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• ### $450 Tuition Credit & Official CAT Packs FREE December 15, 2018 December 15, 2018 10:00 PM PST 11:00 PM PST Get the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### FREE Quant Workshop by e-GMAT! December 16, 2018 December 16, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. # What is the tens digit of the positive integer r?  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Manager Joined: 06 Apr 2010 Posts: 117 What is the tens digit of the positive integer r? [#permalink] ### Show Tags Updated on: 08 Apr 2012, 02:18 8 46 00:00 Difficulty: 35% (medium) Question Stats: 66% (00:48) correct 34% (00:55) wrong based on 1072 sessions ### HideShow timer Statistics 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, 11:11. Last edited by Bunuel on 08 Apr 2012, 02:18, edited 1 time in total. Edited the question ##### Most Helpful Expert Reply Math Expert Joined: 02 Sep 2009 Posts: 51218 Re: Tens Digit? [#permalink] ### Show Tags 23 Sep 2010, 12:14 27 32 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. Answer: B. _________________ ##### General Discussion Director Status: Apply - Last Chance Affiliations: IIT, Purdue, PhD, TauBetaPi Joined: 17 Jul 2010 Posts: 624 Schools: Wharton, Sloan, Chicago, Haas WE 1: 8 years in Oil&Gas Re: Tens Digit? [#permalink] ### Show Tags 23 Sep 2010, 12:34 2 Do we have to assume it is a3 digit number? Posted from my mobile device _________________ Consider kudos, they are good for health Math Expert Joined: 02 Sep 2009 Posts: 51218 Re: Tens Digit? [#permalink] ### Show Tags 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). _________________ Senior Manager Joined: 25 Feb 2010 Posts: 352 Re: Tens Digit? [#permalink] ### Show Tags 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. Answer: B. I couldn't understand this Question is asking about tens digit ans second statement is providing info about hundreds digit. _________________ GGG (Gym / GMAT / Girl) -- Be Serious Its your duty to post OA afterwards; some one must be waiting for that... Math Expert Joined: 02 Sep 2009 Posts: 51218 Re: Tens Digit? [#permalink] ### Show Tags 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. Answer: B. I couldn't understand this Question is asking about tens digit ans second statement is providing info about hundreds digit. Statement (2) says that hundreds digit of $$10r$$ (not $$r$$) is 6, but hundreds digit of $$10r$$ is tens digit of $$r$$. _________________ Senior Manager Joined: 18 Sep 2009 Posts: 285 Re: Tens Digit? [#permalink] ### Show Tags 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 Math Expert Joined: 02 Sep 2009 Posts: 51218 Re: Tens Digit? [#permalink] ### Show Tags 24 Sep 2010, 11:41 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 _________________ Director Joined: 27 May 2012 Posts: 632 Re: Tens Digit? [#permalink] ### Show Tags 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. 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. _________________ - Stne Math Expert Joined: 02 Sep 2009 Posts: 51218 Re: Tens Digit? [#permalink] ### Show Tags 26 Jun 2013, 00:14 2 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. 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. 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. _________________ Director Joined: 27 May 2012 Posts: 632 Re: What is the tens digit of the positive integer r? [#permalink] ### Show Tags 26 Jun 2013, 00:21 oops! what an eye opener today,this issue always confused me. Never saw the difference , thank you Bunuel. _________________ - Stne Intern Joined: 23 Jan 2014 Posts: 2 Location: India WE: Consulting (Consulting) Re: Tens Digit? [#permalink] ### Show Tags 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. 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 Math Expert Joined: 02 Sep 2009 Posts: 51218 Re: Tens Digit? [#permalink] ### Show Tags 27 Mar 2014, 09:44 2 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. 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. Hope it's clear. _________________ EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13095 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: What is the tens digit of the positive integer r? [#permalink] ### Show Tags 09 Apr 2015, 11:52 4 4 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 Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: What is the tens digit of the positive integer r?  [#permalink]

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11 Apr 2015, 15:28
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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12 Apr 2015, 03:28
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Re: What is the tens digit of the positive integer r?  [#permalink]

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16 May 2015, 06:31
1
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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16 May 2015, 09:43
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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06 Mar 2018, 07:10
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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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What is the tens digit of the positive integer r?  [#permalink]

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21 May 2018, 22:26
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.

Hello Bunuel,

Can you tell me why did you chose a three digit number? If we choose a 4 digit number, then the answer will be different.
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# What is the tens digit of the positive integer r?

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