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What is the tens digit of positive integer x ? [#permalink]
 08 Oct 2012, 02:51
Question Stats:
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The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions ProjectWhat 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
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Re: What is the tens digit of positive integer x ? [#permalink]
08 Oct 2012, 02:51
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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]
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]
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 Answer A
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Re: What is the tens digit of positive integer x ? [#permalink]
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]
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 Answer : A
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Re: What is the tens digit of positive integer x ? [#permalink]
11 Oct 2012, 14:14
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. Kudos points given to everyone with correct solution. Let me know if I missed someone.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat NEW!!!
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!, 11 New DS set. NEW!!!
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Re: What is the tens digit of positive integer x ? [#permalink]
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 ?
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11 Oct 2012, 18:29
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