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If we divide a two-digit number by the sum of its digits, we get 4 as a quotient and 3 as a remainder. Now if we divide that two-digit number by the product of its digits, we get 3 as a quotient and 5 as a remainder and the two-digit number.
- a)25
- b)23
- c)30
- d)27
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Ifwe divide a two-digit number by the sum of its digits, we get4as a q...
To solve this problem, let's assume the two-digit number as '10x + y', where x and y are the digits of the number.
1. Dividing the two-digit number by the sum of its digits:
The sum of the digits is x + y. So, we have the equation:
(10x + y) / (x + y) = 4 + 3/(x + y)
From this equation, we can deduce that x + y is a factor of 3. The possible values for x + y can be 1, 3, or 3.
2. Dividing the two-digit number by the product of its digits:
The product of the digits is xy. So, we have the equation:
(10x + y) / (xy) = 3 + 5/xy
From this equation, we can deduce that xy is a factor of 5. The possible values for xy can be 1 or 5.
Now, let's analyze the options given:
a) 25: The sum of the digits is 2 + 5 = 7. Dividing 25 by 7 gives a quotient of 3 and a remainder of 4, which matches the first condition. However, dividing 25 by 10 gives a quotient of 2 and a remainder of 5, which does not match the second condition. So, option a) is incorrect.
b) 23: The sum of the digits is 2 + 3 = 5. Dividing 23 by 5 gives a quotient of 4 and a remainder of 3, which matches the first condition. Dividing 23 by 6 (product of digits) gives a quotient of 3 and a remainder of 5, which matches the second condition. So, option b) is correct.
c) 30: The sum of the digits is 3 + 0 = 3. Dividing 30 by 3 gives a quotient of 10 and a remainder of 0, which does not match the first condition. So, option c) is incorrect.
d) 27: The sum of the digits is 2 + 7 = 9. Dividing 27 by 9 gives a quotient of 3 and a remainder of 0, which does not match the first condition. So, option d) is incorrect.
Therefore, the correct answer is option b) 23.
1. Dividing the two-digit number by the sum of its digits:
The sum of the digits is x + y. So, we have the equation:
(10x + y) / (x + y) = 4 + 3/(x + y)
From this equation, we can deduce that x + y is a factor of 3. The possible values for x + y can be 1, 3, or 3.
2. Dividing the two-digit number by the product of its digits:
The product of the digits is xy. So, we have the equation:
(10x + y) / (xy) = 3 + 5/xy
From this equation, we can deduce that xy is a factor of 5. The possible values for xy can be 1 or 5.
Now, let's analyze the options given:
a) 25: The sum of the digits is 2 + 5 = 7. Dividing 25 by 7 gives a quotient of 3 and a remainder of 4, which matches the first condition. However, dividing 25 by 10 gives a quotient of 2 and a remainder of 5, which does not match the second condition. So, option a) is incorrect.
b) 23: The sum of the digits is 2 + 3 = 5. Dividing 23 by 5 gives a quotient of 4 and a remainder of 3, which matches the first condition. Dividing 23 by 6 (product of digits) gives a quotient of 3 and a remainder of 5, which matches the second condition. So, option b) is correct.
c) 30: The sum of the digits is 3 + 0 = 3. Dividing 30 by 3 gives a quotient of 10 and a remainder of 0, which does not match the first condition. So, option c) is incorrect.
d) 27: The sum of the digits is 2 + 7 = 9. Dividing 27 by 9 gives a quotient of 3 and a remainder of 0, which does not match the first condition. So, option d) is incorrect.
Therefore, the correct answer is option b) 23.
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Community Answer
Ifwe divide a two-digit number by the sum of its digits, we get4as a q...
Let n(a,b) is two digit number.
n(a,b)=10a+b
Given sum of its digitsnumber will give 4 as quotient and 3 as remqinder.
n(a,b)=4(a+b)+3
10a+b=4a+4b+3
6a−3b=3⇒2a=1+b
n(a,b)=3(ab)+5
10a+b=3ab+5
10a+2a−1=3a(2a−1)+5
12a−1=6a2−3a+5
6a2−15a+6=0
2a2−5a+2=0
(2a−1)(a−2)=0
a=2(∵a=21)
∴b=2a−1=3
23 is required number.
So, the correct option is B.
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