How to find the tens digit of a 3 digit number ?

[whizteen123]

Hi guys,

 

I came across the following problem in one of the sample GMAT tests and kinda stumbled on it.

 

If the units digit of the three-digit positive integer k is nonzero, what is the tens digit of k?

(1) The tens digit of k + 9 is 3.

(2) The tens digit of k + 4 is 2.

 

I figured the answer had to be C as if adding 9 to K makes the tens digit become 3 but adding 4 only makes it 2. If the tens digit was 2 and when 9 was added to the units digit, 1 gets carried over to make it 3 but adding 4 to the units digit doesnt change the tens digit as the units digit might be less than 6.

 

However the answer is A. Can someone please explain?

 

Thanks in advance!

[mastermind]

k is an integer who has non zero unit digit

 

from statement 1--k+9 is 3

 

so if we take minimum tenth degit as 1 and maximum as 9 we have to increase the tenth digit by 1 so it must be 2 only-sufficient

 

from statement 2--k+4=2

 

if we take minimum unit digit as 1 and maximum as 9 we have get tenth digit as 2 and 1 respectively. so Insufficient

 

So A

[bungholio]

can you explain it with numbers? i am confused.

 

thanks!

[whizteen123]

Mastermind,

Thanks for the answer. I think I got it now.

 

This is the explanation with numbers.

 

Since the question stem says that the units digit of K is nonzero. We know that it can be a value between 1-9. So lets pick 121, if you add 9 to it, it becomes 130. For any units digit between 1-9, adding nine to it will make 1 carry over to the tens place. So if the tens place is 3 after we add 1 to it, then it had to be 2 before!