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21 Apr 2022, 01:30
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
53% (02:53) correct
47%
(02:30)
wrong
based on 49
sessions
History
Date
Time
Result
Not Attempted Yet
Is the product of six consecutive positive integers a multiple of 576?
(1) The smallest of the integers is a multiple of 24
(2) The fourth largest integer is an odd multiple of 9.
(1) The smallest of the integers is a multiple of 24
(2) The fourth largest integer is an odd multiple of 9.
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Updated on: 22 Apr 2022, 01:36
Originally posted by GMATWhizTeam on 21 Apr 2022, 09:01.
Last edited by GMATWhizTeam on 22 Apr 2022, 01:36, edited 1 time in total.
Last edited by GMATWhizTeam on 22 Apr 2022, 01:36, edited 1 time in total.
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Step 1: Analyse Question Stem
There are 6 consecutive integers.
We have to find out if the product of these 6 integers is a multiple of 576.
Although 576 looks a big number, understanding that it is just the square of 24 will help you break it down quickly.
Now, 24 = \(2^3\) * \(3^1\). Therefore, 576 = \({24}^2\) = \((2^3 * 3^1)^2\) = \(2^6\) * \(3^2\).
Therefore, to find if the product of the 6 integers is a multiple of 576, we have to establish if it contains \(2^6\) * \(3^2\).
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: The smallest of the integers is a multiple of 24
Since the smallest of the 6 consecutive integers is 24,
Product of the 6 consecutive integers = 24 * 25 * 26 * 27 * 28 * 29
Now, 24 = \(2^3\) * \(3^1\), 26 = 2 * 13, 27 = \(3^3\) and 28 = \(2^2\) * 7
Therefore, the product definitely consists of \(2^6\) * \(3^2\) and hence is a multiple of 576.
The data given in statement 1 alone is sufficient to answer the question with a definite YES.
Statement 1 alone is sufficient. Answer options B, C and E can be eliminated.
Statement 2: The fourth largest integer is an odd multiple of 9.
If the fourth largest integer is 9, then the product = 7 * 8 * 9 * 10 * 11* 12
This product has a \(2^6 \)in it; it will be a multiple of 576.
Is the product of 6 consecutive integers a multiple of 576? YES.
If the fourth largest integer is 27, then the product = 25 * 26 * 27 * 28 * 29 * 30
This product only has a \(2^4 \)in it; although it has a \(3^3\), it will not be a multiple of 576 since it does not have \(2^6\).
Is the product of 6 consecutive integers a multiple of 576? NO.
The data in statement 2 is insufficient to answer the question with a definite YES or NO.
Statement 2 alone is insufficient. Answer option D can be eliminated.
The correct answer option is A.
There are 6 consecutive integers.
We have to find out if the product of these 6 integers is a multiple of 576.
Although 576 looks a big number, understanding that it is just the square of 24 will help you break it down quickly.
Now, 24 = \(2^3\) * \(3^1\). Therefore, 576 = \({24}^2\) = \((2^3 * 3^1)^2\) = \(2^6\) * \(3^2\).
Therefore, to find if the product of the 6 integers is a multiple of 576, we have to establish if it contains \(2^6\) * \(3^2\).
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: The smallest of the integers is a multiple of 24
Since the smallest of the 6 consecutive integers is 24,
Product of the 6 consecutive integers = 24 * 25 * 26 * 27 * 28 * 29
Now, 24 = \(2^3\) * \(3^1\), 26 = 2 * 13, 27 = \(3^3\) and 28 = \(2^2\) * 7
Therefore, the product definitely consists of \(2^6\) * \(3^2\) and hence is a multiple of 576.
The data given in statement 1 alone is sufficient to answer the question with a definite YES.
Statement 1 alone is sufficient. Answer options B, C and E can be eliminated.
Statement 2: The fourth largest integer is an odd multiple of 9.
If the fourth largest integer is 9, then the product = 7 * 8 * 9 * 10 * 11* 12
This product has a \(2^6 \)in it; it will be a multiple of 576.
Is the product of 6 consecutive integers a multiple of 576? YES.
If the fourth largest integer is 27, then the product = 25 * 26 * 27 * 28 * 29 * 30
This product only has a \(2^4 \)in it; although it has a \(3^3\), it will not be a multiple of 576 since it does not have \(2^6\).
Is the product of 6 consecutive integers a multiple of 576? NO.
The data in statement 2 is insufficient to answer the question with a definite YES or NO.
Statement 2 alone is insufficient. Answer option D can be eliminated.
The correct answer option is A.
21 Apr 2022, 20:26
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I think that only statement 1 can solve the quiz. Regarding statement 2, shouldn't we count the fourth largest from backwards? For example, we have a set of integers {7,8,9,10,11,12}, the fourth largest integer should be 9. Let me know if I were wrong. Thx in advance.
