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# What is the remainder when the positive integer x is divided

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Manager
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What is the remainder when the positive integer x is divided [#permalink]

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26 Mar 2007, 23:24
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What is the remainder when the positive integer x is divided by 8?
(1) When x is divided by 12, the remainder is 5.
(2) When x is divided by 18, the remainder is 11.

In the decimal representation of x, where 0 < x < 1, what is the tenths digit if x nonzero?
(1) 16x is an integer.
(2) 8x is an integer.

Favorable Unfavorable Not Sure
Candidate M 40 20 40
Candidate N 30 35 35

The table above shows the results of a survey of 100 voters each responded â€œfavorableâ€
Director
Joined: 14 Jan 2007
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27 Mar 2007, 03:21
[quote="GMAThopeful"]What is the remainder when the positive integer x is divided by 8?
(1) When x is divided by 12, the remainder is 5.
(2) When x is divided by 18, the remainder is 11.

Statement 1 - possible values of x are 17, 29, 41, 53, 65....
remainder when x is divided by 8 are 1, 5, 1, 5, 1. So NOT suff

Statement 2 - possible values of x are 29, 47, 65,.......
remainder when x is divided by 8 are 5, 7, 1..... So NOT suff

Combining 1 and 2:
common numbers in statement 1 and 2 are 29, 65,.....
remainder when x is divided by 8 are 5,1 so NOT suff

Director
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27 Mar 2007, 06:25
Answer should be 1) E, 2)
E, 3) C

1) E as explained

2) 16x is an integer so X can be any of these numbers 0.125 or 0.25 or 0.5
similarly 8x can be either 0.125 or 0.5 etc. by combining also we may not get the result. hence

3) from set theory, lets say favorable for M is MF unfavourable for M is M
U, fav for N is NF unfavourable N is NU, while not sure for M and F are MS and NS.

putting the values we have 100 = MF + NF - (MF and NF) + UM + UN-(UM and UN) + MS + NS - (MS and NS)

from 1 will have 40 people have not voted in favour of either M or N. so from this can form another equation i.e.

40 = UM + UN - (UM and UN) + MS + NS - (MS and NS)

and from 2 we have ( UM and UN) = 10

not putting the values will get (MS + NS)

subsituting these valuse in first equation we may know the value of (MF+NF)

neither of 1 or 2 is sufficient by its own.

regards,

Amardeep
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27 Mar 2007, 08:08
how does the forum rate Q3?

in which category would Q3 fall? simple/intermediate/difficult?

I ask this coz I was stumped by Q3
Director
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27 Mar 2007, 16:50
In the decimal representation of x, where 0 < x < 1, what is the tenths digit if x nonzero?
(1) 16x is an integer.
(2) 8x is an integer.

I agree with Amardeep.
Is there any method other than plug-in numbers.
27 Mar 2007, 16:50
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