Dear Reader,
Below are four problems on basic arithmetic calculations.
Directions to solve:
In each of the following question, four parts labelled (a) (b) (c) and (d). One of these parts may not yield the same result as the other three do. Find out the wrong part if there any. The label of that part is the answer. If all the four parts are correctly equated then the answer is e, i.e., No error.
Question 1
(a) 272 x 24 / 18 x 6
(b) 34 x 128 / 12 x 6
(c) 72 x 34 / 18 x 18
(d) 288 x 34 / 27 x 6
Options : a, b, c, d, e.
Answer : option c.
Solution :
Option (a) gives 272 x 24 / 18 x 6
= 136 x 2 x 6 x 4 / 9 x 2 x 6
Cancelling the common terms, we have
= 136 x 4/9 = 544/9 ...(1)
Option (b) gives 34 x 128 / 12 x 6
= 34 x 4 x 2 x 16 / 4 x 3 x 2 x 3
Cancelling the common terms, we have
= 34 x 16 / 3 x 3
= 544/9 ...(2)
Option (c) gives 72 x 34 / 18 x 18
= 2 x 9 x 4 x 34 / 2 x 9 x 2 x 9
Cancelling the common terms, we have
= 34 x 2/9
= 68/9 ...(3)
Option (d) gives 288 x 34 / 27 x 6
= 34 x 16 x 3 x 6 / 9 x 3 x 6
Cancelling the common terms, we have
= 34 x 16/9
= 544/9 ...(4)
From (1), (2), (3) and (4) we have the answer is option c.
Question 2
(a) 145038 x 9999
(b) 48346 x 2997
(c) 24173 x 59994
(d) 1595418 x 909
Options : a, b, c, d, e.
Answer : option e.
Solution :
Option (a) gives 145038 x 9999
= 145038 x (10000 - 1)
= 1450380000 - 145038
= 1450234962 ...(1)
Option (b) gives 48346 x 29997
= 48346 x (30000-3)
= 48346 x 3 x (10000 - 1)
= 145038 (10000 - 1)
= 1450380000 - 145038
= 1450234962 ...(2)
Option (c) gives 24173 x 59994
= 24173 x (600000 - 6)
= 24173 x 6 x (100000 - 1)
= 145038 x (10000 - 1)
= 1450380000 - 145038
= 1450234962 ...(3)
Option (d) gives 1595418 x 909
= 1595418 x (900 + 9)
= 1595418 x 9(100 + 1)
= 14358762 (100 + 1)
= 1435876200 + 14358762
= 1450234962 ...(4)
From (1), (2), (3) and (4) we have the answer is option e.
Question 3
(a) 733x6 + 56x14 - 511x6
(b) 12x111 + 28x28
(c) 13x13x4 + 166x18 - 86x18
(d) 1307x2 - 869x4 + 20x149
Options : a, b, c, d, e.
Answer : option d.
Solution :
Option (a) gives 733x6 + 56x14 - 511x6
= 733x6 - 511x6 + 56x14
= (733-511)x6 + 56x14
= 222x6 + 784
= 2116...(1)
Option (b) gives 12x111 + 28x28
= 1332 + 784
= 2116...(2)
Option (c) gives 13x13x4 + 166x18 - 86x18
= 13x13x4 + (166 - 86)x18
= 676 + 80x18
= 676 + 1440
= 2116...(3)
Option (d) gives 1307x2 - 869x4 + 20x149
= 2614 - 4(869 - 5x149)
= 2614 - 4(869 - 745)
= 2614 - 4x124
= 2614 - 496
= 2118...(4)
The odd one is option (d).
Below are four problems on basic arithmetic calculations.
Directions to solve:
In each of the following question, four parts labelled (a) (b) (c) and (d). One of these parts may not yield the same result as the other three do. Find out the wrong part if there any. The label of that part is the answer. If all the four parts are correctly equated then the answer is e, i.e., No error.
Question 1
(a) 272 x 24 / 18 x 6
(b) 34 x 128 / 12 x 6
(c) 72 x 34 / 18 x 18
(d) 288 x 34 / 27 x 6
Options : a, b, c, d, e.
Answer : option c.
Solution :
Option (a) gives 272 x 24 / 18 x 6
= 136 x 2 x 6 x 4 / 9 x 2 x 6
Cancelling the common terms, we have
= 136 x 4/9 = 544/9 ...(1)
Option (b) gives 34 x 128 / 12 x 6
= 34 x 4 x 2 x 16 / 4 x 3 x 2 x 3
Cancelling the common terms, we have
= 34 x 16 / 3 x 3
= 544/9 ...(2)
Option (c) gives 72 x 34 / 18 x 18
= 2 x 9 x 4 x 34 / 2 x 9 x 2 x 9
Cancelling the common terms, we have
= 34 x 2/9
= 68/9 ...(3)
Option (d) gives 288 x 34 / 27 x 6
= 34 x 16 x 3 x 6 / 9 x 3 x 6
Cancelling the common terms, we have
= 34 x 16/9
= 544/9 ...(4)
From (1), (2), (3) and (4) we have the answer is option c.
Question 2
(a) 145038 x 9999
(b) 48346 x 2997
(c) 24173 x 59994
(d) 1595418 x 909
Options : a, b, c, d, e.
Answer : option e.
Solution :
Option (a) gives 145038 x 9999
= 145038 x (10000 - 1)
= 1450380000 - 145038
= 1450234962 ...(1)
Option (b) gives 48346 x 29997
= 48346 x (30000-3)
= 48346 x 3 x (10000 - 1)
= 145038 (10000 - 1)
= 1450380000 - 145038
= 1450234962 ...(2)
Option (c) gives 24173 x 59994
= 24173 x (600000 - 6)
= 24173 x 6 x (100000 - 1)
= 145038 x (10000 - 1)
= 1450380000 - 145038
= 1450234962 ...(3)
Option (d) gives 1595418 x 909
= 1595418 x (900 + 9)
= 1595418 x 9(100 + 1)
= 14358762 (100 + 1)
= 1435876200 + 14358762
= 1450234962 ...(4)
From (1), (2), (3) and (4) we have the answer is option e.
Question 3
(a) 733x6 + 56x14 - 511x6
(b) 12x111 + 28x28
(c) 13x13x4 + 166x18 - 86x18
(d) 1307x2 - 869x4 + 20x149
Options : a, b, c, d, e.
Answer : option d.
Solution :
Option (a) gives 733x6 + 56x14 - 511x6
= 733x6 - 511x6 + 56x14
= (733-511)x6 + 56x14
= 222x6 + 784
= 2116...(1)
Option (b) gives 12x111 + 28x28
= 1332 + 784
= 2116...(2)
Option (c) gives 13x13x4 + 166x18 - 86x18
= 13x13x4 + (166 - 86)x18
= 676 + 80x18
= 676 + 1440
= 2116...(3)
Option (d) gives 1307x2 - 869x4 + 20x149
= 2614 - 4(869 - 5x149)
= 2614 - 4(869 - 745)
= 2614 - 4x124
= 2614 - 496
= 2118...(4)
The odd one is option (d).
