GMATPrepNow wrote:
N is a 3-digit number, and the sum of its digits is 10. When the digits of N are reversed, the new number is 99 less than N. What is the value of N?
(1) The hundreds digit of N is 1 more than its units digit.
(2) The tens digit of N is 2 more than its hundreds digit.
*kudos for all correct solutions
Target question: What is the value of N? Given: N is a 3-digit number, and the sum of its digits is 10. When the digits of N are reversed, the new number is 99 less than N. Let N = wxy, where w, x and y represent the 3 digits in N
So, the first equation we can write is:
w + x + y = 10Now let's examine the situation where we REVERSE the digits.
First of all, the VALUE of N (wxy) is equal to 100w + 10x + y
Next, the VALUE of the REVERSED number (yxw) is equal to 100y + 10x + w
Since the REVERSED number is 99 less than N, we can write: 100y + 10x + w = 100w + 10x + y - 99
Subtract w from both sides: 100y + 10x = 99w + 10x + y - 99
Subtract 10x from both sides: 100y = 99w + y - 99
Subtract y from both sides: 99y = 99w - 99
Divide both sides by 99 to get:
y = w - 1Now onto the statements....
Statement 1: The hundreds digit of N is 1 more than its units digit. In other words, w = y + 1, which is the SAME as
y = w - 1Notice that this provides NO NEW INFORMATION, since we already concluded that
y = w - 1Since statement 1 provides no new information, it is NOT SUFFICIENT
Statement 2: The tens digit of N is 2 more than its hundreds digit. In other words,
x = w + 2Now that we've written x and w in terms of w (i.e.,
x = w + 2 and
y = w - 1), we can take the given information (
w + x + y = 10), and replace w and x
When we do so, we get: w + (
w + 2) + (
w - 1) = 10
Simplify: 3w + 1 = 10
Solve: w = 3
If w = 3, then x = 5, and y = 2
So,
N =352Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
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