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Set24-Q.26--P/Q-finite no. of digits

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by prachich1987 » Tue Dec 14, 2010 10:49 pm
Does the decimal equivalent of P/Q, where P and Q are positive integers, contain only a finite number of nonzero digits?

(1) P>Q
(2) Q=8

� Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
� Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
� BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE
is sufficient.
� EACH statement ALONE is sufficient
� Statements (1) and (2) TOGETHER are NOT sufficient
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Source: — Data Sufficiency |
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by naremnaresh » Tue Dec 14, 2010 11:39 pm
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE
is sufficient
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by prachich1987 » Tue Dec 14, 2010 11:53 pm
naremnaresh wrote:BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE
is sufficient
yes the OA is C
Thanks naremnaresh..can u plz explain why both the statements are needed?

I have read somewhere on BTG that if the denominator is in (2^x)*(5^x) form then the we always get decimals ending finitely
Hence 2 is sufficient
It hold true even for P<Q
Lets consider 2/8.The answer is 0.25
Plz advise where I am going wrong?
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by goyalsau » Tue Dec 14, 2010 11:59 pm
prachich1987 wrote:Does the decimal equivalent of P/Q, where P and Q are positive integers, contain only a finite number of nonzero digits?

(1) P>Q
(2) Q=8
Question is P/q is in the form of .3333333333 or .4444444444 or .25 or.23 ,

1) P>Q , let p = 4 and q = 3 , p/q = 1.3333333.

let p = 5 or q = 4 , p/q = 1.25

Not sufficient

2) q = 8 , We are given that p is also a positive integer,

Possible remainders when p is divided by q is 1 , 2 , 3 , 4 , 5 , 7 , 0

in every case value of the expression p/q will increase by .125

like 1/8 = .125 , 2/8 = .25 , 3/8 = .375 till 8/8 = 0 (remainder is zero )

so Sufficient

Answer is B
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by abhishekg21 » Wed Dec 15, 2010 12:07 am
one more for B
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by naremnaresh » Wed Dec 15, 2010 12:10 am
from statement 1.
let p=4 and q = 3 then 4/3 = 1.3333333333.................... which is infinite

if you consider both statements q = 8 then
let p =9
9/8 = 1.125
10/8 = 1.25
11/8 = 1.375
........
which is finite.

so both statements are required.
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by naremnaresh » Wed Dec 15, 2010 12:23 am
prachich1987 sorry for the answer
statement 2 is enough.
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by prachich1987 » Wed Dec 15, 2010 12:24 am
naremnaresh wrote:from statement 1.
let p=4 and q = 3 then 4/3 = 1.3333333333.................... which is infinite

if you consider both statements q = 8 then
let p =9
9/8 = 1.125
10/8 = 1.25
11/8 = 1.375
........
which is finite.

so both statements are required.
But even in the cases where P<Q, we get final results
So I don't think statement 1 is required.
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by abhishekg21 » Wed Dec 15, 2010 1:12 am
Answer is B. 8 is enought to tell us that we have finite decimal places
P> Q does not tell us anyhting.
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by nespinoz » Sat Dec 25, 2010 3:04 pm
The answer is B, because all number divided by 8 is finited.
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