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04 Nov 2022, 13:26
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If \(m\) and \(n\) are positive two-digit integers, what is the value of the tens digit of \(m\) minus the tens digit of \(n\) ?
(1) \(m - n = 43\).
(2) The units digit of \(m\) minus the units digit of \(n\) is not a multiple of 3.
(1) \(m - n = 43\).
(2) The units digit of \(m\) minus the units digit of \(n\) is not a multiple of 3.
04 Nov 2022, 13:26
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Official Solution:
If \(m\) and \(n\) are positive two-digit integers, what is the value of the tens digit of \(m\) minus the tens digit of \(n\) ?
Let \(m\) be \(ab\), where \(a\) is the tens digit and \(b\) is the units digit, and \(n\) be \(cd\), where \(c\) is the tens digit and \(d\) is the units digit. The question asks to find the value of \(a - c\).
(1) \(m - n = 43\).
ab
-cd
43
CASE 1: If there is no borrowed 10 from the tens digit of \(m\), so if for example, we have:
55
-12
43
Then, \(a - c=4\).
CASE 2: If there IS borrowed 10 from the tens digit of \(m\), so if for example, we have:
62
-19
43
Then, \(a - c=5\).
Not sufficient.
(2) The units digit of \(m\) minus the units digit of \(n\) is not a multiple of 3.
This one is clearly insufficient.
(1)+(2) We cannot have CASE 1 from (1) because if it were the case then the units digit of \(m\) minus the units digit of \(n\) (\(b-d\)) would simply be 3, which IS a multiple of 3, so we must have CASE 2, which means that \(a - c=5\). Sufficient.
Answer: C
If \(m\) and \(n\) are positive two-digit integers, what is the value of the tens digit of \(m\) minus the tens digit of \(n\) ?
Let \(m\) be \(ab\), where \(a\) is the tens digit and \(b\) is the units digit, and \(n\) be \(cd\), where \(c\) is the tens digit and \(d\) is the units digit. The question asks to find the value of \(a - c\).
(1) \(m - n = 43\).
ab
-cd
43
CASE 1: If there is no borrowed 10 from the tens digit of \(m\), so if for example, we have:
55
-12
43
Then, \(a - c=4\).
CASE 2: If there IS borrowed 10 from the tens digit of \(m\), so if for example, we have:
62
-19
43
Then, \(a - c=5\).
Not sufficient.
(2) The units digit of \(m\) minus the units digit of \(n\) is not a multiple of 3.
This one is clearly insufficient.
(1)+(2) We cannot have CASE 1 from (1) because if it were the case then the units digit of \(m\) minus the units digit of \(n\) (\(b-d\)) would simply be 3, which IS a multiple of 3, so we must have CASE 2, which means that \(a - c=5\). Sufficient.
Answer: C
23 Apr 2023, 09:27
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For c - by trial and error method, can case 2 not be 62-19 > 43 and 61-18 > 43, by that logic 2-9 = 7, not a multiple of 3 and 1-8 = 7, not a multiple of 3, so combining statement 1 and 2 gives more than 1 possible outcome, so should the answer not be E?
