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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] New post 19 Mar 2012, 09:59
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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] New post 19 Mar 2012, 10:10
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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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Re: What is the tens digit of positive integer x ? [#permalink] 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] New post 19 Jun 2014, 08:53
Expert's post
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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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] 19 Jun 2014, 08:53
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