Digit

[guptas08]

What is the tens digit of positive integer r ?

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

[Brent@GMATPrepNow]

What is the tens digit of positive integer r?

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

Target question: What is the tens digit of positive integer r?

Statement 1: The tens digit of r/10 is 3
There are several values of r that satisfy this condition. Here are two:
Case a: r = 312 (since 312/10 = 31.2), in which case the tens digit of r is 1
Case b: r = 352 (since 352/10 = 35.2), in which case the tens digit of r is 5
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The hundreds digit of 10r is 6
Notice what happens when we multiply any positive integer by 10:
34 x 10 = 340
60 x 10 = 600
128 x 10 = 1280
54629 x 10 = 546290
The tens digit in the original number becomes the hundreds digit in the new number.

So, if we're told that the hundreds digit of 10n is 6, then we know that the tens digit in n must be 6
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent

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Hi guptas08,

Brent has properly explained how to answer this question; by TESTing Values, you can have proof of the possibilities. This is a great way to tackle this type of question.

For future reference, the GMAT will test you on this type of "decimal shift" issue (either in DS or PS, or both), so you should be on the lookout for it.

GMAT assassins aren't born, they're made,
Rich