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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]

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08 Oct 2012, 02:51
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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]

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08 Oct 2012, 02:51
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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.

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Re: What is the tens digit of positive integer x ? [#permalink]

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08 Oct 2012, 02:58
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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.

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Re: What is the tens digit of positive integer x ? [#permalink]

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08 Oct 2012, 03:32
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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
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Re: What is the tens digit of positive integer x ? [#permalink]

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08 Oct 2012, 04:44
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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

Solution: A
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Re: What is the tens digit of positive integer x ? [#permalink]

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11 Oct 2012, 13:47
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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

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Re: What is the tens digit of positive integer x ? [#permalink]

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11 Oct 2012, 14:14
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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.

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Re: What is the tens digit of positive integer x ? [#permalink]

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11 Oct 2012, 18:29
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.

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]

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31 Aug 2013, 06:29
Expert's post
Bumping for review and further discussion.
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Re: What is the tens digit of positive integer x ? [#permalink]

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18 May 2014, 11:09
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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
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Re: What is the tens digit of positive integer x ? [#permalink]

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26 Aug 2015, 03:12
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: What is the tens digit of positive integer x ?   [#permalink] 26 Aug 2015, 03:12
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