Ques :- If n
is a positive integer and the tens digit of n+8 is 6, what is the tens digit of n
Tens digit of n+8 is 6, So lets assume that n+8 is 6b
, where b
is units digit.
We are asked the tens digit of n
. that means ques is indirectly asking that if we subtract 8 from 6b (i.e. from n+8) would the tens digit reduce from 6 to 5?
Further examination would tell us that if b
takes any value from 0 to 7 tens digit will become 5 (i.e. will change) and it b
takes value of 8 or 9 tens digit will remain same because when smaller units digit subtracted from larger units digit, the subtraction would not affect the tens digit.So the question is basically asking us What is the units digit of n?
(1) The units digit of n
is a prime number :- Units digit is one from 1,2,5,7. All these values are below 8. So we can say tens digit of n is 5. Sufficient
(2) The tens digit of n-8 is 4 :- This is tricky. (n+8) and (n-8) have difference of 16. n+8 has tens digit as 6 and n-8 has tens digit as 4. So these numbers must be of the form 6b (59<6b<70) and 4a (39<4a<50)
The only pairs of the numbers that obeys above conditions and differed by 16 are as follows
44 and 60
45 and 61
46 and 62
47 and 63
48 and 64
49 and 65
In all the cases we can see the units digit of all 6b (i.e. of n+8) lies between 0 and 5. That means it is below 8. So tens digit of n is 5. SufficientAnswer D
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