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When a number is multiplied by 13 and 13 is added to the product, the resultant is divisible by 5. Find the smallest product possible?
- a)85
- b)130
- c)65
- d)90
- e)105
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
When a number is multiplied by 13 and 13 is added to the product, the ...
13x + 13 which is divisible by 5, or 13(x+1) should be divisible by 5. The smallest value of x = 4 to be put here to make it divisible by 5. So the number is 13(4+1)
Most Upvoted Answer
When a number is multiplied by 13 and 13 is added to the product, the ...
The options itself are wrong. The question is asking the smallest product possible, 65 is the LEAST NUMBER that's divisble according to condition. But the least product should be 52 according to me. As 13 is getting added to the PRODUCT, 65 itself is not the product.
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When a number is multiplied by 13 and 13 is added to the product, the ...
Given, a number is multiplied by 13 and 13 is added to the product, the resultant is divisible by 5.
Let's assume the number to be x.
Formula: 13x + 13 = 13(x+1) which can be written as 13k (where k=x+1)
We know that for a number to be divisible by 5, it should end with either 0 or 5.
Let's check for some values of k:
- For k = 1, 13k = 13 which is not divisible by 5.
- For k = 2, 13k = 26 which is not divisible by 5.
- For k = 3, 13k = 39 which is not divisible by 5.
- For k = 4, 13k = 52 which is not divisible by 5.
- For k = 5, 13k = 65 which is divisible by 5.
Hence, the smallest product possible is 13k = 65, where k=5 and x=k-1=4.
Therefore, the correct answer is option C) 65.
Let's assume the number to be x.
Formula: 13x + 13 = 13(x+1) which can be written as 13k (where k=x+1)
We know that for a number to be divisible by 5, it should end with either 0 or 5.
Let's check for some values of k:
- For k = 1, 13k = 13 which is not divisible by 5.
- For k = 2, 13k = 26 which is not divisible by 5.
- For k = 3, 13k = 39 which is not divisible by 5.
- For k = 4, 13k = 52 which is not divisible by 5.
- For k = 5, 13k = 65 which is divisible by 5.
Hence, the smallest product possible is 13k = 65, where k=5 and x=k-1=4.
Therefore, the correct answer is option C) 65.
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When a number is multiplied by 13 and 13 is added to the product, the resultant is divisible by 5. Find the smallest product possible?a)85b)130c)65d)90e)105Correct answer is option 'C'. Can you explain this answer?
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