What is the tens digit of the positive integer r?

Question

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

(2) The hundreds digit of 10r is 6

Bunuel · Accepted Answer

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.

EMPOWERgmatRichC · Answer

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:  B

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

Bunuel · Answer

Similar questions to practice: what-is-the-hundredths-digit-in-the-decimal-expression-of-104896.html what-is-the-value-of-the-tenths-digit-of-number-x-1-the-88400.html if-n-is-a-positive-integer-and-the-tens-digit-of-n-8-is-6-w-158142.html if-the-units-digit-of-integer-n-is-greater-than-2-what-is-134501.html (OG13) if-n-is-an-integer-what-is-the-units-digit-of-x-135123.html if-n-is-a-positive-integer-what-is-the-tens-digit-of-n-144725.html if-n-is-a-positive-integer-what-is-the-units-digit-of-n-154422.html if-a-b-and-c-are-digits-and-ab-0-what-is-the-value-of-b-130419.html is-the-positive-two-digit-integer-n-less-than-143505.html if-1-d-2-is-the-tenths-digit-of-the-decimal-131532.html if-k-is-a-positive-integer-and-the-tens-digit-of-k-5-is-100041.html if-x-0-abcd-where-a-b-c-and-d-each-represent-a-nonzero-127399.html if-x-0-rstu-where-r-s-t-and-u-each-represent-a-nonzero-109735.html what-is-the-hundredths-digit-of-the-decimal-z-93374.html what-is-the-hundredths-digit-of-the-decimal-m-128272.html what-is-the-hundredths-digit-of-th-decimal-z-126671.html is-the-hundredths-digit-of-the-decimal-d-greater-than-102268.html what-is-the-tens-digit-of-the-positive-integer-r-101570.html what-is-the-hundreths-digit-of-the-decimal-m-1-the-101455.html if-a-is-a-positive-integer-and-if-the-units-digit-of-a-2-is-109036.html if-d-represents-the-hundredths-digit-and-e-represents-the-116821.html in-the-decimal-representation-of-x-where-0-x-1-is-the-99281.html if-digit-h-is-the-hundredths-digit-in-the-decimal-d-0-2h6-101957.html if-t-denotes-the-thousandths-digit-in-the-decimal-138297.html if-1-d-2-is-the-tenths-digit-of-the-decimal-131532.html if-z-is-a-three-digit-positive-integer-what-is-the-value-of-69999.html Hope it helps.

mainhoon · Answer

Do we have to assume it is a3 digit number?

Posted from my mobile device

Bunuel · Answer

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).

TomB · Answer

from statement (1)
 r/10=3
 r=30 . so possible tens digit is 0.

plz correct me if i am wrong

Bunuel · Answer

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  3 0, or 4 3 5, or 12 3 4...

1234.567

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

stne · Answer

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.

Bunuel · Answer

No, that's not correct.

1234.567

1 - THOUSAND S 
2 - HUNDRED S 
3 - TE NS 
4 - UNITS
. - decimal point
5 - TEN THS 
6 - HUNDRED THS 
7 - THOUSAND THS

Notice the difference between TE NS  and TEN THS .

stne · Answer

oops!
what an eye opener today,this issue always confused me. Never saw the difference , thank you Bunuel.

rajatsp · Answer

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

Bunuel · Answer

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.

23a2012 · Answer

Dear Bunuel, Were I can find similar type question above

rajeev90 · Answer

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)

EMPOWERgmatRichC · Answer

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.

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

BrentGMATPrepNow · Answer

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 ?.?     
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     
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

Answer: B

Cheers,
Brent

Shivani170496 · Answer

Hi how can we assume abc/ r is a three digit number ? Its not mentioned in question how many digit r has

If we consider r to be a 4 digit number, the answer is E- Insufficient

Pls explain

Bunuel · Answer

Please read the whole thread - https://gmatclub.com/forum/what-is-the- ... ml#p787270

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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?

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