If the Tens Digit x and the Units Digit y of a Positive GMAT Problem Solving

Question: If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 9 more than n. What is y in terms of x?

1. 10 - x
2. 9 - x
3. x + 9
4. x - 1
5. x + 1

Correct Answer: E

Solution and Explanation:
Approach Solution 1:

Since y and x are the units and tens digits respectively of n,
n = 10x + y .....(i)

If the digits are reversed, then the value of n increases by 9.
Thus, n + 9 = 10y + x....(ii)

Subtracting (i) from (ii),
9 = 9y - 9x
y - x = 9
y = x + 1

Approach Solution 2:

The given positive integer n = 10x + y

The resulting positive integer when the integers are reversed is 10y + x
(10y + x) = (10x + y) + 9
10y + x = 10x + y + 9

Add -y - x to both sides
9y = 9x + 9
y = x + 1

Approach Solution 3:
Positive integer n has the tens digit x and the units digit y, so n= 10x+y;
Reversed integer, say n′, has the tens digit y and the units digit x, so n′= 10y+x;
We are also told that " the resulting integer (so n′) is 9 more than n", which means
n′−n= (10y+x)−(10x+y)= 9 --> y= x+1.

“If the tens digit x and the units digit y of a positive”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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