Let x be a two-digit number. If the sum of the digits of x is 9 GMAT Problem Solving

Question: Let x be a two-digit number. If the sum of the digits of x is 9, then the sum of the digits of the number (x + 10) is:

  1. 1
  2. 8
  3. 10
  4. Either 8 or 10
  5. Either 1 or 10

Approach Solution (1)

Let's take a two-digit number whose digits add up to 9, say, 72
Adding 10 to this number gives 82
The sum of the digits of this number is 10
Now, let's choose another two-digit number whose digits add up to 9, say, 90
Then, x + 10 = 90 + 10 = 100
The sum of the digits of this number is 1
Hence, the sum of the numbers is either 1 or 10

Correct option: E

Approach Solution (2)

Sum of digit: A + B = 9
A + B can be:
1 + 8
2 + 7
3 + 6
4 + 5
5 + 4
6 + 3
7 + 2
8 + 1
9 + 0
If x = 18, x + 10 = 28
Sum of digit = 2 + 8 = 10
If x = 27, x + 10 = 37
Sum of digit = 3 + 7 = 10
If x = 90, x + 10 = 100
Sum of digit = 1 + 0 + 0 = 1

Correct option: E

Approach Solution (3)

18 is the smallest possible value of x.
So, x + 10 = 18 + 10 = 28
2 + 8 = 10
So, the correct answer is either C, D or E
90 is the biggest possible value of x.
So, x + 10 = 90 + 10 = 100
1 + 0 + 0 = 1

Correct option: E

“Let x be a two-digit number. If the sum of the digits of x is 9, then?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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