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.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If x and y are positive integers, and x³ 10x²y 24xy² = 0, which of
[#permalink]
14 Jul 2022, 07:33
14 Jul 2022, 07:33
1
1
00:00
Question Stats:
16% (03:39) correct
83% (02:37) wrong based on 6 sessions
Hide Show timer Statistics
If x and y are positive integers, and x³ – 10x²y – 24xy² = 0, which of the following could be true?
I. x = 0
II. x - 12y = 0
III. x + 2y = 0
A) I only
B) II only
C) I and III only
D) II and III only
E) I, II and III
I. x = 0
II. x - 12y = 0
III. x + 2y = 0
A) I only
B) II only
C) I and III only
D) II and III only
E) I, II and III
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If x and y are positive integers, and x³ 10x²y 24xy² = 0, which of
[#permalink]
15 Jul 2022, 13:34
15 Jul 2022, 13:34
2
Bookmarks
GreenlightTestPrep wrote:
If x and y are positive integers, and x³ – 10x²y – 24xy² = 0, which of the following could be true?
I. x = 0
II. x - 12y = 0
III. x + 2y = 0
A) I only
B) II only
C) I and III only
D) II and III only
E) I, II and III
I. x = 0
II. x - 12y = 0
III. x + 2y = 0
A) I only
B) II only
C) I and III only
D) II and III only
E) I, II and III
Key property: If ABC = 0, then A = 0, B = 0, or C = 0
Given: x³ – 10x²y – 24xy² = 0
First factor out the x on the left side to get: x(x² – 10xy – 24y²) = 0
Now factor the quadratic: x(x - 12y)(x + 2y) = 0
From the property above, we know that x = 0, x - 12y = 0 or x + 2y = 0
However, before we select answer choice E, we must remember that we're told that x and y are positive integers
If x is positive, x can't equal 0, since 0 is neither positive nor negative. So, statement I can't be true.
Similarly, if x and y are positive, then x is positive and 2y is positive, which means the sum x + 2y must positive, which means x + 2y CANNOT equal 0. So, statement III can't be true.
Since statement II is the only statement that can be true, the correct answer is B
gmatclubot
Re: If x and y are positive integers, and x³ 10x²y 24xy² = 0, which of [#permalink]
15 Jul 2022, 13:34
Moderators:
