BTGmoderatorDC wrote:If z is a three-digit positive integer, what is the value of the tens digit of z ?
(1) The tens digit of z - 91 is 3
(2) The units digit of z + 9 is 5
OA C
Source: Official Guide
Given: z is a three-digit positive integer
Target question: What is the value of the tens digit of z ?
Statement 1: The tens digit of z - 91 is 3
Let's examine two EXTREME cases
z - 91 = 30
[tens digit is 3]
z - 91 = 39
[tens digit is 3]
NOTE: These are extreme cases, because 30 is the smallest 2-digit number with tens digit 3, and 39 is the biggest 2-digit number with tens digit 3.
If z - 91 = 30, then z = 121.
So, z COULD be 121, in which case the answer to the target question is
the tens digit of z is 2
If z - 91 = 39, then z = 130.
So, z COULD be 130, in which case the answer to the target question is
the tens digit of z is 3
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The units digit of z + 9 is 5
Let's examine two cases
z + 9 = 135
[units digit is 5]
z + 9 = 145
[units digit is 5]
If z + 9 = 135, then z = 126.
So, z COULD be 126, in which case the answer to the target question is
the tens digit of z is 2
If z + 9 = 145, then z = 136.
So, z COULD be 136, in which case the answer to the target question is
the tens digit of z is 3
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 2 indirectly tells us that the UNITS digit of z is 6
Statement 1 tells us that the tens digit of z - 91 is 3
Now that the units digit of z MUST be 6, let's find some values of z that satisfy
statement 1.
Now that we know the units digit of z is 6, we know that z - 91 will have UNITS digit 5.
Also, statement 1 tells us that z - 91 will have TENS digit 3.
So, we know that: z - 91 = ?35
If z - 91 = 35, then z = 126. So, the answer to the target question is
z has units digit 2
If z - 91 = 135, then z = 226. So, the answer to the target question is
z has units digit 2
If z - 91 = 235, then z = 326. So, the answer to the target question is
z has units digit 2
If z - 91 = 335, then z = 426. So, the answer to the target question is
z has units digit 2
As you can see, the answer to the target question will ALWAYS be
z has units digit 2
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
