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# What is the tens digit of positive integer x ?

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Manager
Joined: 10 Feb 2012
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Location: India
Concentration: Marketing, Strategy
GMAT 1: 640 Q48 V31
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WE: Marketing (Pharmaceuticals and Biotech)
What is the tens digit of positive integer x ? [#permalink]

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19 Mar 2012, 10:59
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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.
[Reveal] Spoiler: OA
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Joined: 02 Sep 2009
Posts: 39581
Re: What is the tens digit of positive integer x ? [#permalink]

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19 Mar 2012, 11:10
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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.

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

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19 Jun 2014, 09:48
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.

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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19 Jun 2014, 09:53
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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.

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

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19 Aug 2015, 07:06
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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17 Nov 2016, 19:22
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Re: What is the tens digit of positive integer x ? [#permalink]

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23 Apr 2017, 06:53
pratikbais 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.

Thank you for this question, but what are choices A, B, C , D & E?
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Re: What is the tens digit of positive integer x ? [#permalink]

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23 Apr 2017, 22:47
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rosmann wrote:
pratikbais 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.

Thank you for this question, but what are choices A, B, C , D & E?

This is a data sufficiency question. Options for DS questions are always the same.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following post ALL YOU NEED FOR QUANT.

Hope this helps.
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Re: What is the tens digit of positive integer x ?   [#permalink] 23 Apr 2017, 22:47
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