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.
Apr 26Get a Top GRE Score with Target Test Prep
12:00 PM EDT
-01:00 PM EDT
The Target Test Prep course represents a quantum leap forward in GRE preparation, a radical reinterpretation of the way that students should study. In fact, more and more Target Test Prep students are scoring 329 and above on the GRE.
Apr 24Get an Extra 30% Off Target Test Prep Plans
08:00 PM EDT
-11:59 PM EDT
Grab 30% off any Target Test Prep GRE plan during our Flash Sale and join Brian and many other students who have used Target Test Prep to score high on the GRE. Just enter the coupon code FLASH30 at checkout to save big.
Apr 25Crafting an Impactful Resume: Balancing Detail with Brevity
10:00 AM EDT
-10:30 AM EDT
Showcase your achievements through impactful storytelling! Get ready for an LIVE session on April 25, Learn how to craft compelling narratives on your resume that resonate with admission committees.
A perfect square is a number that becomes an integer when sq
[#permalink]
14 Apr 2019, 10:11
14 Apr 2019, 10:11
Expert Reply
2
Bookmarks
00:00
Question Stats:
52% (01:57) correct
47% (01:41) wrong based on 82 sessions
Hide Show timer Statistics
A perfect square is a number that becomes an integer when square rooting it. A, B, and C are three positive integers. The ratio of the three numbers is 1 : 2 : 3, respectively. Which one of the following expressions must be a perfect square?
(A) \(A + B + C\)
(B) \(A^2 + B^2 + C^2\)
(C) \(A^3 + B^3 + C^3\)
(D) \(3A^2 + B^2 + C^2\)
(E) \(3A^2 + 4B^2 + 4C^2\)
(A) \(A + B + C\)
(B) \(A^2 + B^2 + C^2\)
(C) \(A^3 + B^3 + C^3\)
(D) \(3A^2 + B^2 + C^2\)
(E) \(3A^2 + 4B^2 + 4C^2\)
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: A perfect square is a number that becomes an integer when sq
[#permalink]
24 Oct 2021, 07:56
24 Oct 2021, 07:56
1
raghav4202 wrote:
option C gives answer as 36 so why cant that be our answer ?
The key word here is must as in: Which one of the following expressions must be a perfect square?
You already discovered that, if A = 1, B = 2 and C = 3, then A³ + B³ + C³ = 1³ + 2³ + 3³ = 36, and 36 is a perfect square.
So, at this point, we know that A³ + B³ + C³ COULD be a perfect square
That is, we can't yet conclude that A³ + B³ + C³ MUST be a perfect square.
Notice that the values A = 2, B = 4 and C = 6 are also in the ratio 1 : 2 : 3
When we test these values, we get: A³ + B³ + C³ = 2³ + 4³ + 6³ = 288, which is NOT a perfect square.
Eliminate C.
Does that help?
General Discussion
Re: A perfect square is a number that becomes an integer when sq
[#permalink]
13 Oct 2019, 02:32
13 Oct 2019, 02:32
1
Since the numbers are in ratio 1:2:3 it would be wise to choose A=1, B=2, C=3 and replace them in the available choices.
When the result of one of those will be a perfect square, that will be the answer.
Answer D is the only one which returns a perfect square: 3*1 + 4 + 9 = 7 + 9 = 16 = 4*4
Hence, D.
When the result of one of those will be a perfect square, that will be the answer.
Answer D is the only one which returns a perfect square: 3*1 + 4 + 9 = 7 + 9 = 16 = 4*4
Hence, D.
