you can actually count this out on your fingers!) The formula for the range is Range = Highest value – Lowest value, and thus we have Range = 60 – 2 = 58.

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Re: What is the range of 30 consecutive even numbers?  [#permalink]

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17 Apr 2018, 06:47
I have one minor confusion. I was wondering why aren't we including the number 0 in this range as well? 0 is an even number as well. Shouldn't the range be 60-0 instead of 60-2? Please help clear my doubt!
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Re: What is the range of 30 consecutive even numbers?  [#permalink]

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17 Apr 2018, 06:54
2
kingyoungin211 wrote:
I have one minor confusion. I was wondering why aren't we including the number 0 in this range as well? 0 is an even number as well. Shouldn't the range be 60-0 instead of 60-2? Please help clear my doubt!

The range of any 30 consecutive even numbers will be 58. If we consider 0 to be the first number in the sequence, then 30th number will be 58. The range = 58 - 0 = 58.
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Re: What is the range of 30 consecutive even numbers? &nbs [#permalink] 17 Apr 2018, 06:54
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