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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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New post 29 Jul 2011, 19:54
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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

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

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New post 29 Jul 2011, 19:56
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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Re: What is the tens digit of positive integer x?  [#permalink]

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New post 30 Jul 2011, 01:26
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.

Therefore the answer is (A).
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Re: What is the tens digit of positive integer x?  [#permalink]

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New post 30 Jul 2011, 06:44
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.

Therefore the answer is (A).


Can you explain how you reached the conclusion for statement (2) that the tens digit will be 4 or 5?
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Re: What is the tens digit of positive integer x?  [#permalink]

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New post 31 Jul 2011, 03:47
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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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Re: What is the tens digit of positive integer x?  [#permalink]

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New post 06 Dec 2017, 03:05
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.

Answer: A.

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? &nbs [#permalink] 06 Dec 2017, 03:05
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