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

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Question Stats: 74% (01:13) correct 26% (01:31) wrong based on 2228 sessions

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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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Question: 58
Page: 280
Difficulty: 600

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

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

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Bunuel chetan2u niks18
amanvermagmat

Quote:
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.

Is it valid to take quotient(p/q) as 0 ? I assumed if divisor is divided by dividend, we need minimum value of quotient to be
non positive for division to be valid.
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Re: What is the tens digit of positive integer x ?  [#permalink]

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Bunuel chetan2u niks18
amanvermagmat

Quote:
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.

Is it valid to take quotient(p/q) as 0 ? I assumed if divisor is divided by dividend, we need minimum value of quotient to be
non positive for division to be valid.

What is the remainder when 30 is divided by 100? Isn't it 30? So, why could not p (or q) be 0?
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Re: What is the tens digit of positive integer x ?  [#permalink]

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Bunuel wrote:
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

Target question: What is the tens digit of positive integer x ?

Statement 1: x divided by 100 has a remainder of 30
ASIDE: When it comes to remainders, we have a nice rule that says:
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
In other words, the possible values of k are: 1, 6, 11, 16, 21, 26, 31, . . . etc.

So, from statement 1, we can conclude that the possible values of x are: 30, 130, 230, 330, 430, 530,. . .
In ALL possible values of x, the tens digit is always 3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x divided by 110 has a remainder of 30
From statement 2, we can conclude that the possible values of x are: 30, 140, 250, 360, 470, 580,. . .
Notice that the the tens digit can have many different values
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

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

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Bunuel , chetan2u,

Does below make sense to solve this ?

X = abcd

1. X/100 = abcd/100 = ab.cd and .cd = 30 so c = tens digit is 3. SUFFICIENT
2. X/110 = abcd/110 gives different value of c NOT SUFFICIENT
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Re: What is the tens digit of positive integer x ?  [#permalink]

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Bunuel wrote:
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.

Practice Questions
Question: 58
Page: 280
Difficulty: 600

1. X is of the form 100p + 30 where possible is a positive integer. No matter what p is, second last digit is going to be 3. Sufficient.

2. X is a 110p + the 30. Now second last digit changes with values of p. Not sufficient.

A is the answer Re: What is the tens digit of positive integer x ?   [#permalink] 30 Oct 2018, 13:20
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