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Number theory -2

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by guerrero » Sat Apr 06, 2013 3:46 am
What is the hundreds digit of the three-digit positive integer k if k<600

(1) The units digit of 2K/100 is 6

(2) The tens digit of 10k is 4

(A)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D)EACH statement ALONE is sufficient.
(E)Statements (1) and (2) TOGETHER are NOT sufficient.

OA
A
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Sat Apr 06, 2013 7:32 am
guerrero wrote:What is the hundreds digit of the three-digit positive integer k if k<600

(1) The units digit of 2K/100 is 6

(2) The tens digit of 10k is 4
Target question: What is the hundreds digit of K?

Statement 1: The units digit of 2K/100 is 6
If the units digit of 2K/100 is 6, then the hundreds digit of 2K must be 6
If the hundreds digit of 2K is 6, then the hundreds digit of K must be 3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The tens digit of 10K is 4
There are several values of K that meet this condition. Here are two:
Case a: K = 224, in which case the hundreds digit of K is 2
Case b: K = 324, in which case the hundreds digit of K is 3
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = C

Cheers,
Brent
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by rintoo22 » Sat Apr 06, 2013 9:49 am
Hi Brent,

Can you please elaborate on
Statement 1: The units digit of 2K/100 is 6
If the units digit of 2K/100 is 6, then the hundreds digit of 2K must be 6
If the hundreds digit of 2K is 6, then the hundreds digit of K must be 3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
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by Brent@GMATPrepNow » Sat Apr 06, 2013 11:31 am
rintoo22 wrote:Hi Brent,

Can you please elaborate on
Statement 1: The units digit of 2K/100 is 6
If the units digit of 2K/100 is 6, then the hundreds digit of 2K must be 6
If the hundreds digit of 2K is 6, then the hundreds digit of K must be 3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Sure.
Let's look at some examples.

M = 123
This means that M/100 = 1.23
The units digit of M/100 is 1
The hundreds digit of M is 1

M = 619
This means that M/100 = 6.19
The units digit of M/100 is 6
The hundreds digit of M is 6

M = 5378
This means that M/100 = 53.78
The units digit of M/100 is 3
The hundreds digit of M is 3

Similarly, if the units digit of 2K/100 is 6, then the hundreds digit of 2K must be 6


Now, let's examine the 2nd part of my solution.

If the hundreds digit of 2K is 6, then 2K = 6 _ _ (with spaces representing the missing digits)
So, what does K look like?
Can K = 2 _ _ ?
No.
If we double 2 _ _, we cannot get a 6 as the hundreds digit.

So, if 2K = 6 _ _, it must be the case that K = 3 _ _
In other words, if the hundreds digit of 2K is 6, then the hundreds digit of K must be 3

Cheers,
Brent
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by rintoo22 » Sat Apr 06, 2013 11:45 am
Thanks Brent.
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