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If x is an integer, does the decimal expression of the fraction x/8 ha

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Bunuel
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If x is an integer, does the decimal expression of the fraction x/8 ha [#permalink] New post   11 Jan 2021, 01:15
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If x is an integer, does the decimal expression of the fraction x/8 have more than 3 non-zero digits?

(1) x is a digit
(2) x ≠ 9


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C
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chetan2u
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Re: If x is an integer, does the decimal expression of the fraction x/8 ha [#permalink] New post   11 Jan 2021, 18:21
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Bunuel wrote:
If x is an integer, does the decimal expression of the fraction x/8 have more than 3 non-zero digits?

(1) x is a digit
(2) x ≠ 9


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Let us analyse the question.
x is an integer. Now x/8=x*1/8=0.125*x

1) x is a digit
The moment x is even, the number of digits would go down further.
If x is less than 8, the value of 0.125*x will be less than 1 and will remain 3-digit for all odd digits.
However if x is 9, the value of 0.125*x will be greater than 1, and we will have 1 on the left if decimal point. => 0.125*9=1.125
Insufficient

2) x is not equal to 9.
If x is between 0 to 8 yes.
If x is 11111111, then no.
Insufficient

Combined
Any value of x from 0 to 8 will give us not more than 3 digits.
Sufficient

C
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Re: If x is an integer, does the decimal expression of the fraction x/8 ha [#permalink] New post   11 Jan 2021, 20:39
answer is c

when we combine 2 statements answer x# 9 and x is digit we definitely get not more than 3 digits
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Re: If x is an integer, does the decimal expression of the fraction x/8 ha [#permalink] New post   12 Jan 2021, 19:06
If x is an integer, does the decimal expression of the fraction x/8 have more than 3 non-zero digits?

x/8= 0.125*x, it has 3 digits in decimal expression.

Stat1: x is a digit
if x is 1 to 8 then x/8 will have 3 digits only, but at x= 9, x/8 will be = 0.125*9= 1.125, means 4 digits in expression. Not sufficient.

Stat2: x ≠ 9
Between x= 1 to 8, x/8 will have 3 digits only, but at x>9, x/8 may have more than 3 digits in the expression. Not sufficient

Combining both, x/8 will have 3 digits only in expression. Sufficient.

So, It is C. :)
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Re: If x is an integer, does the decimal expression of the fraction x/8 ha [#permalink] New post   22 Jan 2021, 02:04
TarunKumar1234 wrote:
If x is an integer, does the decimal expression of the fraction x/8 have more than 3 non-zero digits?

x/8= 0.125*x, it has 3 digits in decimal expression.

Stat1: x is a digit
if x is 1 to 8 then x/8 will have 3 digits only, but at x= 9, x/8 will be = 0.125*9= 1.125, means 4 digits in expression. Not sufficient.

Stat2: x ≠ 9
Between x= 1 to 8, x/8 will have 3 digits only, but at x>9, x/8 may have more than 3 digits in the expression. Not sufficient

Combining both, x/8 will have 3 digits only in expression. Sufficient.

So, It is C. :)


Appreciate your response but could you shed some light on State 1 where x/8 = 1.125 and quest stem asks us about non zero digits in decimal expression which is only 3 (.125 ) and hence suffice to come to conclusion.
Thanks
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Re: If x is an integer, does the decimal expression of the fraction x/8 ha [#permalink] New post   23 Jan 2021, 02:30
ShubhamA wrote:
TarunKumar1234 wrote:
If x is an integer, does the decimal expression of the fraction x/8 have more than 3 non-zero digits?

x/8= 0.125*x, it has 3 digits in decimal expression.

Stat1: x is a digit
if x is 1 to 8 then x/8 will have 3 digits only, but at x= 9, x/8 will be = 0.125*9= 1.125, means 4 digits in expression. Not sufficient.

Stat2: x ≠ 9
Between x= 1 to 8, x/8 will have 3 digits only, but at x>9, x/8 may have more than 3 digits in the expression. Not sufficient

Combining both, x/8 will have 3 digits only in expression. Sufficient.

So, It is C. :)


Appreciate your response but could you shed some light on State 1 where x/8 = 1.125 and quest stem asks us about non zero digits in decimal expression which is only 3 (.125 ) and hence suffice to come to conclusion.
Thanks


ShubhamA, Decimal expression doesn't mean the digits after the decimal points. It just means dividing the fraction. 1.20, 0.34, 1.0, 99.0, 100.12 are all decimal expressions of some or the other fractions.
And in this case, 1.125 gives us 4 non-zero digits (1,1,2 and 5)
Hope this helps! :)
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Re: If x is an integer, does the decimal expression of the fraction x/8 ha [#permalink] New post   12 Mar 2021, 07:23
No where does it say that x can't be more than 9? For eg: if you combine A and B, we can take 10/9 as the number and resultant fraction would be 1.125 (4 non zero digits) or 12/9 (1.375). We can also take 11/9 yielding 1.25 (3 non zero digits), giving a yes and no answer.

Not sure why is the OA C? IMO it should be E.
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Re: If x is an integer, does the decimal expression of the fraction x/8 ha [#permalink] New post   12 Mar 2021, 22:15
ravigupta2912 wrote:
No where does it say that x can't be more than 9? For eg: if you combine A and B, we can take 10/9 as the number and resultant fraction would be 1.125 (4 non zero digits) or 12/9 (1.375). We can also take 11/9 yielding 1.25 (3 non zero digits), giving a yes and no answer.

Not sure why is the OA C? IMO it should be E.


ravigupta2912, statement 1 clearly says that X is a digit. Digits are from 0 to 9.
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Re: If x is an integer, does the decimal expression of the fraction x/8 ha [#permalink]
12 Mar 2021, 22:15
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