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Question

Difficulty: MediumProperties of Integers

A student is required to identify a calculation that yields a value greater than zero. Which of the following arithmetic expressions produces a positive integer result?

  1. A
    −5+(−2)-5 + (-2)
  2. B
    4−3×24 - 3 \times 2
  3. C
    −∣−8∣+5-|-8| + 5
  4. (−3)×(−4)−10(-3) \times (-4) - 10Answer

Answer

The expression (−3)×(−4)−10(-3) \times (-4) - 10 produces a positive integer.
The expression (−3)×(−4)−10(-3) \times (-4) - 10 evaluates to a positive integer because the product of −3-3 and −4-4 is a positive 1212, and subtracting 1010 from 1212 leaves 22.

Step-by-Step Solution

1
Evaluate the first expression: −5+(−2)-5 + (-2).
−5+(−2)=−7-5 + (-2) = -7.
Adding a negative integer to a negative integer results in a smaller negative integer.
2
Evaluate the second expression: 4−3×24 - 3 \times 2.
4−6=−24 - 6 = -2.
Following the order of operations (PEMDAS), multiplication is performed before subtraction.
3
Evaluate the third expression: −∣−8∣+5-|-8| + 5.
−8+5=−3-8 + 5 = -3.
The absolute value of −8-8 is positive 88. The negative sign outside makes it −8-8. Adding 55 results in a negative integer.
4
Evaluate the fourth expression: (−3)×(−4)−10(-3) \times (-4) - 10.
12−10=212 - 10 = 2.
Multiplying two negative integers yields a positive integer (1212). Subtracting 1010 from 1212 leaves a positive integer.

Key Concept

Integer operations combining sign rules, absolute value, and the order of operations.
Estimated Time:50s
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Topics

Properties of Integers

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