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28 Oct 2019, 21:23
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If m and n are two two-digit positive integers with reversed digits (e.g 26 and 62 are 2 two-digit integers with reversed digits), what is the value of m?
(1) m is 82 greater than the tens digit of m.
(2) n is 18 greater than the tens digit of n.
28 Oct 2019, 22:07
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If m and n are two two-digit positive integers with reversed digits (e.g 26 and 62 are 2 two-digit integers with reversed digits), what is the value of m?
There is a relationship between m and n in main statement and then in each statement, so both should be sufficient.
m=10a+b and n=10b+a
(1) m is 82 greater than the tens digit of m.
So m=82+a......10a+b=82+a.....9a=82-b
a as 9 gives b as 1....m=91
a as 2 will give b as 10, a 2-digit number... Not possible
Sufficient
(2) n is 18 greater than the tens digit of n.
n=18+b........10b+a=18+b......9b=18-a
Only value of b is 1 for both a and b to be single digit.
Number n=19
Sufficient
D
There is a relationship between m and n in main statement and then in each statement, so both should be sufficient.
m=10a+b and n=10b+a
(1) m is 82 greater than the tens digit of m.
So m=82+a......10a+b=82+a.....9a=82-b
a as 9 gives b as 1....m=91
a as 2 will give b as 10, a 2-digit number... Not possible
Sufficient
(2) n is 18 greater than the tens digit of n.
n=18+b........10b+a=18+b......9b=18-a
Only value of b is 1 for both a and b to be single digit.
Number n=19
Sufficient
D
28 Oct 2019, 22:21
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Let m=xy, then n=yx. We are to determine m. The given condition is that m and n are two-digit numbers.
Statement 1: m is 82 greater than the tens digit of m
Sufficient. Statement 1 tells us that m > 90 since only a value greater than 90 will yield a difference between itself and it's tens digit to be 82.
With this information in mind, we can narrow down to 91 as the value of m, since it is the only value greater than 90 that yields a difference of 82 when 9 is taken out of it.
Statement 2: n is 18 greater than the tens digit of n.
Sufficient. Statement 2 tells us that m<21, since only a value less than 21 will yield a difference between itself and it's tens digit to be 19. Two values less than 21 satisfy the given condition in statement 2: 19 and 20. The reverse of 19 is 91, which is a two-digit number, but the reverse of 20 is 2, which is not a two-digit number. We can, therefore, discard 20 as n, and conclude that n=19. This further implies that m=91.
Both statements are sufficient on their own to determine the value of m.
The answer is therefore D.
Statement 1: m is 82 greater than the tens digit of m
Sufficient. Statement 1 tells us that m > 90 since only a value greater than 90 will yield a difference between itself and it's tens digit to be 82.
With this information in mind, we can narrow down to 91 as the value of m, since it is the only value greater than 90 that yields a difference of 82 when 9 is taken out of it.
Statement 2: n is 18 greater than the tens digit of n.
Sufficient. Statement 2 tells us that m<21, since only a value less than 21 will yield a difference between itself and it's tens digit to be 19. Two values less than 21 satisfy the given condition in statement 2: 19 and 20. The reverse of 19 is 91, which is a two-digit number, but the reverse of 20 is 2, which is not a two-digit number. We can, therefore, discard 20 as n, and conclude that n=19. This further implies that m=91.
Both statements are sufficient on their own to determine the value of m.
The answer is therefore D.
