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Well, one thing we know for sure that r is at least 2 digit number as we are asked to find the tens digit of r. You can try for example r to be 2-digit number ab, as it really doesn't matter how many digit integer r is (by the way the fact that r is an integer is irrelevant too).
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Let \(r=abc\), tens digit would be \(b\), so the question is \(b=?\)

(1) The tens digit of r/10 is 3 --> \(\frac{r}{10}=ab.c\) --> tens digit of this number is \(a\), so \(a=3\). No info about \(b\). Not sufficient.

(2) The hundreds digit of 10r is 6 --> \(10r=abc0\) --> hundreds digit of this number is \(b\), so \(b=6\). Sufficient.

Answer: B.

Hi Can anybody explain to me in the case ab.c above, tens digit can be a as well as c , can't it. In a decimal notation there is one units digit but 2 tens and 2 hundreds etc . eg 12345.678 here 5 - units place 4 tens place also 6 tens place

so when we have ab.c and we talk of tens digit how do I know we are talking of a or c ? Thanks.
_________________

Let \(r=abc\), tens digit would be \(b\), so the question is \(b=?\)

(1) The tens digit of r/10 is 3 --> \(\frac{r}{10}=ab.c\) --> tens digit of this number is \(a\), so \(a=3\). No info about \(b\). Not sufficient.

(2) The hundreds digit of 10r is 6 --> \(10r=abc0\) --> hundreds digit of this number is \(b\), so \(b=6\). Sufficient.

Answer: B.

Hi Can anybody explain to me in the case ab.c above, tens digit can be a as well as c , can't it. In a decimal notation there is one units digit but 2 tens and 2 hundreds etc . eg 12345.678 here 5 - units place 4 tens place also 6 tens place

so when we have ab.c and we talk of tens digit how do I know we are talking of a or c ? Thanks.

Let \(r=abc\), tens digit would be \(b\), so the question is \(b=?\)

(1) The tens digit of r/10 is 3 --> \(\frac{r}{10}=ab.c\) --> tens digit of this number is \(a\), so \(a=3\). No info about \(b\). Not sufficient.

(2) The hundreds digit of 10r is 6 --> \(10r=abc0\) --> hundreds digit of this number is \(b\), so \(b=6\). Sufficient.

Answer: B.

Hi Bunuel

Excellent explanation!! Big fan!!

ive understood statement 2 well how ever I tried to use a 2 digit for statement 1.

and this is how I went about it:-

let r = ab

so r/10 = 3 (or r/10 = 3.0)

in the same way ab/10 = 3 ;

which follows a.b = 3

or a.b = 3.0

That leaves us with no tens digit.

so is this the correct reason that a two digit number does not fit for this example?

Also you mentioned that using an integer or any number makes no difference. Please can you elucidate the same.

Thank You

Rajat

The tens digit of r/10 is the hundreds digit of r. For example, if r=300, then the hundreds digit of r is 3 and the tens digit of r/10=30 is 3. So, from (1) we can tell that r is at least a 3-digit number, while from the stem we could imply that r is at least a 2-digit number.

As for an integer part: r not necessary to be an integer, for example, consider r=abc.def, we still need the value of b:

(1) r/10=ab.cdef --> the tens digit of this number is a, so s=3. Not sufficient.

(2)10r=abcd.ef --> the hundreds digit of this number is b, so b=6. Sufficient.

This DS question is based on pattern-matching with a little bit of "math" thrown in. It's perfect for TESTing VALUES.

We're told that R is a positive integer. We're asked for the TENS DIGIT of R.

Fact 1: The tens digit of R/10 = 3

If…. R = 310, then 310/10 = 31 which fits the given information. In this case, the TENS DIGIT of 310 = 1 R = 320, then 320/10 = 32 which fits the given information. In this case, the TENS DIGIT of 320 = 2 Fact 1 is INSUFFICIENT

Fact 2: The hundreds digit of 10R = 6

If…. R = 61, then 10R = 610, which fits the given information. In this case, the TENS DIGIT of 61 = 6 R = 62, then 10R = 620, which fits the given information. In this case, the TENS DIGIT of 62 = 6 We could TEST additional values, but we have enough information here to prove a pattern: for the hundreds digit of 10R to = 6, the TENS DIGIT of R MUST = 6. The answer to the question will ALWAYS be 6. Fact 2 is SUFFICIENT

Yes, your way of organizing the information works nicely to help answer the question. As you continue to practice, you're going to find that almost all of the Quant questions that you face can be solved in a variety of ways, so whatever explanation is included with the question is probably NOT the only approach.

In that same way though, you can't afford to get 'stuck' in one way of thinking. The best Test Takers are flexible enough in their thinking that they can take advantage of how the questions are written to find the fastest way to get to the correct answer. This is all meant to say that it's beneficial to know more than one approach.