Written Instructions:
For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..
For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.
Leave your answers in the simplest form or correct to two decimal places.
1) The sum of 2 consecutive integers is 21. Find the numbers.
Answer:_______________ |
2) The sum of 2 consecutive integers is 27. Find the numbers.
Answer:_______________ |
3) The sum of 2 consecutive integers is 29. Find the numbers.
Answer:_______________ |
4) The sum of 2 consecutive integers is 47. Find the numbers.
Answer:_______________ |
5) The sum of 2 consecutive integers is 23. Find the numbers.
Answer:_______________ |
6) The sum of 2 consecutive integers is 49. Find the numbers.
Answer:_______________ |
7) The sum of 2 consecutive integers is 37. Find the numbers.
Answer:_______________ |
8) The sum of 2 consecutive integers is 43. Find the numbers.
Answer:_______________ |
9) The sum of 2 consecutive integers is 31. Find the numbers.
Answer:_______________ |
10) The sum of 2 consecutive integers is 41. Find the numbers.
Answer:_______________ |
1) The sum of 2 consecutive integers is 21. Find the numbers. Answer: 10 Answer: 11 SOLUTION 1 : Let the required number be x. ⇒ 2 times = 2x Given: x + (x + !) = 21 ⇒ x + x +1 = 21 ( Grouping the like terms ) ⇒ (x + x) + 1 = 21 2x = 21 - 1 ( on transposing +1 becomes - 1 ) 2x = 20 = ( Dividing both the sides by 2 ) x = 10. x + 1 = 10 + 1 = 11 Hence, the consecutive numbers are 10 and 11. |
2) The sum of 2 consecutive integers is 27. Find the numbers. Answer: 13 Answer: 14 SOLUTION 1 : Let the required number be x. ⇒ 2 times = 2x Given: x + (x + !) = 27 ⇒ x + x +1 = 27 ( Grouping the like terms ) ⇒ (x + x) + 1 = 27 2x = 27 - 1 ( on transposing +1 becomes - 1 ) 2x = 26 = ( Dividing both the sides by 2 ) x = 13. x + 1 = 13 + 1 = 14 Hence, the consecutive numbers are 13 and 14. |
3) The sum of 2 consecutive integers is 29. Find the numbers. Answer: 14 Answer: 15 SOLUTION 1 : Let the required number be y. ⇒ 2 times = 2y Given: y + (y + !) = 29 ⇒ y + y +1 = 29 ( Grouping the like terms ) ⇒ (y + y) + 1 = 29 2y = 29 - 1 ( on transposing +1 becomes - 1 ) 2y = 28 = ( Dividing both the sides by 2 ) y = 14. y + 1 = 14 + 1 = 15 Hence, the consecutive numbers are 14 and 15. |
4) The sum of 2 consecutive integers is 47. Find the numbers. Answer: 23 Answer: 24 SOLUTION 1 : Let the required number be y. ⇒ 2 times = 2y Given: y + (y + !) = 47 ⇒ y + y +1 = 47 ( Grouping the like terms ) ⇒ (y + y) + 1 = 47 2y = 47 - 1 ( on transposing +1 becomes - 1 ) 2y = 46 = ( Dividing both the sides by 2 ) y = 23. y + 1 = 23 + 1 = 24 Hence, the consecutive numbers are 23 and 24. |
5) The sum of 2 consecutive integers is 23. Find the numbers. Answer: 11 Answer: 12 SOLUTION 1 : Let the required number be x. ⇒ 2 times = 2x Given: x + (x + !) = 23 ⇒ x + x +1 = 23 ( Grouping the like terms ) ⇒ (x + x) + 1 = 23 2x = 23 - 1 ( on transposing +1 becomes - 1 ) 2x = 22 = ( Dividing both the sides by 2 ) x = 11. x + 1 = 11 + 1 = 12 Hence, the consecutive numbers are 11 and 12. |
6) The sum of 2 consecutive integers is 49. Find the numbers. Answer: 24 Answer: 25 SOLUTION 1 : Let the required number be x. ⇒ 2 times = 2x Given: x + (x + !) = 49 ⇒ x + x +1 = 49 ( Grouping the like terms ) ⇒ (x + x) + 1 = 49 2x = 49 - 1 ( on transposing +1 becomes - 1 ) 2x = 48 = ( Dividing both the sides by 2 ) x = 24. x + 1 = 24 + 1 = 25 Hence, the consecutive numbers are 24 and 25. |
7) The sum of 2 consecutive integers is 37. Find the numbers. Answer: 18 Answer: 19 SOLUTION 1 : Let the required number be y. ⇒ 2 times = 2y Given: y + (y + !) = 37 ⇒ y + y +1 = 37 ( Grouping the like terms ) ⇒ (y + y) + 1 = 37 2y = 37 - 1 ( on transposing +1 becomes - 1 ) 2y = 36 = ( Dividing both the sides by 2 ) y = 18. y + 1 = 18 + 1 = 19 Hence, the consecutive numbers are 18 and 19. |
8) The sum of 2 consecutive integers is 43. Find the numbers. Answer: 21 Answer: 22 SOLUTION 1 : Let the required number be y. ⇒ 2 times = 2y Given: y + (y + !) = 43 ⇒ y + y +1 = 43 ( Grouping the like terms ) ⇒ (y + y) + 1 = 43 2y = 43 - 1 ( on transposing +1 becomes - 1 ) 2y = 42 = ( Dividing both the sides by 2 ) y = 21. y + 1 = 21 + 1 = 22 Hence, the consecutive numbers are 21 and 22. |
9) The sum of 2 consecutive integers is 31. Find the numbers. Answer: 15 Answer: 16 SOLUTION 1 : Let the required number be x. ⇒ 2 times = 2x Given: x + (x + !) = 31 ⇒ x + x +1 = 31 ( Grouping the like terms ) ⇒ (x + x) + 1 = 31 2x = 31 - 1 ( on transposing +1 becomes - 1 ) 2x = 30 = ( Dividing both the sides by 2 ) x = 15. x + 1 = 15 + 1 = 16 Hence, the consecutive numbers are 15 and 16. |
10) The sum of 2 consecutive integers is 41. Find the numbers. Answer: 20 Answer: 21 SOLUTION 1 : Let the required number be y. ⇒ 2 times = 2y Given: y + (y + !) = 41 ⇒ y + y +1 = 41 ( Grouping the like terms ) ⇒ (y + y) + 1 = 41 2y = 41 - 1 ( on transposing +1 becomes - 1 ) 2y = 40 = ( Dividing both the sides by 2 ) y = 20. y + 1 = 20 + 1 = 21 Hence, the consecutive numbers are 20 and 21. |