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Three consecutive even numbers are such that thrice the first number

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Three consecutive even numbers are such that thrice the first number  [#permalink]

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New post 25 Oct 2010, 02:15
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Three consecutive even numbers are such that thrice the first number exceeds double the third by two, the third number is

a) 12
b) 6
c) 8
d) 10
e) 14
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Re: Three consecutive even numbers are such that thrice the first number  [#permalink]

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New post 25 Oct 2010, 03:16
feruz77 wrote:
Three consecutive even numbers are such that thrice the first number exceeds double the third by two, the third number is
a) 12
b) 6
c) 8
d) 10
e) 14



Here you go:
Let's say the first even number is P. So the next two numbers would be P+2 and P+4.
The question says-
3P = 2(P+4) + 2
P = 10
Hence the third number would be - P + 4 => 14

You can also solve this by plugging-in the answers.
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Re: Three consecutive even numbers are such that thrice the first number  [#permalink]

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New post 22 Mar 2017, 12:41
feruz77 wrote:
Three consecutive even numbers are such that thrice the first number exceeds double the third by two, the third number is

a) 12
b) 6
c) 8
d) 10
e) 14


Let the first even # be \(x\) (so the 3 consecutive integers are \(x\), \(x+2\), and \(x+4\)), then: \(3x=2(x+4)+2\) --> \(x=10\) --> third # is \(x+4=10+4=14\).

OR:
If we take the first integer to be \(x-2\) (so the 3 consecutive integers are \(x-2\), \(x\), and \(x+2\)) then: \(3(x-2)=2(x+2)+2\) --> \(x=12\) --> third # is \(x+2=12+2=14\)

Answer: E.

Hope it's clear.
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Re: Three consecutive even numbers are such that thrice the first number  [#permalink]

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New post 22 Mar 2017, 13:24
3 consecutive even integers = n, n+2, n+4

The prompt can be translated to: 3n=2(n+4)+2, simplified we get: 3n=2n+10.

Scanning the answer choices, the simplest "n" value to test would be 10. Plug 10 in for all "n"s.

3(10)=2(10)+10, simplified 30=30. This is the only answer choice that will produce this result. "N" has to be 10. Plug 10 into the equation for the third value and the result is 14. Answer choice E.
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Re: Three consecutive even numbers are such that thrice the first number  [#permalink]

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New post 16 Apr 2018, 16:22
feruz77 wrote:
Three consecutive even numbers are such that thrice the first number exceeds double the third by two, the third number is

a) 12
b) 6
c) 8
d) 10
e) 14


We can let x = 1st even number, (x + 2) = 2nd even number and (x + 4) = 3rd even number. Thus we have:

3x = 2(x + 4) + 2

3x = 2x + 10

x = 10

Since x = 10, the third number is 10 + 4 = 14.

Answer: E
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Re: Three consecutive even numbers are such that thrice the first number &nbs [#permalink] 16 Apr 2018, 16:22
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