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# What is the tens digit of the positive integer r?

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

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23 Sep 2010, 11:11
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 08 Apr 2012, 02:18, edited 1 time in total.
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23 Sep 2010, 12:14
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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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23 Sep 2010, 12:34
Do we have to assume it is a3 digit number?

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23 Sep 2010, 12:44
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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23 Sep 2010, 12:52
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

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23 Sep 2010, 12:54
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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24 Sep 2010, 11:30
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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24 Sep 2010, 11:41
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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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24 Sep 2010, 14:05
What is the tens digit of the positive integer r?

Assume r is abc.d, the tens digit is b

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

r/10 = ab.c
tens digit a = 3

insufficient

(2) The hundreds digit of 10r is 6.

10r = abcd
hundreds digit b = 6

sufficient

Ans B

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26 Jun 2013, 00:10
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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26 Jun 2013, 00:14
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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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26 Jun 2013, 00:21
oops!
what an eye opener today,this issue always confused me. Never saw the difference , thank you Bunuel.
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27 Mar 2014, 08:09
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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27 Mar 2014, 09:44
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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

[Reveal] Spoiler:
B

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

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11 Jan 2016, 12:40
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

Assume number 57,367 and we are looking for tens digit (6).

(1) 5736.7 tens digit is 3, as you see it's not sufficient
(2) 573,670 hundreds digit is 6, which is the tens digit of r. Sufficient

Asnwer B
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What is the tens digit of the positive integer r?   [#permalink] 11 Jan 2016, 12:40

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