GMATPrepNow wrote:
N is a 2-digit integer. When the digits of N are reversed, the resulting number is M. If -1 < N – M < 15, what is the value of N?
(1) The sum of N’s digits is 15.
(2) The tens digit of N is 1 greater its units digit
*kudos for all correct solutions
Target question: What is the value of N? Given: N is a 2-digit integer. When the digits of N are reversed, the resulting number is M. -1 < N – M < 15 Let x = the tens digit of N
Let y = the units digit of N
So, the VALUE of N = 10x + y
When we reverse the digits, we get M = yx
So, the VALUE of M = 10y + x
So, N - M = (10x + y) - (10y + x)
= 9x - 9y
= 9(x - y)
In other words, N - M =
some multiple of 9We're told that -1 < N – M < 15
There are exactly two multiples of 9 between -1 and 15. They are 0 and 9.
So EITHER
N – M = 0 OR
N – M = 9Let's examine each case:
CASE A: If
N - M = 0, then 9(x - y) = 0, which means x - y = 0, which means
x = y CASE B: If
N - M = 9, then 9(x - y) = 9, which means x - y = 1, which means
x = y + 1 Statement 1: The sum of N’s digits is 15 In other words, x + y = 15
If x and y are INTEGERS, and if x + y = 15, then
x cannot equal yThis rules out CASE A, which means CASE B must be true. That is,
x = y + 1 We now have two equations:
x + y = 15
x = y + 1 Since we COULD solve this system for x and y, we COULD determine the
value of N Since we COULD answer the
target question with certainty, statement 1 is SUFFICIENT
Aside: If we solve the system, we get: x = 7 and y = 8
So,
N = 78 Statement 2: The tens digit of N is 1 greater its units digitIn other words, x = y + 1
This means CASE B is true (i.e.,
x = y + 1 )
Given this, there are many values of N that statement 2.
For example, it could be the case that
N = 21 or
N = 32 or
N = 43 or
N = 54 etc.
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
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