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For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 1000, what is the maximum possible sum of the length of x and the length of y? ?
- a)5
- b)6
- c)15
- d)16
Correct answer is option 'D'. Can you explain this answer?
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For any integer k > 1, the term “length of an integer” ...
For any integer k, we can write k as k = 2n or k = 2n + 1, where n is an integer.
If k is even, then k = 2n for some integer n. We can substitute this into the equation to get:
(-1)^k = (-1)^(2n) = 1
So, if k is even, then (-1)^k = 1.
If k is odd, then k = 2n + 1 for some integer n. We can substitute this into the equation to get:
(-1)^k = (-1)^(2n + 1) = (-1)^(2n) * (-1)^1 = 1 * (-1) = -1
So, if k is odd, then (-1)^k = -1.
Therefore, for any integer k, (-1)^k is equal to 1 if k is even, and -1 if k is odd.
If k is even, then k = 2n for some integer n. We can substitute this into the equation to get:
(-1)^k = (-1)^(2n) = 1
So, if k is even, then (-1)^k = 1.
If k is odd, then k = 2n + 1 for some integer n. We can substitute this into the equation to get:
(-1)^k = (-1)^(2n + 1) = (-1)^(2n) * (-1)^1 = 1 * (-1) = -1
So, if k is odd, then (-1)^k = -1.
Therefore, for any integer k, (-1)^k is equal to 1 if k is even, and -1 if k is odd.
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For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 1000, what is the maximum possible sum of the length of x and the length of y? ?a)5b)6c)15d)16Correct answer is option 'D'. Can you explain this answer?
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For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 1000, what is the maximum possible sum of the length of x and the length of y? ?a)5b)6c)15d)16Correct answer is option 'D'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 1000, what is the maximum possible sum of the length of x and the length of y? ?a)5b)6c)15d)16Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 1000, what is the maximum possible sum of the length of x and the length of y? ?a)5b)6c)15d)16Correct answer is option 'D'. Can you explain this answer?.
For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 1000, what is the maximum possible sum of the length of x and the length of y? ?a)5b)6c)15d)16Correct answer is option 'D'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 1000, what is the maximum possible sum of the length of x and the length of y? ?a)5b)6c)15d)16Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 1000, what is the maximum possible sum of the length of x and the length of y? ?a)5b)6c)15d)16Correct answer is option 'D'. Can you explain this answer?.
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