To solve the problem, we need to determine how many possible values exist for the sum (X + Y), given that the difference between the two 3-digit numbers XYZ and YXZ is 90.
Let's represent the 3-digit numbers:
- XYZ can be expressed as 100X + 10Y + Z.
- YXZ can be expressed as 100Y + 10X + Z.
The problem states:
- (100X + 10Y + Z) - (100Y + 10X + Z) = 90
Simplifying this equation:
- 100X + 10Y + Z - 100Y - 10X - Z = 90
- (100X - 10X) + (10Y - 100Y) = 90
- 90X - 90Y = 90
- 90(X - Y) = 90
Divide both sides by 90:
- X - Y = 1
This tells us that the digits X and Y are consecutive, with X being one more than Y.
Since X and Y are distinct and non-zero, we calculate the possible pairs:
- Y = 1, X = 2
- Y = 2, X = 3
- Y = 3, X = 4
- Y = 4, X = 5
- Y = 5, X = 6
- Y = 6, X = 7
- Y = 7, X = 8
- Y = 8, X = 9
For each pair, we calculate X + Y:
- For (X, Y) = (2, 1), X + Y = 3
- For (X, Y) = (3, 2), X + Y = 5
- For (X, Y) = (4, 3), X + Y = 7
- For (X, Y) = (5, 4), X + Y = 9
- For (X, Y) = (6, 5), X + Y = 11
- For (X, Y) = (7, 6), X + Y = 13
- For (X, Y) = (8, 7), X + Y = 15
- For (X, Y) = (9, 8), X + Y = 17
The possible sums are 3, 5, 7, 9, 11, 13, 15, 17, providing us with 8 distinct possible sums.
Thus, the number of possible values for (X + Y) is 8.
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Select the answer using the code given below.
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What is the value of 1 2 + 2 2 + 3 2 + ......21 2 ?
Which sequence is correct to represent the hierarchical chain of number system?
(Where N - Natural Numbers
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Q - Rational Numbers
Z - Integers)
What must be added to 45680 to make it exactly divisible by 9?
How many zeroes are there at the end of the following product?
1 x 5 x 10 x 15 x 20 x 25 x 30 x 35 x 40 x 45 x 50 x 55 x 60
Let XYZ be a three-digit number, where (x + y + Z) is not a multiple of 3. Then (XYZ + YZX + ZXY) is not divisible by
