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What is the tens digit of positive integer x ?
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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 ?
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08 Oct 2012, 01:51
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 ?
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08 Oct 2012, 01:58
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 ?
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08 Oct 2012, 02:32
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 ?
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11 Oct 2012, 12:47
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 ?
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19 Jun 2014, 08:48
Bunuel wrote: What is the tens digit of positive integer x ?
(1) x divided by 100 has a remainder of 30 > x=100q+30: 30, 130, 230, ... as you can see every such number has 3 as the tens digit. Sufficient.
(2) x divided by 110 has a remainder of 30 > x=110p+30: 30, 140, 250, 360, ... so, there are more than 1 value of the tens digit possible. Not sufficient.
Answer: A. Question 1) x divided by 100 has a remainder of 30 > x=100q+30: 30, 130, 230, ... as you can see every such number has 3 as the tens digit. Sufficient. QUESTION :How exactly are 30, 130, 230 computed?



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Re: What is the tens digit of positive integer x ?
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19 Jun 2014, 08:53
sagnik242 wrote: Bunuel wrote: What is the tens digit of positive integer x ?
(1) x divided by 100 has a remainder of 30 > x=100q+30: 30, 130, 230, ... as you can see every such number has 3 as the tens digit. Sufficient.
(2) x divided by 110 has a remainder of 30 > x=110p+30: 30, 140, 250, 360, ... so, there are more than 1 value of the tens digit possible. Not sufficient.
Answer: A. Question 1) x divided by 100 has a remainder of 30 > x=100q+30: 30, 130, 230, ... as you can see every such number has 3 as the tens digit. Sufficient. QUESTION :How exactly are 30, 130, 230 computed? If q=0, then x=30; If q=1, then x=130; If q=2, then x=230; If q=3, then x=330; ... All these numbers when divided by 100 gives the remainder of 30. Generally, if \(x\) and \(y\) are positive integers, there exist unique integers \(q\) and \(r\), called the quotient and remainder, respectively, such that \(y =divisor*quotient+remainder= xq + r\) and \(0\leq{r}<x\).For example, when 15 is divided by 6, the quotient is 2 and the remainder is 3 since \(15 = 6*2 + 3\). Notice that \(0\leq{r}<x\) means that remainder is a nonnegative integer and always less than divisor.This formula can also be written as \(\frac{y}{x} = q + \frac{r}{x}\). You really need to brush up fundamentals: Hope this helps.
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Re: What is the tens digit of positive integer x ?
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17 Jan 2018, 17:24
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 ?
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17 Jan 2018, 19:48
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 ?
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06 Mar 2018, 13:27
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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Re: What is the tens digit of positive integer x ?
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Re: What is the tens digit of positive integer x ?
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