Data Sufficiency

BTGModeratorVI wrote: ↑

Mon Jul 13, 2020 8:08 am

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

Answer: A
Source: www.gmatprepnow.com

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 9
We'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 = 9

Let'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 y
This 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 digit
In 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