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If each term in an infinite sequence is found by the equation Sx=8x–6,

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If each term in an infinite sequence is found by the equation Sx=8x–6,  [#permalink]

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New post 03 Feb 2015, 08:42
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If each term in an infinite sequence is found by the equation \(S_x=8^x-6\), and \(S_1=2\), is every term in the sequence divisible by y?

(1) y is an even integer.

(2) At least 2 of the first 4 terms in the sequence are divisible by y.

Kudos for a correct solution.

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Re: If each term in an infinite sequence is found by the equation Sx=8x–6,  [#permalink]

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New post 04 Feb 2015, 00:04
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hi Bunuel, is something missing or typed wrongly in eq Sx..
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Re: If each term in an infinite sequence is found by the equation Sx=8x–6,  [#permalink]

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Re: If each term in an infinite sequence is found by the equation Sx=8x–6,  [#permalink]

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New post Updated on: 04 Feb 2015, 02:37
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Bunuel wrote:
If each term in an infinite sequence is found by the equation \(S_x=8^x-6\), and \(S_1=2\), is every term in the sequence divisible by y?

(1) y is an even integer.

(2) At least 2 of the first 4 terms in the sequence are divisible by y.

Kudos for a correct solution.


S(1)=2; \(S(2)=2^6-6\); \(S(3)=2^9-6\); \(S(4)=2^1^2-6\)

Statement 1: if y = 2, -2, 0 then every term is a multiple of y. If y = 4 then S(1) becomes a proper fraction. Not sufficient.

Statement 2: pick two random terms among those listed above. Each term is divisible by 2, -2, 1, -1, and a multiple of 0 and these values will be divisible by every other number in the senquence.

Answer B.

*Edited: added "a multiple of" before 0.
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Originally posted by gmat6nplus1 on 04 Feb 2015, 01:24.
Last edited by gmat6nplus1 on 04 Feb 2015, 02:37, edited 1 time in total.
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Re: If each term in an infinite sequence is found by the equation Sx=8x–6,  [#permalink]

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New post Updated on: 04 Feb 2015, 02:25
1
Here we go:

S_x=8^x-6, and S_1=2 (Given)

St1: y is an even integer

Well the sequence will always be divisible by 2.
but if we take y as 4 or 6, sequence will not be divisible
Clearly not sufficient.


St2: At least 2 of the first 4 terms in the sequence are divisible by y.

we need to consider the first 4 terms, so better to find out the terms in order to be accurate..

First term = 2 (given) (X = 1)
Second term = 58 = 2*29
Third term = 506 = 2*11*23
Fourth term = 4090 = 2*5*409

Randomly consider any 2 terms.
Common factor : 1, 2, -1, and -2

Option B is correct

Originally posted by DesiGmat on 04 Feb 2015, 02:02.
Last edited by DesiGmat on 04 Feb 2015, 02:25, edited 2 times in total.
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Re: If each term in an infinite sequence is found by the equation Sx=8x–6,  [#permalink]

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New post 09 Feb 2015, 03:45
Bunuel wrote:
If each term in an infinite sequence is found by the equation \(S_x=8^x-6\), and \(S_1=2\), is every term in the sequence divisible by y?

(1) y is an even integer.

(2) At least 2 of the first 4 terms in the sequence are divisible by y.

Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION:

The correct response is (B). If you could determine the value of y, you could say whether every term in the sequence S is divisible by y. Start by expanding the sequence: 2, 58, 506, 4090,…etc. The only way that y can be a factor of ALL the terms is if y = 1 or y = 2.

Statement (1) is not sufficient. If y = 2, then the answer is yes, but if y equals a different even number such as 4, then the answer is no.

Statement (2) tells us that at minimum, two terms are divisible by y. If y = 1 or y = 2, then this holds true and the answer is yes. There is no other common factor of any two of 2, 58, 506, 4090…, etc, so y must equal either 1 or 2. Sufficient.
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Is every term in the sequence divisible by y  [#permalink]

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New post 20 Jan 2017, 19:54
If each term in an infinite sequence is found by the equation S(x)=8^x – 6, and S(1)=2, is every term in the sequence divisible by y?

(1) y is an even integer.

(2) At least 2 of the first 4 terms in the sequence are divisible by y.


(This is a question from Veristasprep. It gave me an explanation for the answer, but I still can't seem to understand the reasoning. Hoping someone can explain the answer. Thank you!!!!)
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Re: Is every term in the sequence divisible by y  [#permalink]

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New post 20 Jan 2017, 21:00
B.

S(1) = 2
S(2) = 58 = 2*29
S(3) = 8^3 - 6 = 2^9 - 6 = 506 = 2*11*23
S(4) = 8^4 - 6 = 2^12 - 6 = 4090 = 2*5*409

Statement 1: y is an even integer
Y can be any one of 2,4,6,.......NOT SUFFICIENT

Statement 2: At least 2 of the first 4 terms in the sequence are divisible by y.
The only common factor is 2. So, Y = 2. SUFFICIENT
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Re: Is every term in the sequence divisible by y  [#permalink]

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New post 21 Jan 2017, 02:23
isoyeon wrote:
If each term in an infinite sequence is found by the equation S(x)=8^x – 6, and S(1)=2, is every term in the sequence divisible by y?

(1) y is an even integer.

(2) At least 2 of the first 4 terms in the sequence are divisible by y.


(This is a question from Veristasprep. It gave me an explanation for the answer, but I still can't seem to understand the reasoning. Hoping someone can explain the answer. Thank you!!!!)


Merging topics. Please refer to the discussion above.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: If each term in an infinite sequence is found by the equation Sx=8x–6,  [#permalink]

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