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If both 112 and 33 are factors of the number a * 43 * 62 * 1311, then what is the smallest possible value of 'a'?
- a)121
- b)3267
- c)363
- d)33
- e)None of the above
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If both 112and 33are factors of the number a * 43* 62* 1311, then what...
Step 1 of solving this GMAT Number Properties Question: Prime factorize the given expression
a * 43 * 62 * 1311 can be expressed in terms of its prime factors as a * 28 * 32 * 1311
Step 2 of solving this GMAT Number Properties Question: Find factors missing after excluding 'a' to make the number divisible by both 112 and 33
112 is a factor of the given number.
If we do not include 'a', 11 is not a prime factor of the given number.
If 112 is a factor of the number, 112 should be a part of 'a'
If we do not include 'a', 11 is not a prime factor of the given number.
If 112 is a factor of the number, 112 should be a part of 'a'
33 is a factor of the given number.
If we do not include 'a', the number has only 32 in it.
Therefore, if 33 has to be a factor of the given number 'a' has to contain 31 in it.
If we do not include 'a', the number has only 32 in it.
Therefore, if 33 has to be a factor of the given number 'a' has to contain 31 in it.
Therefore, 'a' should be at least 112 * 3 = 363 if the given number has 112 and 33 as its factors.
The question is "what is the smallest possible value of 'a'?"
The smallest value that 'a' can take is 363
The smallest value that 'a' can take is 363
Most Upvoted Answer
If both 112and 33are factors of the number a * 43* 62* 1311, then what...
Explanation:
Factors of the given number:
- The given number is a * 43 * 62 * 1311.
- Factors of 43: 1, 43.
- Factors of 62: 1, 2, 31, 62.
- Factors of 1311: 1, 3, 19, 69, 131, 393, 873, 1311.
Common factors:
- Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112.
- Factors of 33: 1, 3, 11, 33.
Smallest possible value of a:
- To find the smallest possible value of 'a', we need to consider the common factors of 112 and 33.
- The common factors of 112 and 33 are 1 and 7.
- So, the smallest possible value of 'a' can be obtained by multiplying 1 and 7 i.e. 7.
Therefore, the smallest possible value of 'a' is 7, which is not provided in the options. Hence, the correct answer is option 'e) None of the above'.
Factors of the given number:
- The given number is a * 43 * 62 * 1311.
- Factors of 43: 1, 43.
- Factors of 62: 1, 2, 31, 62.
- Factors of 1311: 1, 3, 19, 69, 131, 393, 873, 1311.
Common factors:
- Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112.
- Factors of 33: 1, 3, 11, 33.
Smallest possible value of a:
- To find the smallest possible value of 'a', we need to consider the common factors of 112 and 33.
- The common factors of 112 and 33 are 1 and 7.
- So, the smallest possible value of 'a' can be obtained by multiplying 1 and 7 i.e. 7.
Therefore, the smallest possible value of 'a' is 7, which is not provided in the options. Hence, the correct answer is option 'e) None of the above'.
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