GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
If p and q are both positive multiples of 3, which of the following mu
[#permalink]
15 Sep 2022, 10:14
15 Sep 2022, 10:14
Expert Reply
1
Bookmarks
00:00
Question Stats:
91% (00:51) correct
8% (01:06) wrong based on 12 sessions
Hide Show timer Statistics
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
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022) - Gain 20 Kudos & Get FREE Access to GRE Prep Club TESTS
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
Re: If p and q are both positive multiples of 3, which of the following mu
[#permalink]
18 Sep 2022, 11:28
18 Sep 2022, 11:28
Expert Reply
OE
Quote:
Evalute each roman numeral:
I must be true. The sum of two multiples of 3 will always be a multiple of 3. For example, 3 + 6 = 9, and 15 + 30 = 45.
II need not be true. It’s possible, but as we saw with I, 3 + 6 = 9, which is not a multiple of 6.
III must be true. The product of two multiples of 3 will always be a multiple of 9. For example, 3(6) = 18, and 6(12) = 72.
(D) is the correct choice.
I must be true. The sum of two multiples of 3 will always be a multiple of 3. For example, 3 + 6 = 9, and 15 + 30 = 45.
II need not be true. It’s possible, but as we saw with I, 3 + 6 = 9, which is not a multiple of 6.
III must be true. The product of two multiples of 3 will always be a multiple of 9. For example, 3(6) = 18, and 6(12) = 72.
(D) is the correct choice.
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1141
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
If p and q are both positive multiples of 3, which of the following mu
[#permalink]
10 May 2023, 05:39
10 May 2023, 05:39
1
↧↧↧ Weekly Video Solution to the Problem Series ↧↧↧
Given that p and q are both positive multiples of 3. And we need to find which of the following must be true?
p is a multiple of 3
=> p = 3k (where k is an integer)
q is a multiple of 3
=> q = 3t (where t is an integer)
I. p + q is a multiple of 3
p + q = 3k + 3t = 3*(k + t) => a multiple of 3 => TRUE
II. p + q is a multiple of 6
p + q = 3k + 3t = 3*(k + t) => this will be a multiple of 6 only when k + t is even, which is NOT necessary
=> NOT ALWAYS TRUE
III. pq is a multiple of 9
p*q = 3k*3t = 9kt => a multiple of 9 => TRUE
So, Answer will be D
Hope it helps!
Watch the following video to learn the basics of Factors and Multiples
Given that p and q are both positive multiples of 3. And we need to find which of the following must be true?
p is a multiple of 3
=> p = 3k (where k is an integer)
q is a multiple of 3
=> q = 3t (where t is an integer)
I. p + q is a multiple of 3
p + q = 3k + 3t = 3*(k + t) => a multiple of 3 => TRUE
II. p + q is a multiple of 6
p + q = 3k + 3t = 3*(k + t) => this will be a multiple of 6 only when k + t is even, which is NOT necessary
=> NOT ALWAYS TRUE
III. pq is a multiple of 9
p*q = 3k*3t = 9kt => a multiple of 9 => TRUE
So, Answer will be D
Hope it helps!
Watch the following video to learn the basics of Factors and Multiples
