For any integer z, the function PODD(z) is defined as the product of all odd integers between z and z, inclusive. Which of the following numbers will not divide PODD (-15) completely?I. 38II. 55III. 73a)I onlyb)II onlyc)III onlyd)I and II onlye)II and III onlyCorrect answer is option 'E'. Can you explain this answer?

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For any integer z, the function PODD(z) is defined as the product of all odd integers between –z and z, inclusive. Which of the following numbers will not divide PODD (-15) completely?

I. 3⁸

II. 5⁵

III. 7³

a)
I only
b)
II only
c)
III only
d)
I and II only
e)
II and III only

Correct answer is option 'E'. Can you explain this answer?

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For any integer z, the function PODD(z) is defined as the product of a...

Given:

To find: PODD(-15) will not be divisible by which of the given 3 options?

Approach:

The given 3 options involve powers of 3, 5 and 7. So, to answer the question, we’ll find the powers of 3, 5 and 7 in the prime-factorized expression of PODD(-15)
The answer for an option will be YES (meaning that option will not divide PODD(-15) completely) if the power of the prime factor in that option is greater than the power of that prime factor in the prime-factorized expression for PODD(-15)

(For example, 2⁵ will not divide a number of the form 2⁴*3)

Working Out:

Finding the power of 3 in PODD(-15) and evaluating Option I

Look again at the expression for PODD(-15):
- PODD(-15) = (-1)⁸(1*3*5*7*9*11*13*15)²
- Note that each of the above multiples of 3 occurs twice in PODD(-15)
So, power of 3 in PODD(-15) = (1+2+1)*2= 4*2 = 8
Since the power of 3 in Option I is equal to the power of 3 in PODD(-15), 3⁸ will divide PODD(-15) completely.

Finding the power of 5 in PODD(-15) and evaluating Option II

- Since the multiples of 5 and 15 occurs twice in PODD(-15), power of 5 in PODD(-15) = (1+1)*2 = 4
- Since the power of 5 in Option II is greater than the power of 5 in PODD(-15), 5⁵ will not divide PODD(-15) completely.
Finding the power of 7 in PODD(-15) and evaluating Option III
- The only multiple of 7 in PODD(-15) is 7 itself.
- Since 7 occurs twice in PODD(-15), the power of 7 in PODD(-15) = 1*2 = 2
- Since the power of 7 in Option III is greater than the power of 5 in PODD(-15), 7³ will not divide PODD(-15) completely.
Thus we see that only Options II and III will not divide PODD(-15) completely.

Looking at the answer choices, we see that the correct answer is Option E

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For any integer z, the function PODD(z) is defined as the product of all odd integers between –z and z, inclusive. Which of the following numbers will not divide PODD (-15) completely?I. 38II. 55III. 73a)I onlyb)II onlyc)III onlyd)I and II onlye)II and III onlyCorrect answer is option 'E'. Can you explain this answer?

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For any integer z, the function PODD(z) is defined as the product of all odd integers between –z and z, inclusive. Which of the following numbers will not divide PODD (-15) completely?I. 38II. 55III. 73a)I onlyb)II onlyc)III onlyd)I and II onlye)II and III onlyCorrect answer is option 'E'. 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 z, the function PODD(z) is defined as the product of all odd integers between –z and z, inclusive. Which of the following numbers will not divide PODD (-15) completely?I. 38II. 55III. 73a)I onlyb)II onlyc)III onlyd)I and II onlye)II and III onlyCorrect answer is option 'E'. 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 z, the function PODD(z) is defined as the product of all odd integers between –z and z, inclusive. Which of the following numbers will not divide PODD (-15) completely?I. 38II. 55III. 73a)I onlyb)II onlyc)III onlyd)I and II onlye)II and III onlyCorrect answer is option 'E'. Can you explain this answer?.

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