swerve wrote:When the positive number A is rounded to the nearest tenth, the result is the number B. What is the tenths digit of A?
(1) When A is rounded to the nearest integer, the result is less than A.
(2) When B is rounded to the nearest integer, the result is greater than B.
Source: Manhattan Prep
? : tenth´s digit of A
Convention: we assume that the number 0.5 must be rounded to 1, when we are rounding numbers to the nearest integer.
(It´s really just a matter of convention. We explicit our convention so that we can deal with this problem without ambiguity.)
(1) (A rounded to nearest int) < A , i.e. , the tenth´s digit of A (our FOCUS) is less than 5 ...
:: Take A = 0.49 (rounded to the nearest integer is 0, that is less than A) , to answer 4
:: Take A = 0.39 (rounded to the nearest integer is 0, that is less than A), to answer 3
(2) (B rounded to nearest int) > B i.e., the tenth´s digit of B is no less than 5 ...
:: Take A = 0.56 (then B = 0.6 and B rounded to nearest integer is 1, that is greater than B) , to answer 5
:: Take A = 0.66 (then B = 0.7 and B rounded to nearest integer is 1, that is greater than B) , to answer 6
(1+2) We know that the tenth´s digit of A (our FOCUS) is less than 5 AND
when we round A to the nearest tenth´s digit (=B) , the tenth´s digit of this number (B) is no less than 5...
This is enough to guarantee that the tenth´s digit of A is 4 (our FOCUS)... SUFFICIENT!
Without loss of generality, we will still consider 0 < A < 1 only.
The general case (in which A>0 has any other integer part) is dealt in EXACTLY the same way.
In fact:
If 0.5 <= A < 1 , A does not satisfy statement (1) !!
If 0 < A < 0.4 , then B is 0.4 or less, therefore B does not satisfy statement (2) !!
The correct answer is therefore (C).
Regards,
fskilnik.
