The Difference Between a Two-Digit Number and the Number Obtained GMAT Problem Solving

Question: The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 2:1?

1. 4
2. 8
3. 16
4. 20
5. None of these

Correct answer: (B)

Solution and Explanation:

Approach Solution 1:

Let the two digit number be 10x + y
And the number obtained after interchanging be 10y + x
Difference = 9 (x – y) = 36
x – y = 4
Possible combinations are (5, 1) (6, 2) (7, 3) (8, 4) (9, 5)
Also, given that the ratio of the digits is 1:2
Only combination possible is (8, 4)
Sum of the digits = 8 + 4 = 12
Difference of the digits = 8 – 4 = 4
Difference between these two is 12 – 4 = 8

Approach Solution 2:

Since the number is greater than the number obtained on reversing the digits, so the then’s digit is greater than the unit’s digit

Let ten’s and unit’s digits be 2x and x respectively
Then, (10 * 2x + x) – (10x + 2x) = = 36
9x = 36
x = 4

Required difference = (2x + x) – (2x – x) = 2x = 8

Approach Solution 3:

Let’s assume two digit number is 10x + y — (case 1)

Number obtained after reversing = 10y + x
Given, difference between a two-digit number and the number obtained by interchanging the digits is 36.
10y+x - (10x+y)= 36
=> 9 ( y- x) = 36
y -x = 4
Case 2:
Given, x : y = 1: 2
Therefore, y= 2x
Substituting y = 2x in case:1;
x = 4; y = 8
Theeforem the number is 10x+y = 10*4 + 8 = 48
Sum of the digits = 8 + 4 = 12
Difference of the digits = 8 – 4 = 4
Difference between the two is 12 – 4 = 8

“The difference between a two-digit number and the number obtained by interchanging”- 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 practice papers assist the candidates to go through several sorts of questions that will enable them to enhance their mathematical understanding.

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