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Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following could be the sum of G and H? ?
- a)153
- b)150
- c)129
- d)89
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Each digit in the two-digit number G is halved to form a new two-digit...
Two-step solution:
G + G/2 = 3G/2 --> the sum is a multiple of 3.
G is a two-digit number --> G < 100 --> 3G/2 < 150.
Among the answer choices the only multiple of 3 which is less than 150 is 129.
Most Upvoted Answer
Each digit in the two-digit number G is halved to form a new two-digit...
To find the sum of the two-digit number G and the number obtained by halving each digit of G, we need to consider all the possibilities for G and H. Let's analyze each option provided and see if it satisfies the given condition.
Option a) 153
The number 153 cannot be the sum of G and H because it is a three-digit number, not a two-digit number.
Option b) 150
Let's consider G = 50. When we halve each digit, we get H = 25. The sum of G and H is 50 + 25 = 75, which is not equal to 150. Therefore, option b) is not a possible sum.
Option c) 129
Let's consider G = 29. When we halve each digit, we get H = 14. The sum of G and H is 29 + 14 = 43, which is not equal to 129. However, we can also consider G = 14. When we halve each digit, we get H = 07. The sum of G and H is 14 + 07 = 21, which is not equal to 129. Therefore, option c) is not a possible sum.
Option d) 89
Let's consider G = 89. When we halve each digit, we get H = 44. The sum of G and H is 89 + 44 = 133, which is not equal to 89. Therefore, option d) is not a possible sum.
From the analysis above, we can conclude that none of the options provided could be the sum of G and H.
Option a) 153
The number 153 cannot be the sum of G and H because it is a three-digit number, not a two-digit number.
Option b) 150
Let's consider G = 50. When we halve each digit, we get H = 25. The sum of G and H is 50 + 25 = 75, which is not equal to 150. Therefore, option b) is not a possible sum.
Option c) 129
Let's consider G = 29. When we halve each digit, we get H = 14. The sum of G and H is 29 + 14 = 43, which is not equal to 129. However, we can also consider G = 14. When we halve each digit, we get H = 07. The sum of G and H is 14 + 07 = 21, which is not equal to 129. Therefore, option c) is not a possible sum.
Option d) 89
Let's consider G = 89. When we halve each digit, we get H = 44. The sum of G and H is 89 + 44 = 133, which is not equal to 89. Therefore, option d) is not a possible sum.
From the analysis above, we can conclude that none of the options provided could be the sum of G and H.
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Community Answer
Each digit in the two-digit number G is halved to form a new two-digit...
G + G/2 = 3G/2 --> the sum is a multiple of 3.
G is a two-digit number --> G < 100 --> 3G/2 < 150.
Among the answer choices the only multiple of 3 which is less than 150 is 129.
Answer: D.
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