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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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03 Feb 2015, 08:42
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Difficulty:

85% (hard)

Question Stats:

53% (02:48) correct 47% (02:07) wrong based on 221 sessions

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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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04 Feb 2015, 00:04
1
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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04 Feb 2015, 01:00
chetan2u wrote:
hi Bunuel, is something missing or typed wrongly in eq Sx..

Edited formatting error. Thank you.
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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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Updated on: 04 Feb 2015, 02:37
1
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.

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

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09 Sep 2018, 00:49
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Re: If each term in an infinite sequence is found by the equation Sx=8x–6,   [#permalink] 09 Sep 2018, 00:49
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