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K is positive three digit integer

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K is positive three digit integer

by KICKGMATASS123 » Sat Jun 06, 2009 8:08 am
If K is a positive three-digit integer, what is the hundreds digit of K?

(1) The hundreds digit of K + 150 is 4.

(2) The tens digit of K + 25 is 7.

Please explain how you got your answer.

OA is E

I spent so much time on this question and still picked C.. Is there an easier way to approach this question???
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by KICKGMATASS123 » Sat Jun 06, 2009 8:31 am
Anyone??????
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by ssmiles08 » Sat Jun 06, 2009 8:46 am
Maybe someone has a better logical explanation for this.

The way I approached it was:

Choice 1 states that the hundredth's digit is 4.

suppose k is composed of digits x y z

since you are adding 1 to x you can have x to have a value of 3.
you can also have a value of 2 for x if y > 5 since you have a carryover of 1.

there are 2 possibilities for choice 1: Insufficient.

Choice 2 states that y + 2 = 7

y can obviously have a value of 5. But y can also have a value of 4 if z > 5

so you have 2 possibilities for y as well. And this doesn't give us the hundreth's digit of x.

Together it is still ambigous since there are 2 combinations for x and 2 combinations for y
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Re: K is positive three digit integer

by nervesofsteel » Sun Jun 07, 2009 9:28 am
KICKGMATASS123 wrote:If K is a positive three-digit integer, what is the hundreds digit of K?

(1) The hundreds digit of K + 150 is 4.

(2) The tens digit of K + 25 is 7.

Please explain how you got your answer.

OA is E

I spent so much time on this question and still picked C.. Is there an easier way to approach this question???
IMO ans is E

K+150 = 4**

This means hundreds digit of k =3 or k =2

2) k+25 = *7*

This means tenths digit of K = 5 or 4

Now if we take tenths digit of K as 5 ... then according to 1 ..
there will be 1 carry forward ( K+150) .. which implies hundreds digit is 2

if we take tenths digit of K as 4 ... then according to 1 ..
there will be 0 carry forward ( K+150) .. which implies hundreds digit is 3

Thus E
Note : ones digits of K can have any value 0...9... thus we can assume there can be or cannot be a carry forward from ones digits....
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by Mo_Star » Tue Aug 24, 2010 2:34 pm
I'm a visual learner, so I use this method to solve these type of problems:

K = XYZ and we are looking for X (the hundreds digit)

Statement 1

The hundreds digit of K + 150 = 4

Then you can write ---> 400 <= K + 150 <=499
Subtract 150 from all three parts of the inequality ---> 250 <= K <= 349

So the hundreds digit is either 2 or 3 - Statement 1 is insufficient

Statement 2

The tens digit of K + 25 = 7

Then you can write ----> 70 <= K + 25 <= 79
Subtract 25 from all three parts of the inequality ---> 45 <= K <= 54

So the tenths digit is either 4 or 5, but that does not tell you anything about the hundreds digit. Statement 2 is insufficient.

Combine Statement 1 and 2:

We know that the tenths digit is a 4 or 5 and that 250 <= K <= 349 but that provides multiple answers: K could equal anything from 250-259 or 340-349 and the hundreds digit could still be 2 or 3. Therefore, the answer is E.

Hope that helps!
Monika
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by tomada » Wed Aug 25, 2010 10:38 am
Excellent explanation, Monika.

Mo_Star wrote:I'm a visual learner, so I use this method to solve these type of problems:

K = XYZ and we are looking for X (the hundreds digit)

Statement 1

The hundreds digit of K + 150 = 4

Then you can write ---> 400 <= K + 150 <=499
Subtract 150 from all three parts of the inequality ---> 250 <= K <= 349

So the hundreds digit is either 2 or 3 - Statement 1 is insufficient

Statement 2

The tens digit of K + 25 = 7

Then you can write ----> 70 <= K + 25 <= 79
Subtract 25 from all three parts of the inequality ---> 45 <= K <= 54

So the tenths digit is either 4 or 5, but that does not tell you anything about the hundreds digit. Statement 2 is insufficient.

Combine Statement 1 and 2:

We know that the tenths digit is a 4 or 5 and that 250 <= K <= 349 but that provides multiple answers: K could equal anything from 250-259 or 340-349 and the hundreds digit could still be 2 or 3. Therefore, the answer is E.

Hope that helps!
I'm really old, but I'll never be too old to become more educated.
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