GMAT Exam > GMAT Questions > If both 112and 33are factors of the number a ...
Start Learning for Free
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: 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: 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
Choice C is the correct answer.
Most Upvoted Answer
If both 112and 33are factors of the number a * 43* 62* 1311, then what...
Factors of the given number
- The number in question is a * 43 * 62 * 1311.
- We are given that both 112 and 33 are factors of this number.
Finding the smallest possible value of a
- To find the smallest possible value of a, we need to find the common factors of the given number with 112 and 33.
- Factors of 112 are 1, 2, 4, 8, 14, 16, 28, 56, 112.
- Factors of 33 are 1, 3, 11, 33.
- We need to find the common factors of 112, 33, and the given number.
Common factors of 112, 33, and the given number
- The common factors of 112, 33, and the given number are 1 and 33.
- Since we are looking for the smallest possible value of a, a must be the smallest common factor, which is 33.
Smallest possible value of a
- Therefore, the smallest possible value of a is 33.
- Hence, the correct answer is option 'C' - 363.
- The number in question is a * 43 * 62 * 1311.
- We are given that both 112 and 33 are factors of this number.
Finding the smallest possible value of a
- To find the smallest possible value of a, we need to find the common factors of the given number with 112 and 33.
- Factors of 112 are 1, 2, 4, 8, 14, 16, 28, 56, 112.
- Factors of 33 are 1, 3, 11, 33.
- We need to find the common factors of 112, 33, and the given number.
Common factors of 112, 33, and the given number
- The common factors of 112, 33, and the given number are 1 and 33.
- Since we are looking for the smallest possible value of a, a must be the smallest common factor, which is 33.
Smallest possible value of a
- Therefore, the smallest possible value of a is 33.
- Hence, the correct answer is option 'C' - 363.
|
Explore Courses for GMAT exam
|
|
Top Courses for GMATView all
Question Description
If both 112and 33are factors of the number a * 43* 62* 1311, then what is the smallest possible value of a?a)121b)3267c)363d)33e)None of the aboveCorrect answer is option 'C'. 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 If both 112and 33are factors of the number a * 43* 62* 1311, then what is the smallest possible value of a?a)121b)3267c)363d)33e)None of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If both 112and 33are factors of the number a * 43* 62* 1311, then what is the smallest possible value of a?a)121b)3267c)363d)33e)None of the aboveCorrect answer is option 'C'. Can you explain this answer?.
If both 112and 33are factors of the number a * 43* 62* 1311, then what is the smallest possible value of a?a)121b)3267c)363d)33e)None of the aboveCorrect answer is option 'C'. 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 If both 112and 33are factors of the number a * 43* 62* 1311, then what is the smallest possible value of a?a)121b)3267c)363d)33e)None of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If both 112and 33are factors of the number a * 43* 62* 1311, then what is the smallest possible value of a?a)121b)3267c)363d)33e)None of the aboveCorrect answer is option 'C'. Can you explain this answer?.
Solutions for If both 112and 33are factors of the number a * 43* 62* 1311, then what is the smallest possible value of a?a)121b)3267c)363d)33e)None of the aboveCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.
Here you can find the meaning of If both 112and 33are factors of the number a * 43* 62* 1311, then what is the smallest possible value of a?a)121b)3267c)363d)33e)None of the aboveCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If both 112and 33are factors of the number a * 43* 62* 1311, then what is the smallest possible value of a?a)121b)3267c)363d)33e)None of the aboveCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for If both 112and 33are factors of the number a * 43* 62* 1311, then what is the smallest possible value of a?a)121b)3267c)363d)33e)None of the aboveCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of If both 112and 33are factors of the number a * 43* 62* 1311, then what is the smallest possible value of a?a)121b)3267c)363d)33e)None of the aboveCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If both 112and 33are factors of the number a * 43* 62* 1311, then what is the smallest possible value of a?a)121b)3267c)363d)33e)None of the aboveCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice GMAT tests.
|
|
Explore Courses for GMAT exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup on EduRev and stay on top of your study goals
10M+ students crushing their study goals daily