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18 Mar 2020, 10:15
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A
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Difficulty:
5%
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Question Stats:
85% (00:53) correct
15%
(01:12)
wrong
based on 91
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Is \(\frac{z}{12} - 9\) an integer?
(1) \(\frac{z + 24}{12}\) is an integer.
(2) z is a multiple of 6.
(1) \(\frac{z + 24}{12}\) is an integer.
(2) z is a multiple of 6.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
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minustark
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18 Mar 2020, 11:27
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Bunuel
z has to be a multiple of 12 to make z/ 12 -9 an integer.
1) z/12 + 2 is an integer. That means z is a multiple of 12. Sufficient
2) Not all multiples of 6 is also multiple of 12. Not sufficient.
A is the answer.
18 Mar 2020, 23:58
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The given expression \(\frac{z}{12}\) -9 can be an integer only if \(\frac{z}{12}\) is an integer. \(\frac{z}{12}\) is an integer only when z is divisible by 12.
From statement I alone, we have \(\frac{(z+24)}{12}\) = integer. This can be written as z+24 = 12*integer. The number on the RHS is a multiple of 12 and so is 24. Therefore, z = 12*integer – 24 which means that z is essentially a multiple of 12.
Since z is a multiple of 12, \(\frac{z}{12}\) will be an integer. Therefore, \(\frac{z}{12}\) – 9 will also be an integer. Statement I alone is sufficient to answer the question with a unique YES. Answer options B, C and E can be eliminated. The possible answer options are A or D.
From statement II alone, z is a multiple of 6. But, this does not mean that z is necessarily a multiple of 12. Therefore, \(\frac{z}{12}\) -9 is not necessarily an integer always and so we will get a YES AND a NO. Statement II alone is insufficient. Answer option D can be eliminated.
The correct answer option is A.
Hope that helps!
From statement I alone, we have \(\frac{(z+24)}{12}\) = integer. This can be written as z+24 = 12*integer. The number on the RHS is a multiple of 12 and so is 24. Therefore, z = 12*integer – 24 which means that z is essentially a multiple of 12.
Since z is a multiple of 12, \(\frac{z}{12}\) will be an integer. Therefore, \(\frac{z}{12}\) – 9 will also be an integer. Statement I alone is sufficient to answer the question with a unique YES. Answer options B, C and E can be eliminated. The possible answer options are A or D.
From statement II alone, z is a multiple of 6. But, this does not mean that z is necessarily a multiple of 12. Therefore, \(\frac{z}{12}\) -9 is not necessarily an integer always and so we will get a YES AND a NO. Statement II alone is insufficient. Answer option D can be eliminated.
The correct answer option is A.
Hope that helps!
