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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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Re: What is the tens digit of positive integer x ? [#permalink]
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SOLUTIONWhat 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]
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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. Hence answer A
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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 nonnegative 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 nonnegative integer. Thus x can take following values 30,140,250,380....etc So the ten's digit in not unique InSufficient Answer A
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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 Sufficient2) 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 130,230,330in 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]
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11 Oct 2012, 18:29
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) 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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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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What is the tens digit of positive integer x ? [#permalink]
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17 Jan 2018, 18:24
Bunuel chetan2u niks18 amanvermagmatQuote: 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. 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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17 Jan 2018, 20:48
adkikani wrote: Bunuel chetan2u niks18 amanvermagmatQuote: 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. 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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06 Mar 2018, 14:27
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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, 1 30, 2 30, 3 30, 4 30, 5 30,. . . In ALL possible values of x, the tens digit is always 3Since we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: x divided by 110 has a remainder of 30From statement 2, we can conclude that the possible values of x are: 30, 1 40, 2 50, 3 60, 4 70, 5 80,. . . Notice that the the tens digit can have many different valuesSince we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Answer: A Cheers, Brent
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