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Re: What is the tens digit of positive integer x ? [#permalink]
08 Oct 2012, 01:51

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Expert's post

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SOLUTION

What is the tens digit of positive integer x ?

(1) x divided by 100 has a remainder of 30 --> \(x=100q+30\), so \(x\) can be: 30, 130, 230, ... Each has the tens digit of 3. Sufficient.

(2) x divided by 110 has a remainder of 30 --> \(x=110p+30\), so \(x\) can be: 30, 250, ... We already have two values for the tens digit. Not sufficient.

Re: What is the tens digit of positive integer x ? [#permalink]
08 Oct 2012, 01:58

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St 1: Sufficient: X should be number such as 130, 230, 330, 430.... In all case if we divide X by 100 the remainder is 30. so the tens digit is 3 St 2: Insufficient: Let say X be 140 : In this case the remainder is 30 when divided by 110, So tens digit is 4 Let say X be 250: In this case the remainder is 30 when divided by 110, So tens digit is 5.

Re: What is the tens digit of positive integer x ? [#permalink]
08 Oct 2012, 02:32

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The best way to solve this question is to use equation rather than getting stuck in remainder part 1) x = 100a+30 , where a is non-negative integer. Thus x can take following values 30,130,230,330....etc So the ten's digit always will be 3 Sufficient 2) x = 110a+30 , where a is non-negative integer. Thus x can take following values 30,140,250,380....etc So the ten's digit in not unique In-Sufficient Answer A _________________

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Re: What is the tens digit of positive integer x ? [#permalink]
11 Oct 2012, 12:47

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What is the tens digit of positive integer x ?

(1) x divided by 100 has a remainder of 30. Means, x=100n+30 ; n=1,2,3... x can be 130,230,330-in all cases tens place is held by 3- sufficient

(2) x divided by 110 has a remainder of 30. Means, x=110n+30 ; n =1,2,3... x can be 110,220,330- the tens place is changing with changing value of n - insufficient

Answer : A _________________

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Re: What is the tens digit of positive integer x ? [#permalink]
11 Oct 2012, 13:14

Expert's post

SOLUTION

What is the tens digit of positive integer x ?

(1) x divided by 100 has a remainder of 30 --> \(x=100q+30\), so \(x\) can be: 30, 130, 230, ... Each has the tens digit of 3. Sufficient. (2) x divided by 110 has a remainder of 30 --> \(x=110p+30\), so \(x\) can be: 30, 250, ... We already have two values for the tens digit. Not sufficient.

Answer: A.

Kudos points given to everyone with correct solution. Let me know if I missed someone. _________________

Re: What is the tens digit of positive integer x ? [#permalink]
11 Oct 2012, 17:29

Expert's post

Bunuel wrote:

SOLUTION

What is the tens digit of positive integer x ?

(1) x divided by 100 has a remainder of 30 --> \(x=100q+30\), so \(x\) can be: 30, 130, 230, ... Each has the tens digit of 3. Sufficient. (2) x divided by 110 has a remainder of 30 --> \(x=110p+30\), so \(x\) can be: 30, 250, ... We already have two values for the tens digit. Not sufficient.

Answer: A.

Even picking numbers approach work fast here (may be not as your and I thought too)