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hundredths digit of k

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hundredths digit of k

by gmatdriller » Sun Oct 10, 2010 1:36 pm
What is the hundredth digit of a three-digit number k?

(1) the hundredths digit of k + 143 is 2
(2) the tenths digit of k + 25 is 7

solution

I only carved out this question in other to understand the concepts better.
My approach:
(1) 200 <= k+143 <= 299......since hundredths digit is "2"
from 200 <= k+143, we get k >= 57
from k+143 <= 299, we get k<= 156
57 <= k <= 156
hundredths digit can be "0" or "1"
INSUFFICIENT

(2) 70 <= k+25 <= 79.......implementing the tenths digit of k only
from 70 <= k+25, we get k >= 45
from k+25 <= 79, we get k <= 54
tenths digit: 4 or 5; we cannot determine the hundredths digit of k
INSUFFICIENT

(1) and (2) combined:
hundredths digit: 0 or 1(57 - 156); tenths digit: 4 or 5(45 - 54)
stuck here: how to use the various combinations of 0/1 for hundredths digit
and 4/5 for tenths digit to arrive at the final range within allowed time.

Please assist in providing a brief conclusion to final part.
Thanks.

IMO answer is


[spoiler]C: the range of k: 145 - 154[/spoiler]
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by Jim@Grockit » Sun Oct 10, 2010 8:14 pm
gmatdriller wrote:What is the hundredth digit of a three-digit number k?

(1) the hundredths digit of k + 143 is 2
(2) the tenths digit of k + 25 is 7

solution

I only carved out this question in other to understand the concepts better.
My approach:
(1) 200 <= k+143 <= 299......since hundredths digit is "2"
from 200 <= k+143, we get k >= 57
from k+143 <= 299, we get k<= 156
57 <= k <= 156
hundredths digit can be "0" or "1"
INSUFFICIENT

(2) 70 <= k+25 <= 79.......implementing the tenths digit of k only
from 70 <= k+25, we get k >= 45
from k+25 <= 79, we get k <= 54
tenths digit: 4 or 5; we cannot determine the hundredths digit of k
INSUFFICIENT

(1) and (2) combined:
hundredths digit: 0 or 1(57 - 156); tenths digit: 4 or 5(45 - 54)
stuck here: how to use the various combinations of 0/1 for hundredths digit
and 4/5 for tenths digit to arrive at the final range within allowed time.

Please assist in providing a brief conclusion to final part.
Thanks.

IMO answer is


[spoiler]C: the range of k: 145 - 154[/spoiler]
Are you missing decimal places in your questions/statements? Or do you mean "hundreds" place? As written, statement 1 is sufficient, because adding a whole number to a decimal does not change the decimal portion of the number. If k is 4.02, adding 143 just makes it 147.02.
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by Geva@EconomistGMAT » Mon Oct 11, 2010 2:30 am
gmatdriller wrote:What is the hundredth digit of a three-digit number k?

(1) the hundredths digit of k + 143 is 2
(2) the tenths digit of k + 25 is 7

solution

I only carved out this question in other to understand the concepts better.
My approach:
(1) 200 <= k+143 <= 299......since hundredths digit is "2"
from 200 <= k+143, we get k >= 57
from k+143 <= 299, we get k<= 156
57 <= k <= 156
hundredths digit can be "0" or "1"
INSUFFICIENT

(2) 70 <= k+25 <= 79.......implementing the tenths digit of k only
from 70 <= k+25, we get k >= 45
from k+25 <= 79, we get k <= 54
tenths digit: 4 or 5; we cannot determine the hundredths digit of k
INSUFFICIENT

(1) and (2) combined:
hundredths digit: 0 or 1(57 - 156); tenths digit: 4 or 5(45 - 54)
stuck here: how to use the various combinations of 0/1 for hundredths digit
and 4/5 for tenths digit to arrive at the final range within allowed time.

Please assist in providing a brief conclusion to final part.
Thanks.

IMO answer is


[spoiler]C: the range of k: 145 - 154[/spoiler]
I'm working under the assumption that the question used "hundreds" and "tens", and not "hundredths", and "tenths".
What you lack is a step back and a look at what the question is asking. You don't need to know the exact value of k, or even the range of possible values of k: you just need to know whether it has more than one possible value for its hundreds digit.
Stat. (1): obviously, we can find an example of k with a hundreds digit of 1: if k+143=243, then k=100. The question is, can we find a counter example, i.e a value of with a different hundreds digit?
If we take the upper extreme k+143=299, we'll still get a number in the 100+ range (no need to calculate all the way - you just care about the hundreds digit!), so hundreds digit is still 1.
If we take the lower extreme, k+143=200, we'll get a number in the 0-99 range (again, no need to work out all the way). My problem here is that k is defined by the question stem as a "three-digit number", which to me eliminates this range completely: 057 is not really a three digit number. Thus, IMHO, stat. (1) actually limits 3 digit number k to a hundreds digit of 1, and is actually sufficient.

(2) stat. only talks about the tens digit of k. If K+25 has a tens digit of 7, then K+25 could equal 270, or 370, or 370, or 570, etc., allowing k itself to be in any of the ranges above. Insufficient.

The answer is therefore A, provided that the definition of the k as a three digit number was in the original question.

As a general note, don't make the rookie mistake of reading the stem and then diving immediately into the statements - hover around the question stem first, and come up with an initial approach, a definition of what you need to do. In many DS questions, the initial approach should be to try and "break the question" - first try and show that the statement(s) is insufficient (e.g. "I need to find that k has more than one possible hundreds digit"), and only if you can't find a counter example, take a step back and try to see why the statement actually does lead to a single value.
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by gmatdriller » Mon Oct 11, 2010 12:03 pm
Oops! this must be a blind error!
It should be "hundreds" and "tens" digit

Sorry about that.
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by gmatdriller » Mon Oct 11, 2010 12:24 pm
@Jim,
Thanks for your observation and suggestions.

@Geva stern,
You are absolutely correct; the question stem has placed a restriction
saying k is a "three-digit number." In that case, I agree (1) is sufficient, but (2) is not.

Meanwhile, if the question says k is an integer, and we are asked to determine the
hundreds digit. In that case, we would need to extend to combining (1) and (2) since
(1) gives 2- and 3-digit integers, right?

I do appreciate your contributions.
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