UGCNET Questions

Let the number be x. The statement “three times the number decreased by 5 equals 16” translates to the equation 3x − 5 = 16. Adding 5 to both sides gives 3x = 21, and then dividing by 3 yields x = 7. Substituting back into the original relation, 3 × 7 − 5 equals 21 − 5 = 16, confirming that 7 satisfies the condition.

Option A:
Option A, 5, when substituted gives 3 × 5 − 5 = 10, which is not equal to 16. Thus, it fails to satisfy the equation implied by the verbal statement.

Option B:
Option B fits the equation exactly, turning 3x − 5 into 16 when x is 7. This closes the loop between the word problem and its algebraic representation.

Option C:
Option C, 9, would make 3 × 9 − 5 = 22, overshooting the stated result 16, so it cannot be correct.

Option D:
Option D, 11, yields 3 × 11 − 5 = 28, which is even further from 16 and clearly inconsistent.

To solve 5x + 3 = 18, we first subtract 3 from both sides to isolate the term with x. This gives 5x = 15. Dividing both sides by 5, we get x = 15 ÷ 5 = 3. Therefore, the solution of the equation is x = 3.

Option A:
Option A, 2, does not satisfy the equation because substituting x = 2 yields 5 × 2 + 3 = 13, which is not equal to 18. So this value fails to make both sides equal.

Option B:
Option B, 3, when substituted gives 5 × 3 + 3 = 15 + 3 = 18, which matches the right side and confirms that x = 3 is the correct solution.

Option C:
Option C, 4, produces 5 × 4 + 3 = 23, which is greater than 18 and so cannot be the solution.

Option D:
Option D, 5, gives 5 × 5 + 3 = 28, which again does not equal 18, and therefore cannot solve the equation.