If k is a positive integer and the tens digit of k+5 is 4

[gphil]

I would appreciate help with the following problem. Thanks!

If k is a positive integer and the tens digit of k+5 is 4, what is the tens digit of k?

1) k > 35
2) The units digit of k is greater than 5.

The correct answer is B) Statement 2) alone is sufficient.

[RonPurewal]

Your first task is to decode the given fact that the tens digit of (k+5) is 4. This means 40 < k+5 < 49, which means that 35 < k < 44.

(1)
All this tells you is that k isn't 35. That still leaves everything from 36 to 44, so the tens digit could still be either 3 or 4: insufficient.

(2)
Of the aforementioned possibilities, only 35, 36, 37, 38, 39 fit this bill. therefore the tens digit must be 3. Sufficient.

[gphil]

Thanks a lot for great explanation!

[RonPurewal]

[armandollaza]

I chose E because k could be a 3 digit number, in which case 85, 86, 87, 88, 89 would satisfy the condition that the tens digit of k+5 is 4. Hence, either 3 or 8 could be k's tens digit. Did I miss something?

[AndreaDB]

It is uninfluent if we have 2 or more digit numbers in the evaluation of the tenth digit.
86+4=90 => digit number is 9 not 4
if we suppose the number to be 136+4= 140 the things go ahead the same way than in the case of 1 digit number.

Have I fallen a wire of your thoughts?

[RonPurewal]

I chose E because k could be a 3 digit number, in which case 85, 86, 87, 88, 89 would satisfy the condition that the tens digit of k+5 is 4. Hence, either 3 or 8 could be k's tens digit. Did I miss something?

how's that? if k is 85, 86, 87, 88, or 89, then k + 5 is 90, 91, 92, 93, or 94, respectively. the tens digit of these numbers is 9, not 4.

--

you are right, though, that k could be a three-digit number. this doesn't change anything, though, since all that's relevant to the problem is the last 2 digits of the number.
GENERAL FACT: if you want to know what happens to the last N digits of a number under multiplication, addition, or subtraction, then all you ever need to know is the last N digits.
division is the only operation under which any digit can ever be affected by the digits to its left.
therefore, 140 < k < 149, 240 < k < 249, etc. will behave in EXACTLY the same way as 40 < k < 49.
i should have written "LAST TWO DIGITS are 40 < k < 49", with all the commentary also applying to the last 2 digits only.