Numbers

[ASPIRE800]

If 'K' is a three digit integer where units place not equal to zero, then find the tens digit of K?

1. Tens digit of (k+4) is 3.
2. Tens digit of (k+9) is 4.

[Target2009]

IMO = B
Since Unit digit of K is non zero it can have value from (1 to 9 )

Now lets analyse stmt 1 : K + 4 give 3 as 10th unit. so if go by substitution method then
i> for unit value (1 to 5 ) + 4 , we should have 3 itself as 10th digit
ii> for unit value ( 6 to 9 ) + $ , we should have 2 as 10th value
which mean we can have either 2 or 3 as 10th place which make this statement insufficient.

Let move on to 2nd statement.
for any value for unit place ( 1 to 9 ) , we must have 3 as 10th unit to give k + 9 = 4 as 10th unit.
Since we have absolute value for 10th digit here, this statement is sufficient.

[ASPIRE800]

IMO = B
Since Unit digit of K is non zero it can have value from (1 to 9 )

Now lets analyse stmt 1 : K + 4 give 3 as 10th unit. so if go by substitution method then
i> for unit value (1 to 5 ) + 4 , we should have 3 itself as 10th digit
ii> for unit value ( 6 to 9 ) + $ , we should have 2 as 10th value
which mean we can have either 2 or 3 as 10th place which make this statement insufficient.

Let move on to 2nd statement.
for any value for unit place ( 1 to 9 ) , we must have 3 as 10th unit to give k + 9 = 4 as 10th unit.
Since we have absolute value for 10th digit here, this statement is sufficient.

K is given as three digt number but not mentioned whether positive/negative.
What if it is negative?
Statement 2 becomes insufficient

[nisha.menon294]

IMO B , what is the OA ?

[ASPIRE800]

OA: C