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12 May 2020, 20:11
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D
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Difficulty:
95%
(hard)
Question Stats:
27% (02:20) correct
73%
(02:33)
wrong
based on 49
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p is a positive integer greater than 100. Is p divisible by 36?
(1) There are 8 positive integers, including 1 and p, which divide p.
(2) The highest positive integer less than or equal to 100 that divides p is 75.
(1) There are 8 positive integers, including 1 and p, which divide p.
(2) The highest positive integer less than or equal to 100 that divides p is 75.
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:
Data Sufficiency Forum
Data Sufficiency Forum
12 May 2020, 20:27
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p is a positive integer greater than 100. Is p divisible by 36?
Notice that 36 = 2^2*3^2 and has (2 + 1)(2 + 1) = 9 factors.
(1) There are 8 positive integers, including 1 and p, which divide p.
The number of factors of p (8) is less than the number of factors of 36 (9), so p cannot be divisible by 36. Sufficient.
(2) The highest positive integer less than or equal to 100 that divides p is 75.
p is divisible by 75. So, p is divisible by 25. If p were also divisible by 36 = 2^2*3^2, then it would have been divisible by 4, so the highest positive integer less than or equal to 100 that divides p would have been 25*4 = 100, not 75. Therefore, p cannot be divisible by 36. Sufficient.
Answer: D.
Notice that 36 = 2^2*3^2 and has (2 + 1)(2 + 1) = 9 factors.
(1) There are 8 positive integers, including 1 and p, which divide p.
The number of factors of p (8) is less than the number of factors of 36 (9), so p cannot be divisible by 36. Sufficient.
(2) The highest positive integer less than or equal to 100 that divides p is 75.
p is divisible by 75. So, p is divisible by 25. If p were also divisible by 36 = 2^2*3^2, then it would have been divisible by 4, so the highest positive integer less than or equal to 100 that divides p would have been 25*4 = 100, not 75. Therefore, p cannot be divisible by 36. Sufficient.
Answer: D.
12 May 2020, 20:54
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From statement 1
P in order to he divisible by 36,it should be a multiple of 36 and 36 has nine factors so p should have more than 9 factors. Hence we can say p is not divisible by 36. Sufficient
From statement 2
P is not divisible by 4 because it is not divisible by 100 therefore it is not divisible by 36. Sufficient
Hence D is the answer.
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P in order to he divisible by 36,it should be a multiple of 36 and 36 has nine factors so p should have more than 9 factors. Hence we can say p is not divisible by 36. Sufficient
From statement 2
P is not divisible by 4 because it is not divisible by 100 therefore it is not divisible by 36. Sufficient
Hence D is the answer.
Posted from my mobile device
