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by shovan85 » Thu Jan 06, 2011 9:10 am
Viper83 wrote:what is the ten digit of the positive integer r?

1. the tens digit of r/10 is 3
2. the hundreds digit of 10r is 6

b
Let us understand this:

xyz.ab be the format of a decimal,
where x = hundreds place
y = tens place
z = unit place
a = tenth place
b = hundredth place

Objective: ten digit of the positive integer r, means, the digit in the place of y?

1: the tens digit of r/10 is 3

y position of r/10 is 3 then we cannot say the y position of r but the x position of r.
Thus the hundreds position of r = 3 but no idea about tens position.

Not Sufficient.

2: the hundreds digit of 10r is 6
divide 10r by 10 we can get the corresponding hundreds/10 = tens place
r = 6
Sufficient

IMO B
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by MAAJ » Thu Jan 06, 2011 1:54 pm
Assume that "r" is some number with digits xyz, and we are looking for y:

1) r/10 = xyz/10 = xy.z HENCE x = 3 [Not sufficient]

2) 10r = xyz x 10 = xyz0 HENCE y = 6 [Sufficient]

The correct answer is (B)
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by GMATGuruNY » Thu Jan 06, 2011 2:46 pm
Viper83 wrote:what is the ten digit of the positive integer r?

1. the tens digit of r/10 is 3
2. the hundreds digit of 10r is 6

b
Statement 1: The tens digit of r/10 is 3
r=300 works, because 300/10 = 30, giving us a tens digit of 3. The tens digit of r=300 is 0.
r=310 works, because 310/10 = 31, giving us a tens digit of 3. The tens digit of r=310 is 1.
Since the tens digit of r can be different values, insufficient.

Statement 2: The hundreds digit of 10r is 6
The only values that will work are 60-69. For example:
r=60, 10r = 600, giving us a hundreds digit of 6.
r=61, 10r = 610, giving us a hundreds digit of 6.
And so on.
Since the tens digit of every integer from 60 to 69 is 6, sufficient.

The correct answer is B.
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