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Intern
Joined: 05 Nov 2005
Posts: 2

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05 Nov 2005, 20:34
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Hello everybody! This is my first time joinning here
I have 2 questions below to ask....I know the answer but I don't know how to do it! I will come back and post the answer tomorrow..

1. What is the remainder when the positive integer x is devided by 8?
(1) When x is divided by 12, the remainder is 5.
(2) When x is divided by 18, the remainder is 11.

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

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VP
Joined: 22 Aug 2005
Posts: 1111

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Location: CA

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05 Nov 2005, 21:13
1. E.

seperatlety both statements are not sufficient
(1)
5 = 5 mod 12 and 5 = 5 mod 8
17 = 5 mod 12 and 17 = 1 mod 8
insufficient

(2)
11 = 11 mod 18 and 11 = 3 mod 8
29 = 11 mod 18 and 29 = 5 mod 8

together:
29 and 65 both satisfy both statements but
29 = 5 mod 8
65 = 1 mod 8

2. B

(1) x = n/16, 0 if n = 1, non zero if n>1
(2) x = n/8 tenths digit non-zero always
1/8 = 0.125
2/8 = 0.25
etc

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Intern
Joined: 01 Jun 2005
Posts: 40

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05 Nov 2005, 22:27
mimihmy wrote:
Hello everybody! This is my first time joinning here
I have 2 questions below to ask....I know the answer but I don't know how to do it! I will come back and post the answer tomorrow..

1. What is the remainder when the positive integer x is devided by 8?
(1) When x is divided by 12, the remainder is 5.
(2) When x is divided by 18, the remainder is 11.

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

1. from (1): x = 12n + 5 . Since n ould be any integer, x could be the sum of 5 and any multiple of 12. Not SUff!

from (2) x = 18m + 5 . Same logic as above. Not SUff

(1) and (2) --> 2 equations, 3 unkowns. not Suff! E it is

2.
from 1: 16x could be 1, 2, 3 etc. the smallest value of x (if tenths digit is 0, the number is smaller than if it is not) would be 1/16 = .0625. for 2, 3, 4... the tenths digit is non zero. Since we have both cases Not suff!

from 2: similarly, 1/8 = .125 for 2/8 3/8 etc the tenths digit has to be nonzero as well since they will be larger than .125. Sufficient

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Intern
Joined: 05 Nov 2005
Posts: 2

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08 Nov 2005, 04:35
You are both correct.

1. Ans = E
2. Ans = B

The explanations of both of yours are very clear and useful for me..Many thanks again..

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08 Nov 2005, 04:35
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