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What is the tens digit of positive integer x ?

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

(1) x divided by 100 has a remainder of 30.
(2) x divided by 110 has a remainder of 30.

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

Answer: A.
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Re: What is the tens digit of positive integer x ? [#permalink] New post 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.

Hence answer A
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Re: What is the tens digit of positive integer x ? [#permalink] New post 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] New post 08 Oct 2012, 03:44
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1) The number x can be written as 100 * d + 30. No matter what the d value is, the ten's digit will always be 3 Sufficient

2) The number x can be written as 110 * d + 30. Take d = 1 then x = 140. Take d = 2 then the x = 250. Insufficent

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

Answer: A.

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

Answer: A.


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

1) 230 / 100 = 3 10th digit idem for 1530 / 100

2) 250 / 110 = 5 and 470 / 110 = 7

A wins
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Re: What is the tens digit of positive integer x ? [#permalink] New post 31 Aug 2013, 05:29
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Re: What is the tens digit of positive integer x ? [#permalink] New post 18 May 2014, 10:09
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1 ---- the number x can be written as 100 * d + 30.. no matter what the d value is, the ten's digit will always be 3 --- 1 is sufficient

2 ---- 110 * d + 30... take d = 1 then x = 140 .. take d = 2 then x value is 250.. Ten's digit changed.. so 2 is not sufficent

hence A
Re: What is the tens digit of positive integer x ?   [#permalink] 18 May 2014, 10:09
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