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Directions: Select all the answer choice.


Q. Two different positive integers x and y are selected from the odd integers that are less than 10. If z = x + y and z is less than 10, which of the following integers could be the sum of x, y, and z?


Indicate all such integers.

  • a)
    8

  • b)
    9

  • c)
    10

  • d)
    12

  • e)
    16

Correct answer is option 'A,D,E'. Can you explain this answer?
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Directions: Select all the answer choice.Q. Two different positive int...
To find the possible values for the sum of x, y, and z, we need to consider the values of x and y that satisfy the given conditions.

Given:
- x and y are positive integers.
- x and y are selected from the odd integers less than 10.
- z = x * y and z is less than 10.

Odd Integers Less than 10:
The odd integers less than 10 are 1, 3, 5, 7, and 9.

Possible Values for x and y:
Since x and y are different positive integers, we need to consider all possible combinations of x and y from the odd integers less than 10.

The possible combinations are:
- x = 1, y = 3
- x = 1, y = 5
- x = 1, y = 7
- x = 1, y = 9
- x = 3, y = 5
- x = 3, y = 7
- x = 3, y = 9
- x = 5, y = 7
- x = 5, y = 9
- x = 7, y = 9

Calculating z:
For each combination, we calculate the value of z = x * y.

The values of z for each combination are:
- z = 1 * 3 = 3
- z = 1 * 5 = 5
- z = 1 * 7 = 7
- z = 1 * 9 = 9
- z = 3 * 5 = 15
- z = 3 * 7 = 21
- z = 3 * 9 = 27
- z = 5 * 7 = 35
- z = 5 * 9 = 45
- z = 7 * 9 = 63

Possible Values for the Sum of x, y, and z:
Now we need to determine which of the given answer choices could be the sum of x, y, and z.

The sum of x, y, and z can be calculated as:
sum = x + y + z

For each combination, we calculate the sum of x, y, and z.

The sum for each combination is:
- sum = 1 + 3 + 3 = 7
- sum = 1 + 5 + 5 = 11
- sum = 1 + 7 + 7 = 15
- sum = 1 + 9 + 9 = 19
- sum = 3 + 5 + 15 = 23
- sum = 3 + 7 + 21 = 31
- sum = 3 + 9 + 27 = 39
- sum = 5 + 7 + 35 = 47
- sum = 5 + 9 + 45 = 59
- sum = 7 + 9 + 63 = 79

From the above calculations, we can see that the sum of x, y, and z can take the values 7, 11, 15, 19, 23, 31, 39, 47, 59, and 79.

Comparing with the Answer Choices:
Now we compare these possible values with
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Directions: Select all the answer choice.Q. Two different positive integers x and y are selected from the odd integers that are less than 10. If z = x + y and z is less than 10, which of the following integers could be the sum of x, y, and z?Indicate all such integers.a)8b)9c)10d)12e)16Correct answer is option 'A,D,E'. Can you explain this answer?
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