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27 Jan 2025, 01:30
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Difficulty:
15%
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Question Stats:
79% (00:57) correct
21%
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wrong
based on 102
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If p and q are both positive multiples of 3, which of the following must be true?
I. p + q is a multiple of 3
II. p + q is a multiple of 6
III. pq is a multiple of 9
(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III
I. p + q is a multiple of 3
II. p + q is a multiple of 6
III. pq is a multiple of 9
(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III
27 Jan 2025, 02:09
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Given: p and q are positive multiples of 3.
I. p + q is a multiple of 3.
The sum of multiples of a given number will always be a multiple of said number.
Ex: 9 + 12 = 21, which is a multiple of 3.
Must be TRUE
II. p + q is a multiple of 6
If we take the sum of two odd multiples of 3 OR two even multiples of 3, the result will be a multiple of 6.
Ex: 3 + 27 = 30, which is a multiple of 6.
6 + 30 = 36, which is a multiple of 6.
If we take the sum of an even multiple of 3 and an odd multiple of 3, the result will not be a multiple of 6.
Ex: 12 + 27 = 39, which is not a multiple of 6.
This statement may or may not be true.
III. pq is a multiple of 9
The product of two multiples of 3 will always be a multiple of 9. In order to be a multiple of 9, an integer needs at least two factors of 3, which is the case when you take the product of two multiples of 3.
Ex: 3*9 = 27, which is a multiple of 9.
Must be TRUE
IMO Option D (I and III Only)
I. p + q is a multiple of 3.
The sum of multiples of a given number will always be a multiple of said number.
Ex: 9 + 12 = 21, which is a multiple of 3.
Must be TRUE
II. p + q is a multiple of 6
If we take the sum of two odd multiples of 3 OR two even multiples of 3, the result will be a multiple of 6.
Ex: 3 + 27 = 30, which is a multiple of 6.
6 + 30 = 36, which is a multiple of 6.
If we take the sum of an even multiple of 3 and an odd multiple of 3, the result will not be a multiple of 6.
Ex: 12 + 27 = 39, which is not a multiple of 6.
This statement may or may not be true.
III. pq is a multiple of 9
The product of two multiples of 3 will always be a multiple of 9. In order to be a multiple of 9, an integer needs at least two factors of 3, which is the case when you take the product of two multiples of 3.
Ex: 3*9 = 27, which is a multiple of 9.
Must be TRUE
IMO Option D (I and III Only)
27 Jan 2025, 08:18
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But the question says p and q are positive multiples of 3 - So even Option II is correct. As even sum will always be a multiple of 2 and hence can be factorized by 2x3.
e3thekid
Given: p and q are positive multiples of 3.
I. p + q is a multiple of 3.
The sum of multiples of a given number will always be a multiple of said number.
Ex: 9 + 12 = 21, which is a multiple of 3.
Must be TRUE
II. p + q is a multiple of 6
If we take the sum of two odd multiples of 3 OR two even multiples of 3, the result will be a multiple of 6.
Ex: 3 + 27 = 30, which is a multiple of 6.
6 + 30 = 36, which is a multiple of 6.
If we take the sum of an even multiple of 3 and an odd multiple of 3, the result will not be a multiple of 6.
Ex: 12 + 27 = 39, which is not a multiple of 6.
This statement may or may not be true.
III. pq is a multiple of 9
The product of two multiples of 3 will always be a multiple of 9. In order to be a multiple of 9, an integer needs at least two factors of 3, which is the case when you take the product of two multiples of 3.
Ex: 3*9 = 27, which is a multiple of 9.
Must be TRUE
IMO Option D (I and III Only)
I. p + q is a multiple of 3.
The sum of multiples of a given number will always be a multiple of said number.
Ex: 9 + 12 = 21, which is a multiple of 3.
Must be TRUE
II. p + q is a multiple of 6
If we take the sum of two odd multiples of 3 OR two even multiples of 3, the result will be a multiple of 6.
Ex: 3 + 27 = 30, which is a multiple of 6.
6 + 30 = 36, which is a multiple of 6.
If we take the sum of an even multiple of 3 and an odd multiple of 3, the result will not be a multiple of 6.
Ex: 12 + 27 = 39, which is not a multiple of 6.
This statement may or may not be true.
III. pq is a multiple of 9
The product of two multiples of 3 will always be a multiple of 9. In order to be a multiple of 9, an integer needs at least two factors of 3, which is the case when you take the product of two multiples of 3.
Ex: 3*9 = 27, which is a multiple of 9.
Must be TRUE
IMO Option D (I and III Only)
