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# X1=1, for all positive integers, Xn=1+7Xn-1 , what is the units digit

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Math Revolution GMAT Instructor
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X1=1, for all positive integers, Xn=1+7Xn-1 , what is the units digit  [#permalink]

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08 Feb 2016, 17:45
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15% (low)

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84% (02:10) correct 16% (02:05) wrong based on 106 sessions

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X1=1, for all positive integers, Xn=1+7Xn-1 , what is the units digit of X102?

A. 3
B. 5
C. 8
D. 11
E. 15

Attachment:

X1=1.jpg [ 7.25 KiB | Viewed 1460 times ]

* A solution will be posted in two days.

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Re: X1=1, for all positive integers, Xn=1+7Xn-1 , what is the units digit  [#permalink]

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08 Feb 2016, 19:30
MathRevolution wrote:
X1=1, for all positive integers, Xn=1+7Xn-1 , what is the units digit of X102?

A. 3
B. 5
C. 8
D. 11
E. 15

Attachment:
X1=1.jpg

* A solution will be posted in two days.

X1 = 1
x2 = 1+7*1 = 8
X3 = 1+7*8 = 57
X4 = 1+7*57 = 400

From this we can see for all even X the unit digit is even and for Odd it is Odd.
From the answer choices only C is even hence that is the correct choice.
Math Expert
Joined: 02 Aug 2009
Posts: 7102
Re: X1=1, for all positive integers, Xn=1+7Xn-1 , what is the units digit  [#permalink]

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08 Feb 2016, 20:04
ankushjain wrote:
MathRevolution wrote:
X1=1, for all positive integers, Xn=1+7Xn-1 , what is the units digit of X102?

A. 3
B. 5
C. 8
D. 11
E. 15

Attachment:
X1=1.jpg

* A solution will be posted in two days.

X1 = 1
x2 = 1+7*1 = 8
X3 = 1+7*8 = 57
X4 = 1+7*57 = 400

From this we can see for all even X the unit digit is even and for Odd it is Odd.
From the answer choices only C is even hence that is the correct choice.

hi ankush,
if there was a choice as 0 or 4 also, then what would you have done..
you have to look for patterns in these Qs..
if you check for x5 it will be 1, since x4 had a 0 in units digit..
and thereafter ti will keep following the pattern..
1,8,7,0,1,8,7,0..
repetition is after every 4th number..
102= 4*25 + 2..
so it will have the same units digit as the second number, which is 8..
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Re: X1=1, for all positive integers, Xn=1+7Xn-1 , what is the units digit  [#permalink]

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10 Feb 2016, 20:55
X1=1, for all positive integers, Xn=1+7Xn-1 , what is the units digit of X102?

A. 3
B. 5
C. 8
D. 11
E. 15

--> When substituting, it becomes X1=1, X2=~8, X3=~7. X4=~0, X5=~1. That is, 1 -> 8 -> 7 -> 0 -> 1.. are repeated every 4 cycle.
Thus, X102=X4*25+2 -> X2=~8 and the answer is C.
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Re: X1=1, for all positive integers, Xn=1+7Xn-1 , what is the units digit  [#permalink]

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16 Feb 2016, 02:04
1
Xn=1+7Xn-1

So when n=1, X1 = 1 + 7X(1-1) = 1 (which is true per question) therefore X0=0.
when n=2, X2 = 1 + 7X(2-1) = 1 + 7X1 = 1 + 7(1) = 8 (here we know X1 = 1 from the previous step).

Whatever value N may be, the value of X(n-1) is less than 1.

If N =102, then X(n-1) = 101.

Substituting in the equation,
X102 = 1 + 7(101) = 1 + 707 = 708.
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Re: X1=1, for all positive integers, Xn=1+7Xn-1 , what is the units digit  [#permalink]

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01 Aug 2018, 08:41
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Re: X1=1, for all positive integers, Xn=1+7Xn-1 , what is the units digit &nbs [#permalink] 01 Aug 2018, 08:41
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# X1=1, for all positive integers, Xn=1+7Xn-1 , what is the units digit

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