What is the tens digit of positive integer x ? : GMAT Data Sufficiency (DS)
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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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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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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.
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Resources:
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Collection of Questions:
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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., 11 New DS set.


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

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New post 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 ? [#permalink]

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New post 19 Jun 2014, 08:53
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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 non-negative 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:
Theory on remainders problems: remainders-144665.html

Units digits, exponents, remainders problems: new-units-digits-exponents-remainders-problems-168569.html

All DS remainders problems to practice: search.php?search_id=tag&tag_id=198
All PS remainders problems to practice: search.php?search_id=tag&tag_id=199


Hope this helps.
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Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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. ,11 Mixed Questions, 12 Fresh Meat

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., 11 New DS set.


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

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New post 19 Aug 2015, 06:06
This is interesting am benefiting well
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Re: What is the tens digit of positive integer x ? [#permalink]

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Re: What is the tens digit of positive integer x ?   [#permalink] 17 Nov 2016, 18:22
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