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21 Jul 2021, 07:30
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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:
95%
(hard)
Question Stats:
30% (01:48) correct
70%
(01:56)
wrong
based on 129
sessions
History
Date
Time
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The absolute difference between a two digit number and the number formed by reversing the digits of that number is D. What is the number?
(1) D = 36
(2) The sum of the digits of the number is 12.
(1) D = 36
(2) The sum of the digits of the number is 12.
21 Jul 2021, 07:54
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Even using both Statements, because D is the absolute difference, we'll get two solutions: if AB is a two-digit number that works, BA will be another one. So the answer is E.
It turns out with the specific data provided that 84 and 48 are the two possible values of the number, but we don't need to figure that out here.
It turns out with the specific data provided that 84 and 48 are the two possible values of the number, but we don't need to figure that out here.
25 Jul 2021, 05:29
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Bunuel
Reversing digits is a common number property topic. If we represent two digits with x and y, we can build two numbers with reversed digits: \(10x + y\) and \(x + 10y\). Their difference would be \(9x - 9y\) or \(9y - 9x\), either way the difference is divisible by 9 and we can represent the difference with \(9*|x -y|\).
Statement 1:
Plugging in what we had above, we can find |x - y| = 4, hence the digits have an absolute difference of 4. There are too many options so insufficient.
Statement 2:
Even if we found a single combination of digits, we still have two different numbers by reversing the digits. Insufficient.
Combined:
We have the same problem in both statements, we can find a specific combination of digits (digits 8 and 4) but we don't know if we want the smaller number (48) or larger number (84). Insufficient.
Ans: E
