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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 ?

Wed Dec 06, 2017 5:34 am
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.

What's the best way to determine whether statement 1 is sufficient? Can any experts help?

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Wed Dec 06, 2017 6:06 am
ardz24 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.
Statement 1:
Since dividing x by 100 leaves a remainder of 30, x is 30 MORE THAN A MULTIPLE OF 100.
In math terms:
x = 100a + 30, where a is a nonnegative integer.
Options for x:
30, 130, 230, 330...
In every case, the tens digit of x is 3.
SUFFICIENT.

Statement 2:
Since dividing x by 110 leaves a remainder of 30, x is 30 MORE THAN A MULTIPLE OF 110.
In math terms:
x = 110b + 30, where b is a nonnegative integer.
Options for x:
30, 140, 250, 360...
Since the tens digit of x can be different values, INSUFFICIENT.

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