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04 Nov 2018, 09:33
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
62% (02:18) correct
38%
(02:12)
wrong
based on 195
sessions
History
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Not Attempted Yet
If r and s are non negative integers, \(p=1.9*10^r\) and \(q = 1.9*10^s\), what is the units digit of 10(p+q)?
(1) r is divisible by 2
(2) s is not divisible by 2
(1) r is divisible by 2
(2) s is not divisible by 2
04 Nov 2018, 10:33
Kudos
Bookmarks
depending on the values of s and r, p and q each have a units digit of either 1 (if r or s are 0, making the value 1.9), 9 (if r/s are 1, making the value 19), or 0 (if r/s >1, for which the value will be 190, 1900...etc)
Clearly, both statements on their own are insufficient, since each only gives information on one of r and s, and not on the other.
Combined: from 1), p's units digit is 0 (r=2 ==> 19, r = 4 ==> 19,00, etc). from 2), q's units digit can either 1 (s=0), 9 (s=1), or 0 (s>2). specifically, if s=0, then P+q will have a decimal digit of 9 (x.9), and 10(p+q) will have a units digit of 9. Since we don't if this is the case or not, this is insufficient.
Clearly, both statements on their own are insufficient, since each only gives information on one of r and s, and not on the other.
Combined: from 1), p's units digit is 0 (r=2 ==> 19, r = 4 ==> 19,00, etc). from 2), q's units digit can either 1 (s=0), 9 (s=1), or 0 (s>2). specifically, if s=0, then P+q will have a decimal digit of 9 (x.9), and 10(p+q) will have a units digit of 9. Since we don't if this is the case or not, this is insufficient.
04 Nov 2018, 10:33
Kudos
Bookmarks
Question : Unit digit of 10(p+q) = \(10(1.9*10^r+1.9*10^s)\) = \(19(10^r+10^s)\)
From statement 1:
r is divisible by 2.
Then r could be 0,2,4,6...
If r is 0 then 10^0 = 1.
If r is 2 then 10^1 = 10.
But no info about s.
Insufficient.
From statement 2:
s is not divisible by 2.
Then s could be 1,3,5...
Again r is unknown.
Insufficient.
Combining both:
Let r = 0. s = 1.
10^0 = 1 and 10^1 = 10. then 19(11) = last digit is 9.
If r = 2. and s= 3.
Then unit digit will be 0.
Combining is also insufficient.
E is the answer.
From statement 1:
r is divisible by 2.
Then r could be 0,2,4,6...
If r is 0 then 10^0 = 1.
If r is 2 then 10^1 = 10.
But no info about s.
Insufficient.
From statement 2:
s is not divisible by 2.
Then s could be 1,3,5...
Again r is unknown.
Insufficient.
Combining both:
Let r = 0. s = 1.
10^0 = 1 and 10^1 = 10. then 19(11) = last digit is 9.
If r = 2. and s= 3.
Then unit digit will be 0.
Combining is also insufficient.
E is the answer.
