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# What is the tens digit of positive integer x?

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Manager
Joined: 17 Dec 2010
Posts: 91
Location: Australia
GMAT 1: 690 Q48 V37
GPA: 3.37
WE: Engineering (Consulting)
What is the tens digit of positive integer x? [#permalink]

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29 Jul 2011, 20:54
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5% (low)

Question Stats:

79% (00:41) correct 21% (00:53) wrong based on 163 sessions

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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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/what-is-the- ... 40248.html
[Reveal] Spoiler: OA

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Manager
Joined: 17 Dec 2010
Posts: 91
Location: Australia
GMAT 1: 690 Q48 V37
GPA: 3.37
WE: Engineering (Consulting)
Re: What is the tens digit of positive integer x? [#permalink]

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29 Jul 2011, 20:56
False alarm - it's all 100% clear to me now

Even though the statements net different outcomes (i.e. "x" is a different number in each of the statements), the two statements aren't contradictory
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VP
Joined: 24 Jul 2011
Posts: 1353
GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Re: What is the tens digit of positive integer x? [#permalink]

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30 Jul 2011, 02:26
Using statement (1), x will have a tens digit of 3 always. Sufficient.
Using statement (2), x can have a tens digit of 4 (as in 140) or 5(as in 250) and so on. Insufficient.

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Manager
Joined: 30 Jul 2011
Posts: 108
Location: United States (NJ)
Concentration: General Management, Finance
GMAT 1: 520 Q40 V21
GPA: 2.95
Re: What is the tens digit of positive integer x? [#permalink]

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30 Jul 2011, 07:44
GyanOne wrote:
Using statement (1), x will have a tens digit of 3 always. Sufficient.
Using statement (2), x can have a tens digit of 4 (as in 140) or 5(as in 250) and so on. Insufficient.

Can you explain how you reached the conclusion for statement (2) that the tens digit will be 4 or 5?
VP
Joined: 24 Jul 2011
Posts: 1353
GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Re: What is the tens digit of positive integer x? [#permalink]

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31 Jul 2011, 04:47
1
KUDOS
restore,

If x=140, then x divided by 110 will leave a remainder of 30. In this case the tens digit of x is 4.
If x=250, then x divided by 110 will leave a remainder of 30. In this case the tens digit of x is 5.

I used these two as examples just to illustrate that two different answers are possible for the tens digit, and so statement (2) alone is insufficient. These two examples do not form an exhaustive set of examples for the tens digit in x as defined. In fact, if we list out all cases, x can have a tens digit of 0 to 9 (both inclusive), and still leave 30 as a remainder when divided by 110.

Hope this clarified.
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Math Expert
Joined: 02 Sep 2009
Posts: 44636
Re: What is the tens digit of positive integer x? [#permalink]

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06 Dec 2017, 04:05
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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/what-is-the- ... 40248.html
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Re: What is the tens digit of positive integer x?   [#permalink] 06 Dec 2017, 04:05
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