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# If n is a positive integer that is less than 10, what is

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If n is a positive integer that is less than 10, what is [#permalink]  26 Jul 2006, 08:51
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hi

plz hwo do u approach this one ? Plz post explanations

If n is a positive integer that is less than 10, what is the value of n?
(1) n is the tenth digit in the decimal representation of 1/n.
(2) n is the hundredth digit in the decimal representation of 1/n

THANKS
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[#permalink]  26 Jul 2006, 09:08
n<10
lets plug in numbers
n=2 1/n-->5
n=3 1/n-->3

and so on it is obviously insuff

lets check st 2
n=2 1/n--> the hundredth digit =0
n=3 1/3---> the hundredth digit =3
n=4 1/4--> the hundredth digit=5
Hence second statement alone insuff
Both together n can be only 3 since 1/3 has 3 as tenth and the hundredth digit
And my bet on C
Hope this helps
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[#permalink]  26 Jul 2006, 09:09
S1: Given 1/n = 0.n

The only number that satisfies this is 3
Sufficient.

S2: Given 1/n = 0.xn where x is some digit.
Two numbers satisfy this 3 and 6.
Not sufficient.

Answer: A.

I don't know of a shortcut to do this problem, you need to quickly know atleast 1/2, 1/3, 1/4, 1/5. This is half the problem. 1/6, 1/7, 1/8, 1/9 need to be computed upto the hundredth.
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Re: DS DIGIT5 [#permalink]  26 Jul 2006, 09:16
mand-y wrote:
:) hi

plz hwo do u approach this one ? Plz post explanations

If n is a positive integer that is less than 10, what is the value of n?
(1) n is the tenth digit in the decimal representation of 1/n.
(2) n is the hundredth digit in the decimal representation of 1/n

THANKS

Yes, A is correct.
(1) we only need to know that 1/3 = 0.33333 , 1/2= 0.5 , for other n we have n> 3>2 --> 1/n< 1/3<1/2 ---> the tenth digit in the decimal 1/n < that of 1/3 (for n> 3) ---> this tenth digit is always < 3 while n is increasingly > 3 ---> this tenth digit is never= n for n> 3 --> the only fit case is n=3 . This is the shortcut in which we only need to know 1/3
--> suff

(2) the first case is n= 3 --> 1/n= 0.3333 ...divide this by 2 we get (1/3)/2 = 0.33333/2= 0.166666 --> there are two cases of n ---> insuff
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[#permalink]  26 Jul 2006, 12:26
A

This is not time consuming.
1/2 = 0.50
1/3 = 0.33
etc.....

St1: Only n = 3 satisfies: SUFF

St2: n = 3 or 6 both satisfies this : INSUFF

Note down:
1/7 = 0.1428 : Notice double of 7 and then double of 14
1/14 = 0.071428: Notice half of 7 and then double of 7 and then double of 14.
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[#permalink]  26 Jul 2006, 20:08
E
consider 1/6 = 0.16666... and 1/3 = 0.333333333....

both of them satisfy I and II
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[#permalink]  26 Jul 2006, 20:10
ps_dahiya wrote:
A

This is not time consuming.
1/2 = 0.50
1/3 = 0.33
etc.....

St1: Only n = 3 satisfies: SUFF

St2: n = 3 or 6 both satisfies this : INSUFF

Note down:
1/7 = 0.1428 : Notice double of 7 and then double of 14
1/14 = 0.071428: Notice half of 7 and then double of 7 and then double of 14.

oops just read other answers...so it is 1/10ths digit and 1/100th digit that makes more sense...i take my ans back....dahiya is correct...
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[#permalink]  28 Jul 2006, 00:36
A.

1) only n=3 satisifies the conditions 1/3 = 0.333

2) Not suff n=3, n=6 satisify the condition
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[#permalink]  28 Jul 2006, 21:16
yep, just keep plugging those numbers ... as simple as that
the man/woman with fastest fingers wins!
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[#permalink]  29 Jul 2006, 20:34
1. Expressing this as math:
1/n = 0 + n/10 + other fractions
equivalent to saying
1/n > n/10
or n^2 < 10
therefore n = 3. (n =1 and 2 are ruled out as they dont fulfil this condition)
- SUFFICIENT
2. Again this implies
1/n = 0 + 1/P + 1/n + (other fractions)
brute force gives 2 results: 3 and 6 - INSUFF

Answer: A
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Re: DS DIGIT5 [#permalink]  29 Jul 2006, 23:34
Clear A

S1. 1/3 = 0.3333 thus n=3
S2. insufficient.
ex.
1/3 = 0.3333.. n=3
but
1/6 = 0.1666.. n=6
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Re: DS DIGIT5   [#permalink] 29 Jul 2006, 23:34
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