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Manager  Joined: 06 Apr 2010
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What is the tens digit of the positive integer r?  [#permalink]

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Question Stats: 68% (01:18) correct 32% (01:45) wrong based on 924 sessions

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What is the tens digit of the positive integer r?

(1) The tens digit of r/10 is 3

(2) The hundreds digit of 10r is 6

Originally posted by udaymathapati on 23 Sep 2010, 12:11.
Last edited by Bunuel on 08 Apr 2012, 03:18, edited 1 time in total.
Edited the question
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What is the tens digit of the positive integer r?

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.

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Do we have to assume it is a3 digit number?

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mainhoon wrote:
Do we have to assume it is a3 digit number?

Posted from my mobile device

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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Bunuel wrote:
What is the tens digit of the positive integer r?

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.

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onedayill wrote:
Bunuel wrote:
What is the tens digit of the positive integer r?

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.

I couldn't understand this Statement (2) says that hundreds digit of $$10r$$ (not $$r$$) is 6, but hundreds digit of $$10r$$ is tens digit of $$r$$.
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from statement (1)
r/10=3
r=30 . so possible tens digit is 0.

plz correct me if i am wrong
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TomB wrote:
from statement (1)
r/10=3
r=30 . so possible tens digit is 0.

plz correct me if i am wrong

First of all: as (1) says that the tens digit of r/10 is 3 then r/10 can not equal to 3. r/10 can equal to 30, or 435, or 1234...

1234.567

1 - THOUSANDS
2 - HUNDREDS
3 - TENS
4 - UNITS
. - decimal point
5 - TENTHS
6 - HUNDREDTHS
7 - THOUSANDTHS
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Bunuel wrote:
What is the tens digit of the positive integer r?

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.

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.
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stne wrote:
Bunuel wrote:
What is the tens digit of the positive integer r?

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.

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.

No, that's not correct.

1234.567

1 - THOUSANDS
2 - HUNDREDS
3 - TENS
4 - UNITS
. - decimal point
5 - TENTHS
6 - HUNDREDTHS
7 - THOUSANDTHS

Notice the difference between TENS and TENTHS.
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Re: What is the tens digit of the positive integer r?  [#permalink]

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oops!
what an eye opener today,this issue always confused me. Never saw the difference , thank you Bunuel.
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Bunuel wrote:
What is the tens digit of the positive integer r?

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.

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
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rajatsp wrote:
Bunuel wrote:
What is the tens digit of the positive integer r?

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.

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.

Hope it's clear.
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Re: What is the tens digit of the positive integer r?  [#permalink]

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Hi All,

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

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

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Dear Bunuel, Were I can find similar type question above
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Re: What is the tens digit of the positive integer r?  [#permalink]

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

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Bunuel wrote:
What is the tens digit of the positive integer r?

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.

Sir, I think there's an algebraic approach to this too, can you please tell me if its correct -

let r = 100x + 10y + z

r/10 = 10x + y + z/10
10r = 1000x + 100y + 10z

Stmt 1 - gives x = 3 (tens digit of r/10 which is no use)
Stmt 2 - gives y = 6 (hundreds digit of 10r which is what we need)

Thus ans (B)
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Re: What is the tens digit of the positive integer r?  [#permalink]

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Hi rajeev90,

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.

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

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udaymathapati wrote:
What is the tens digit of the 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 the positive integer r?

Given: r is a positive integer

Statement 1: The tens digit of r/10 is 3
Since r is an INTEGER, 10/r will have 1 digit to the right of the decimal place.
So, r/10 = ????3?.? [each ? represents a digit. Notice that 3 is in the tens position of r/10]
Multiply both sides by 10 to get: r = ????3??
We can see that the HUNDREDS digit of r is 3, but we don't know the TENS digit of r
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The hundreds digit of 10r is 6
Since r is an INTEGER, 10r will have a zero in the units position.
So, 10r = ????6?0 [Notice that 6 is in the hundreds position of 10r]
Divide both sides by 10 to get: r = ????6?
Perfect - the TENS digit of r is 6
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
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