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Except for the first two numbers, every number in the sequence –1, 3,

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Except for the first two numbers, every number in the sequence –1, 3,  [#permalink]

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New post Updated on: 10 Jul 2019, 05:06
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Except for the first two numbers, every number in the sequence –1, 3, 2, . . . is the sum of the two immediately preceding numbers. How many numbers of this sequence are even?

(A) none
(B) one
(C) two
(D) three
(E) more than three

Source: Nova GMAT
Difficulty Level: 550

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Originally posted by rohan2345 on 16 May 2017, 00:32.
Last edited by SajjadAhmad on 10 Jul 2019, 05:06, edited 2 times in total.
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Re: Except for the first two numbers, every number in the sequence –1, 3,  [#permalink]

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New post 16 May 2017, 00:40
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Re: Except for the first two numbers, every number in the sequence –1, 3,  [#permalink]

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New post 16 May 2017, 05:45
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rohan2345 wrote:
Except for the first two numbers, every number in the sequence –1, 3, 2, . . . is the sum of the two immediately preceding numbers. How many numbers of this sequence are even?

(A) none
(B) one
(C) two
(D) three
(E) more than three


Another approach is to ignore the numerical values and just apply the rules for EVEN/ODD integers.
So, -1, 3, 2, . . . becomes ODD, ODD, EVEN, . . .

When we apply the ODD/EVEN rules, we get: ODD, ODD, EVEN, ODD, ODD, EVEN, ODD, ODD, EVEN, ODD, ODD, EVEN, ODD, ODD, ....

Answer:

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Re: Except for the first two numbers, every number in the sequence –1, 3,  [#permalink]

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New post 16 May 2017, 08:12
rohan2345 wrote:
Except for the first two numbers, every number in the sequence –1, 3, 2, . . . is the sum of the two immediately preceding numbers. How many numbers of this sequence are even?

(A) none
(B) one
(C) two
(D) three
(E) more than three


Let's expand the series - { -1 , 3 ,2, 5 , 7 , 12, 19 , 31 , 50 , 81 , 131 , 212.............. }

Thus, by adding a few numbers ( Actually ) we come to know that the correct answer will be (E) more than three
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Re: Except for the first two numbers, every number in the sequence –1, 3,  [#permalink]

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New post 19 May 2017, 06:17
rohan2345 wrote:
Except for the first two numbers, every number in the sequence –1, 3, 2, . . . is the sum of the two immediately preceding numbers. How many numbers of this sequence are even?

(A) none
(B) one
(C) two
(D) three
(E) more than three


We are given the sequence –1, 3, 2, ... Let’s denote this sequence by a(n). So we have a(1) = –1, a(2) = 3, and a(3) = 2. Let’s also find a few more terms of the sequence. Keep in mind that every term after the first two terms is the sum of the two immediately preceding terms.

a(4) = 3 + 2 = 5

a(5) = 2 + 5 = 7

a(6) = 5 + 7 = 12

a(7) = 7 + 12 = 19

a(8) = 12 + 19 = 31

a(9) = 19 + 31 = 50

As we can see, if n is a multiple of 3, then a(n) is even [notice that a(3) = 2, a(6) = 12, a(9) = 50]. Thus, terms such as a(12), a(15), ... will be also even. We can see that the number of terms that will be even must be more than three.

Answer: E
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Re: Except for the first two numbers, every number in the sequence –1, 3,  [#permalink]

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New post 17 Jan 2019, 05:09
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Re: Except for the first two numbers, every number in the sequence –1, 3,   [#permalink] 17 Jan 2019, 05:09
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