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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8149
GMAT 1: 760 Q51 V42 GPA: 3.82
There is a sequence An for a positive integer n such that when An-2 is  [#permalink]

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12 00:00

Difficulty:   55% (hard)

Question Stats: 65% (02:32) correct 35% (02:54) wrong based on 88 sessions

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There is a sequence An for a positive integer n such that when An-2 is divided by An-1 the remainder is An. If A3=6, A4=0, which of the following can be the value of A1?
Attachment: positive integer.jpg [ 14.57 KiB | Viewed 1839 times ]

A. 48
B. 50
C. 52
D. 56
E. 58

* A solution will be posted in two days.

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Marshall & McDonough Moderator D
Joined: 13 Apr 2015
Posts: 1677
Location: India
There is a sequence An for a positive integer n such that when An-2 is  [#permalink]

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When A1/A2, Remainder = A3 = 6 --> A1 = xA2 + 6

When A2/A3, Remainder = A4 = 0 --> A2 = yA3

A1 = xyA3 + 6 = kA3 + 6 = 6(k + 1) --> A1 must be a multiple of 6

Only option A is a multiple of 6

Manager  Joined: 12 Jun 2015
Posts: 78
Re: There is a sequence An for a positive integer n such that when An-2 is  [#permalink]

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An-2 =(An-1)Q + An

A2 = (A3)Q + A4

A2 = 6Q + 0 = 6Q

therefore
A1 = (6Q)Q + 6 = 6Q^2 + 6 = 6(Q^2 + 1)

Thus A1 is definitely divisible by 6
Out of the given options, only A is divisible by 6

Correct Option : A
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8149
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: There is a sequence An for a positive integer n such that when An-2 is  [#permalink]

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There is a sequence An for a positive integer n such that when An-2 is divided by An-1 the remainder is An. If A3=6, A4=0, which of the following can be the value of A1?

A. 48
B. 50
C. 52
D. 56
E. 58

==> If n=4, A2=A3Q+A4=6Q+0=6Q is derived.
If n=3, from A1=A2P+A3=6QP+6=6(QP+1), it becomes always a multiple of 6.
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Joined: 18 Jul 2019
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Re: There is a sequence An for a positive integer n such that when An-2 is  [#permalink]

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MathRevolution wrote:
There is a sequence An for a positive integer n such that when An-2 is divided by An-1 the remainder is An. If A3=6, A4=0, which of the following can be the value of A1?
Attachment:
positive integer.jpg

A. 48
B. 50
C. 52
D. 56
E. 58

* A solution will be posted in two days.

Does the question imply that when A1/A2 the remainder is A3. If yes then A3=6, which means when A1/A2 the remainder should be 6. --> Since, when A2/A3 , remainder is A4=0, A2should be also a multiple of 6. --> when A1 / A2( multiple of 6) remainder should be 6 as per q. If 48 / multiple of 6, remainder is 0 and not 6. I am confused.
Intern  B
Joined: 08 May 2019
Posts: 17
There is a sequence An for a positive integer n such that when An-2 is  [#permalink]

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MathRevolution wrote:
There is a sequence An for a positive integer n such that when An-2 is divided by An-1 the remainder is An. If A3=6, A4=0, which of the following can be the value of A1?
Attachment:
positive integer.jpg

A. 48
B. 50
C. 52
D. 56
E. 58

* A solution will be posted in two days.

Here A4=A2/A3
Hence A2 should be a multiple of 6.(6,12,18,24....so on).

Now A3=A1/A2

Here A3=6(reminder) and A2=6 or 12 or 18 and so on

Therefore reminder should be 6 when A1 is divided by 6k.

In none on the mentioned options above condition gets satisfied.

Kindly correct where I am wrong. There is a sequence An for a positive integer n such that when An-2 is   [#permalink] 19 Oct 2019, 21:24
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