CAT Exam > CAT Questions > DIRECTIONS for the question: Solve the follow...
Start Learning for Free
DIRECTIONS for the question: Solve the following question.
Consider the set X = {1, 2, 3, ..., 9, 10}. A and B are two non-empty disjoint subsets of X such that A ∪ B = X. The products of all the elements in A and B are represented by prod(A) and prod(B) respectively. If prod(A) is a multiple of prod(B), and quotient is the smallest possible integer, then what is the minimum difference between the sum of all elements in A and the sum of all elements in B? (in numerical value)
Correct answer is '1'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
DIRECTIONS for the question: Solve the following question.Consider the...
The prime factors of the numbers in set {1, 2, 3, ..., 9, 10} are 2, 3, 5 and 7. Now, 7 is the only number in X which has a prime factor 7 and therefore, it cannot appear in B (otherwise the 7 in the denominator would not get canceled). So, 7 must be in A. From this, we now know that prod(A) / prod(B) ≥ 7.
The numbers having prime factor 3 are 3, 6 and 9. Since we want the quotient to be as small as possible, 3 and 6 are in A and 9 is in B. Similarly, since 5 divides 5 and 10, 5 is in A and 10 is in B. Extending this logic, we can take 1, 2 and 4 in A and 8 in B. So, the two sets are A = {1, 2, 3, 4, 5, 6, 7} and B = {8, 9, 10} so that prod(A) = 7! = 5040 and prod(B) = 720 so that prod(A) / prod(B) is a minimum of 7. The sum of the elements in A is 28 and the sum of the elements in B is 27. Thus the requried difference is 1.
Note: the 1 can also be moved to set B in which case sum of elements in A is 27 and the sum of elements in B is 28. The difference would still be 1.
Most Upvoted Answer
DIRECTIONS for the question: Solve the following question.Consider the...
To solve this question, we need to find the number of possible values for the sum of the elements in set A and set B.
Since A and B are non-empty disjoint subsets of X, this means that each number from 1 to 10 must be either in set A or set B, but not in both.
Let's consider the smallest number, 1. It can either be in set A or set B. Let's assume it is in set A.
Next, let's consider the largest number, 10. It cannot be in set A since 1 is in set A. Therefore, it must be in set B.
Now, we have assigned the smallest and largest numbers to set A and set B respectively. We are left with the numbers from 2 to 9.
For each of the remaining numbers, we have two choices: either to put it in set A or set B. Since A and B are non-empty sets, we cannot leave any number out.
Therefore, for each of the remaining numbers, we have 2 choices. Since there are 8 remaining numbers, the total number of possible combinations for these numbers is 2^8 = 256.
So, the number of possible values for the sum of the elements in set A and set B is 256.
Since A and B are non-empty disjoint subsets of X, this means that each number from 1 to 10 must be either in set A or set B, but not in both.
Let's consider the smallest number, 1. It can either be in set A or set B. Let's assume it is in set A.
Next, let's consider the largest number, 10. It cannot be in set A since 1 is in set A. Therefore, it must be in set B.
Now, we have assigned the smallest and largest numbers to set A and set B respectively. We are left with the numbers from 2 to 9.
For each of the remaining numbers, we have two choices: either to put it in set A or set B. Since A and B are non-empty sets, we cannot leave any number out.
Therefore, for each of the remaining numbers, we have 2 choices. Since there are 8 remaining numbers, the total number of possible combinations for these numbers is 2^8 = 256.
So, the number of possible values for the sum of the elements in set A and set B is 256.
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Top Courses for CATView all
DIRECTIONS for the question: Solve the following question.Consider the set X = {1, 2, 3, ..., 9, 10}. A and B are two non-empty disjoint subsets of X such that A ∪ B = X. The products of all the elements in A and B are represented by prod(A) and prod(B) respectively. If prod(A) is a multiple of prod(B), and quotient is the smallest possible integer, then what is the minimum difference between the sum of all elements in A and the sum of all elements in B? (in numerical value)Correct answer is '1'. Can you explain this answer?
Question Description
DIRECTIONS for the question: Solve the following question.Consider the set X = {1, 2, 3, ..., 9, 10}. A and B are two non-empty disjoint subsets of X such that A ∪ B = X. The products of all the elements in A and B are represented by prod(A) and prod(B) respectively. If prod(A) is a multiple of prod(B), and quotient is the smallest possible integer, then what is the minimum difference between the sum of all elements in A and the sum of all elements in B? (in numerical value)Correct answer is '1'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about DIRECTIONS for the question: Solve the following question.Consider the set X = {1, 2, 3, ..., 9, 10}. A and B are two non-empty disjoint subsets of X such that A ∪ B = X. The products of all the elements in A and B are represented by prod(A) and prod(B) respectively. If prod(A) is a multiple of prod(B), and quotient is the smallest possible integer, then what is the minimum difference between the sum of all elements in A and the sum of all elements in B? (in numerical value)Correct answer is '1'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTIONS for the question: Solve the following question.Consider the set X = {1, 2, 3, ..., 9, 10}. A and B are two non-empty disjoint subsets of X such that A ∪ B = X. The products of all the elements in A and B are represented by prod(A) and prod(B) respectively. If prod(A) is a multiple of prod(B), and quotient is the smallest possible integer, then what is the minimum difference between the sum of all elements in A and the sum of all elements in B? (in numerical value)Correct answer is '1'. Can you explain this answer?.
DIRECTIONS for the question: Solve the following question.Consider the set X = {1, 2, 3, ..., 9, 10}. A and B are two non-empty disjoint subsets of X such that A ∪ B = X. The products of all the elements in A and B are represented by prod(A) and prod(B) respectively. If prod(A) is a multiple of prod(B), and quotient is the smallest possible integer, then what is the minimum difference between the sum of all elements in A and the sum of all elements in B? (in numerical value)Correct answer is '1'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about DIRECTIONS for the question: Solve the following question.Consider the set X = {1, 2, 3, ..., 9, 10}. A and B are two non-empty disjoint subsets of X such that A ∪ B = X. The products of all the elements in A and B are represented by prod(A) and prod(B) respectively. If prod(A) is a multiple of prod(B), and quotient is the smallest possible integer, then what is the minimum difference between the sum of all elements in A and the sum of all elements in B? (in numerical value)Correct answer is '1'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTIONS for the question: Solve the following question.Consider the set X = {1, 2, 3, ..., 9, 10}. A and B are two non-empty disjoint subsets of X such that A ∪ B = X. The products of all the elements in A and B are represented by prod(A) and prod(B) respectively. If prod(A) is a multiple of prod(B), and quotient is the smallest possible integer, then what is the minimum difference between the sum of all elements in A and the sum of all elements in B? (in numerical value)Correct answer is '1'. Can you explain this answer?.
Solutions for DIRECTIONS for the question: Solve the following question.Consider the set X = {1, 2, 3, ..., 9, 10}. A and B are two non-empty disjoint subsets of X such that A ∪ B = X. The products of all the elements in A and B are represented by prod(A) and prod(B) respectively. If prod(A) is a multiple of prod(B), and quotient is the smallest possible integer, then what is the minimum difference between the sum of all elements in A and the sum of all elements in B? (in numerical value)Correct answer is '1'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of DIRECTIONS for the question: Solve the following question.Consider the set X = {1, 2, 3, ..., 9, 10}. A and B are two non-empty disjoint subsets of X such that A ∪ B = X. The products of all the elements in A and B are represented by prod(A) and prod(B) respectively. If prod(A) is a multiple of prod(B), and quotient is the smallest possible integer, then what is the minimum difference between the sum of all elements in A and the sum of all elements in B? (in numerical value)Correct answer is '1'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
DIRECTIONS for the question: Solve the following question.Consider the set X = {1, 2, 3, ..., 9, 10}. A and B are two non-empty disjoint subsets of X such that A ∪ B = X. The products of all the elements in A and B are represented by prod(A) and prod(B) respectively. If prod(A) is a multiple of prod(B), and quotient is the smallest possible integer, then what is the minimum difference between the sum of all elements in A and the sum of all elements in B? (in numerical value)Correct answer is '1'. Can you explain this answer?, a detailed solution for DIRECTIONS for the question: Solve the following question.Consider the set X = {1, 2, 3, ..., 9, 10}. A and B are two non-empty disjoint subsets of X such that A ∪ B = X. The products of all the elements in A and B are represented by prod(A) and prod(B) respectively. If prod(A) is a multiple of prod(B), and quotient is the smallest possible integer, then what is the minimum difference between the sum of all elements in A and the sum of all elements in B? (in numerical value)Correct answer is '1'. Can you explain this answer? has been provided alongside types of DIRECTIONS for the question: Solve the following question.Consider the set X = {1, 2, 3, ..., 9, 10}. A and B are two non-empty disjoint subsets of X such that A ∪ B = X. The products of all the elements in A and B are represented by prod(A) and prod(B) respectively. If prod(A) is a multiple of prod(B), and quotient is the smallest possible integer, then what is the minimum difference between the sum of all elements in A and the sum of all elements in B? (in numerical value)Correct answer is '1'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice DIRECTIONS for the question: Solve the following question.Consider the set X = {1, 2, 3, ..., 9, 10}. A and B are two non-empty disjoint subsets of X such that A ∪ B = X. The products of all the elements in A and B are represented by prod(A) and prod(B) respectively. If prod(A) is a multiple of prod(B), and quotient is the smallest possible integer, then what is the minimum difference between the sum of all elements in A and the sum of all elements in B? (in numerical value)Correct answer is '1'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup