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17 Jul 2022, 06:15
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B
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:
48% (02:09) correct
52%
(02:20)
wrong
based on 63
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If y is a positive integer, is \(\frac{(y^3 + 5)^2}{4}\) an integer ?
(1) The square root of y has three prime factors.
(2) Each prime factor of y^3 is greater than 5.
Are You Up For the Challenge: 700 Level Questions
(1) The square root of y has three prime factors.
(2) Each prime factor of y^3 is greater than 5.
Are You Up For the Challenge: 700 Level Questions
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
17 Jul 2022, 06:39
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#1
The square root of y has three prime factors.
this means that square root value of y is a perfect square of a prime number
y= 16, 81, 625
we get no at 16,81 and yes at 625
insufficient
#2
Each prime factor of y^3 is greater than 5.
y=7,11,13,17... so on
we get yes for all values
sufficient
option B
The square root of y has three prime factors.
this means that square root value of y is a perfect square of a prime number
y= 16, 81, 625
we get no at 16,81 and yes at 625
insufficient
#2
Each prime factor of y^3 is greater than 5.
y=7,11,13,17... so on
we get yes for all values
sufficient
option B
Bunuel
17 Jul 2022, 07:58
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If y is a positive integer, is \(\frac{(y^3 + 5)^2}{4}\) an integer ?
i.e. \((y^3 + 5)^2\) must be a multiple of 4.
i.e. \(y^6 + 5^2 + 10y^3\)
i.e. \(y^6 + 10y^3 + 1 + 24\)
i.e. \(y^6 + 10y^3 + 1\) must be a multiple of 4
For
y = 1, YES
y = 2, NO
y = 3, YES
y = 4, NO
Certainly some pattern is there i.e. y must be odd but which number is the big question.
(1) The square root of y has three prime factors.
Example:
Y has \(2^2, 3^2, 5^2\) as factors then NO
Y has \(3^2, 5^2, 7^2\) as factors then YES(if not sure then calculated guess by taking a cue from above)
INSUFFICIENT.
(2) Each prime factor of y^3 is greater than 5.
Since 2 is not prime factor of Y, it is not a multiple of 4 i.e. odd. Hence YES.
SUFFICIENT.
Answer B.
i.e. \((y^3 + 5)^2\) must be a multiple of 4.
i.e. \(y^6 + 5^2 + 10y^3\)
i.e. \(y^6 + 10y^3 + 1 + 24\)
i.e. \(y^6 + 10y^3 + 1\) must be a multiple of 4
For
y = 1, YES
y = 2, NO
y = 3, YES
y = 4, NO
Certainly some pattern is there i.e. y must be odd but which number is the big question.
(1) The square root of y has three prime factors.
Example:
Y has \(2^2, 3^2, 5^2\) as factors then NO
Y has \(3^2, 5^2, 7^2\) as factors then YES(if not sure then calculated guess by taking a cue from above)
INSUFFICIENT.
(2) Each prime factor of y^3 is greater than 5.
Since 2 is not prime factor of Y, it is not a multiple of 4 i.e. odd. Hence YES.
SUFFICIENT.
Answer B.
