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What is the tens digit of the positive integer r?

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Guest
 Post subject: What is the tens digit of the positive integer r?
 Post Posted: Tue Jul 01, 2008 9:48 pm 
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.

Data Suff.-Gmat Prep 1

How can I go about solving this problem?

Your input is appreciated....
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Guest
 Post subject: Re: What is the tens digit of the positive integer r?
 Post Posted: Wed Jul 02, 2008 12:34 am 
[quote="Anonymous"]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.

B

let the number be xxxx6x
stem 2 says
The hundreds digit of 10r is 6.
thus my new number will xxxx6xx
so unit digit has to be 6 in original number

from stem 1
original number xxxx6x
divide by 10 gives 3 in tens
xxx36
hence no information can be inferred
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Guest
 Post subject:
 Post Posted: Wed Jul 02, 2008 11:56 am 
Hi instructors,
Could you please see if I have a good understanding of the problem from what I have written below? Your input is greatly appreciated....

Is statement 1 insuf. because you are dividing by a power of 10 and when you divide by a power the number of zeros decreases, since here you are dealing with a whole number and no decimal. So, the tens place becomes the units place and therefore the answer is insuf.

In statement 2 you are multiplying by a power of 10, in this case, you are adding zeros, so the 6 now becomes the tens place as opposed to the hundreds place.

The answer is B.


Thanks
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RonPurewal
 Post subject:
 Post Posted: Sat Jul 12, 2008 4:35 am 
Offline
ManhattanGMAT Staff


Posts: 7146
Anonymous wrote:
Hi instructors,
Could you please see if I have a good understanding of the problem from what I have written below? Your input is greatly appreciated....

Is statement 1 insuf. because you are dividing by a power of 10 and when you divide by a power the number of zeros decreases, since here you are dealing with a whole number and no decimal. So, the tens place becomes the units place and therefore the answer is insuf.

In statement 2 you are multiplying by a power of 10, in this case, you are adding zeros, so the 6 now becomes the tens place as opposed to the hundreds place.

The answer is B.


Thanks


correct.

interestingly, the fact that r is an integer is completely irrelevant to the solution; the properties of digits of non-integers are exactly the same as the properties of digits of integers.
there are some special facts about integers, though, because all of their decimal places are 0 (i.e., there's nothing after the decimal point of an integer, except 0000....). for instance, if x is an integer, then both the units and tens digits of 100x must be 0. etc.
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birgiolasj
 Post subject: Re: What is the tens digit of the positive integer r?
 Post Posted: Tue May 17, 2011 10:20 pm 
Offline
Forum Guests


Posts: 1
Given: r is an int > 0
Question: ten's digit of r?
---
1: ten's digit of r/10 is 3
r/10 = 3_
r=3_ * 10
r=3_0
_ is the 10's digit -> not sufficient

---
2: hundreds digit of 10r is 6
6__ = 10r
6_._=r
6 is the 10's digit -> sufficient

B
-----------------
Alternatively,
1: ten's digit of r/10 is 3
number r divided by 10 is thirty something
so, r is three hundred something
don't have ten's -> insufficient

2: hundreds digit of 10r is 6
number r times 10 is 6 hundred something
so, r must be sixty something
got ten's -> sufficient

---
-Justas
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RonPurewal
 Post subject: Re: What is the tens digit of the positive integer r?
 Post Posted: Sat May 21, 2011 4:24 am 
Offline
ManhattanGMAT Staff


Posts: 7146
that's the idea, yes.
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rachelhong2012
 Post subject: Re: What is the tens digit of the positive integer r?
 Post Posted: Sun Feb 12, 2012 4:48 pm 
Offline
Course Students


Posts: 47
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.

one strategy is to put down the rank on a piece of paper
thousands hundreds tens ones tenths hundredths

as you go from left to right, you're decreasing by 10 by each rank spot
as you move from right to left, you're increasing by 10 by each rank spot

(1) by dividing by 10, the decimal had been demoted 1 rank spot to the right. to recover to original number, we have to multiply by 10 and shift 1 rank spot to the left, so the current tens digit would become hundreds digit. doesn't tell us about tens digit, insuff

(2) same logic. by multiplying by 10, the decimal had been promoted and shifted 1 space to the left, so to undo this effect and return to original, we have to shift one rank spot to the right. so the hundreds becomes tens. we know the tens digit. suff

B
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RonPurewal
 Post subject: Re: What is the tens digit of the positive integer r?
 Post Posted: Fri Feb 17, 2012 5:45 am 
Offline
ManhattanGMAT Staff


Posts: 7146
rachel -- good.

it may be more instructive to illustrate what rachel is saying with notation:


statement 1:

we can write r/10 = ...XXX3X.X
(note that the X's don't necessarily stand for the same digit; they are just complete mystery digits. also, note that r/10 has at most one decimal place, because r is an integer.)

multiply both sides by 10 to give
r = ...XXX3XX
in other words, the hundreds digit of r is 3. that is cute, but it doesn't help us answer the question.



statement 2:

we can write 10r = ...XXX6X0
(note that the last digit of 10r has to be zero, because r is an integer.)

divide both sides by 10 to give
r = ...XXX6X
this gives us what we want: the tens digit is 6.
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