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What is the smallest positive 2-digit whole number divisible by 3 and such that the sum of its digits is 9?
- a)27
- b)33
- c)72
- d)18
- e)90
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
What is the smallest positive 2-digit whole number divisible by 3 and ...
Let xy be the whole number with x and y the two digits that make up the number. The number is divisible by 3 may be written as follows
10 x + y = 3 k
The sum of x and y is equal to 9.
x + y = 9
Solve the above equation for y
y = 9 - x Substitute y = 9 - x in the equation 10 x + y = 3 k to obtain.
10 x + 9 - x = 3 k
Solve for x
x = (k - 3) / 3
x is a positive integer smaller than 10
Let k = 1, 2, 3, ... and select the first value that gives x as an integer. k = 6 gives x = 1
Find y using the equation y = 9 - x = 8
The number we are looking for is 18 and the answer is D. It is divisible by 3 and the sum of its digits is equal to 9 and it is the smallest and positive whole number with such properties.
10 x + y = 3 k
The sum of x and y is equal to 9.
x + y = 9
Solve the above equation for y
y = 9 - x Substitute y = 9 - x in the equation 10 x + y = 3 k to obtain.
10 x + 9 - x = 3 k
Solve for x
x = (k - 3) / 3
x is a positive integer smaller than 10
Let k = 1, 2, 3, ... and select the first value that gives x as an integer. k = 6 gives x = 1
Find y using the equation y = 9 - x = 8
The number we are looking for is 18 and the answer is D. It is divisible by 3 and the sum of its digits is equal to 9 and it is the smallest and positive whole number with such properties.
Most Upvoted Answer
What is the smallest positive 2-digit whole number divisible by 3 and ...
Problem:
What is the smallest positive 2-digit whole number divisible by 3 and such that the sum of its digits is 9?
Solution:
To solve this problem, we need to find the smallest 2-digit number that is divisible by 3 and has a digit sum of 9.
Step 1: Finding the Divisibility Rule
To determine if a number is divisible by 3, we can check if the sum of its digits is divisible by 3. In this case, we need to find a number whose digits add up to 9.
Step 2: Identifying the Possible Numbers
Since we are looking for a 2-digit number, the possible numbers range from 10 to 99. Let's list all the possible numbers and their digit sums:
10: 1 + 0 = 1
11: 1 + 1 = 2
12: 1 + 2 = 3
...
98: 9 + 8 = 17
99: 9 + 9 = 18
Step 3: Finding the Smallest Number
Out of all the possible numbers, we can see that 12 and 18 have digit sums of 3 and 9, respectively. However, 12 is not divisible by 3, so we can eliminate it.
Therefore, the smallest 2-digit number that is divisible by 3 and has a digit sum of 9 is 18.
Answer:
Hence, the correct answer is option 'D' - 18.
What is the smallest positive 2-digit whole number divisible by 3 and such that the sum of its digits is 9?
Solution:
To solve this problem, we need to find the smallest 2-digit number that is divisible by 3 and has a digit sum of 9.
Step 1: Finding the Divisibility Rule
To determine if a number is divisible by 3, we can check if the sum of its digits is divisible by 3. In this case, we need to find a number whose digits add up to 9.
Step 2: Identifying the Possible Numbers
Since we are looking for a 2-digit number, the possible numbers range from 10 to 99. Let's list all the possible numbers and their digit sums:
10: 1 + 0 = 1
11: 1 + 1 = 2
12: 1 + 2 = 3
...
98: 9 + 8 = 17
99: 9 + 9 = 18
Step 3: Finding the Smallest Number
Out of all the possible numbers, we can see that 12 and 18 have digit sums of 3 and 9, respectively. However, 12 is not divisible by 3, so we can eliminate it.
Therefore, the smallest 2-digit number that is divisible by 3 and has a digit sum of 9 is 18.
Answer:
Hence, the correct answer is option 'D' - 18.
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What is the smallest positive 2-digit whole number divisible by 3 and such that the sum of its digits is 9?a)27b)33c)72d)18e)90Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about What is the smallest positive 2-digit whole number divisible by 3 and such that the sum of its digits is 9?a)27b)33c)72d)18e)90Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the smallest positive 2-digit whole number divisible by 3 and such that the sum of its digits is 9?a)27b)33c)72d)18e)90Correct answer is option 'D'. Can you explain this answer?.
What is the smallest positive 2-digit whole number divisible by 3 and such that the sum of its digits is 9?a)27b)33c)72d)18e)90Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about What is the smallest positive 2-digit whole number divisible by 3 and such that the sum of its digits is 9?a)27b)33c)72d)18e)90Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the smallest positive 2-digit whole number divisible by 3 and such that the sum of its digits is 9?a)27b)33c)72d)18e)90Correct answer is option 'D'. Can you explain this answer?.
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