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# 26 Does the decimal equivalent of P/Q, where P and Q are

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26 Does the decimal equivalent of P/Q, where P and Q are [#permalink]

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22 May 2008, 20:39
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

26
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

A
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
B
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
C
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D
EACH statement ALONE is sufficient
E
Statements (1) and (2) TOGETHER are NOT sufficient

I think the answer should be E. The two statements together are not sufficient.
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22 May 2008, 20:45
I agree its E - S1 is insufficient, eliminates A and D, S2 is insufficient, eliminates B - even with both together, we cant determine - eliminates D. So the answer is E
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22 May 2008, 20:47
B

any number divide by 8 has a finite number of decimal
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22 May 2008, 22:20
I will try to explain - not sure if fool proof:

Statement 1: 9/3 or 10/3 so insufficient

Statement 2: P/8 noe P= 2n or 2n+1 (either even or odd)

= n/4 or n/4 + 1/8 hence need to see if n/4 is fixed or repeating since 1/8 is fixed

again n is either of the form 2m or 2m+1 hence again check 2m/4 or (2m+1)/4 which leads to to check if m/2 is fixed or not..follwoing the same logic we see tht it has to be always fixed in length.

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22 May 2008, 22:42
Thanks.

confused by the statement2. any number divided by 8 has a finite number of decimal?
If p=8,16,24..., and Q=8, then P/Q=1,2,3..., it's an integer, no decimal number. I think S2 not sufficient alone.

So I chose E.
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22 May 2008, 23:39
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redmouse wrote:
Thanks.

confused by the statement2. any number divided by 8 has a finite number of decimal?
If p=8,16,24..., and Q=8, then P/Q=1,2,3..., it's an integer, no decimal number. I think S2 not sufficient alone.

So I chose E.

You miss the point. The question is whether there will be a finite(0 or 1 or 2 .. countable) number of decimal digits or simply an inifinite chain like ( 0.33333..._ or 0.124145254785....(non recurring)_ ).

Since 1/8 = 0.125 (finite 3 digits), when it is multiplied with any integer, the no. of digits will be finite.
Thus B.
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23 May 2008, 10:54
anirudhoswal wrote:
redmouse wrote:
Thanks.

confused by the statement2. any number divided by 8 has a finite number of decimal?
If p=8,16,24..., and Q=8, then P/Q=1,2,3..., it's an integer, no decimal number. I think S2 not sufficient alone.

So I chose E.

You miss the point. The question is whether there will be a finite(0 or 1 or 2 .. countable) number of decimal digits or simply an inifinite chain like ( 0.33333..._ or 0.124145254785....(non recurring)_ ).

Since 1/8 = 0.125 (finite 3 digits), when it is multiplied with any integer, the no. of digits will be finite.
Thus B.

Does the decimal equivalent of P/Q, where P and Q are positive integers, contain only a finite number of nonzero digits?
Quest ion says it decimal contains finite number of non zero digits.

in the above case 16/8 (p/Q)= 2.000 that means decimal has zero digits right?

So I will chose E
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Re: a math question   [#permalink] 23 May 2008, 10:54
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