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In a certain deck of cards, each card has a positive integer written on it. In a multiplication game, a child draws a card and multiplies the integer on the card by the next larger integer. If each possible product is between 15 and 200, then the least and greatest integers on the cards could be
- a)3 and 15
- b)3 and 20
- c)4 and 13
- d)4 and 14
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
In a certain deck of cards, each card has a positive integer written o...
If the least number was 3, then 3*4=12<15, does not fulfill the requirement. So, the least number is 4.
If the greatest number is 14, then 14*15=210>200, does not fulfill the requirement.
So, answer is "4 and 13"
If the greatest number is 14, then 14*15=210>200, does not fulfill the requirement.
So, answer is "4 and 13"
Most Upvoted Answer
In a certain deck of cards, each card has a positive integer written o...
To find the least and greatest integers on the cards, we need to consider the possible products that can be obtained within the given range of 15 to 200. Let's analyze the given options to determine the correct answer.
Option A: 3 and 15
If the least integer on the card is 3, the next larger integer would be 4. However, 3 multiplied by 4 equals 12, which is less than the given lower limit of 15. Therefore, this option is not valid.
Option B: 3 and 20
Similar to the previous option, if the least integer on the card is 3, the next larger integer would be 4. The product of 3 and 4 is 12, which is still less than 15. Therefore, this option is also not valid.
Option C: 4 and 13
If the least integer on the card is 4, the next larger integer would be 5. The product of 4 and 5 is 20, which is within the given range of 15 to 200. This satisfies the lower limit. Now, we need to check if the upper limit is also satisfied. The largest integer on the card would be one less than the next smaller integer, which is 12. The product of 12 and 13 is 156, which is also within the given range. Therefore, this option is valid.
Option D: 4 and 14
If the least integer on the card is 4, the next larger integer would be 5. The product of 4 and 5 is 20, which satisfies the lower limit. However, the largest integer on the card would be one less than the next smaller integer, which is 13. The product of 13 and 14 is 182, which exceeds the given upper limit. Therefore, this option is not valid.
Hence, the correct answer is option C: 4 and 13.
Option A: 3 and 15
If the least integer on the card is 3, the next larger integer would be 4. However, 3 multiplied by 4 equals 12, which is less than the given lower limit of 15. Therefore, this option is not valid.
Option B: 3 and 20
Similar to the previous option, if the least integer on the card is 3, the next larger integer would be 4. The product of 3 and 4 is 12, which is still less than 15. Therefore, this option is also not valid.
Option C: 4 and 13
If the least integer on the card is 4, the next larger integer would be 5. The product of 4 and 5 is 20, which is within the given range of 15 to 200. This satisfies the lower limit. Now, we need to check if the upper limit is also satisfied. The largest integer on the card would be one less than the next smaller integer, which is 12. The product of 12 and 13 is 156, which is also within the given range. Therefore, this option is valid.
Option D: 4 and 14
If the least integer on the card is 4, the next larger integer would be 5. The product of 4 and 5 is 20, which satisfies the lower limit. However, the largest integer on the card would be one less than the next smaller integer, which is 13. The product of 13 and 14 is 182, which exceeds the given upper limit. Therefore, this option is not valid.
Hence, the correct answer is option C: 4 and 13.
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In a certain deck of cards, each card has a positive integer written on it. In a multiplication game, a child draws a card and multiplies the integer on the card by the next larger integer. If each possible product is between 15 and 200, then the least and greatest integers on the cards could bea)3 and 15b)3 and 20c)4 and 13d)4 and 14Correct answer is option 'C'. Can you explain this answer?
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