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21 Jun 2023, 01:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
76% (01:19) correct
24%
(01:11)
wrong
based on 33
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If y is a positive integer is y divisible by 21?
(1) y^2 is divisible by 21.
(2) y^3 is divisible by 63.
(1) y^2 is divisible by 21.
(2) y^3 is divisible by 63.
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
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21 Jun 2023, 03:31
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(1) Only
If y*y is divisible by 21 = 3*7
Each y has to contribute at least one 3 and at least one 7.
So y is divisible by 3*7=21
Sufficient. The answer is Yes.
(2) Only
If y*y*y is divisible by 63 = 3 * 3 * 7
Each y has to contribute at least one 3 and at least one 7.
So y is divisible by 3*7=21
Sufficient. The answer is Yes.
Choose (D).
If y*y is divisible by 21 = 3*7
Each y has to contribute at least one 3 and at least one 7.
So y is divisible by 3*7=21
Sufficient. The answer is Yes.
(2) Only
If y*y*y is divisible by 63 = 3 * 3 * 7
Each y has to contribute at least one 3 and at least one 7.
So y is divisible by 3*7=21
Sufficient. The answer is Yes.
Choose (D).
21 Jun 2023, 04:32
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Let's analyze each statement:
Statement (1): y^2 is divisible by 21.
To determine whether y is divisible by 21, we need to consider the prime factorization of 21, which is 3 * 7. If y^2 is divisible by 21, it means y^2 must have at least one factor of 3 and one factor of 7.
Since y is a positive integer, if y^2 has factors of 3 and 7, it implies that y itself must have factors of 3 and 7 as well. Therefore, statement (1)sufficient.
Statement (2): y^3 is divisible by 63.
To determine whether y is divisible by 21, we need to consider the prime factorization of 63, which is 3 * 3 * 7. If y^3 is divisible by 63, it means y^3 must have at least two factors of 3 and one factor of 7.
Similar to statement (1), since y is a positive integer, if y^3 has the required factors of 3 and 7, it implies that y itself must have factors of 3 and 7 as well. Therefore, statement (2) is also sufficient.
Option D is the answer.
Statement (1): y^2 is divisible by 21.
To determine whether y is divisible by 21, we need to consider the prime factorization of 21, which is 3 * 7. If y^2 is divisible by 21, it means y^2 must have at least one factor of 3 and one factor of 7.
Since y is a positive integer, if y^2 has factors of 3 and 7, it implies that y itself must have factors of 3 and 7 as well. Therefore, statement (1)sufficient.
Statement (2): y^3 is divisible by 63.
To determine whether y is divisible by 21, we need to consider the prime factorization of 63, which is 3 * 3 * 7. If y^3 is divisible by 63, it means y^3 must have at least two factors of 3 and one factor of 7.
Similar to statement (1), since y is a positive integer, if y^3 has the required factors of 3 and 7, it implies that y itself must have factors of 3 and 7 as well. Therefore, statement (2) is also sufficient.
Option D is the answer.
