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A perfect square is a number that becomes an integer when square rooti
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Updated on: 24 Jul 2019, 05:18
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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 Source: Nova GMAT Difficulty Level: 700
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Originally posted by Bunuel on 10 Apr 2019, 00:51.
Last edited by SajjadAhmad on 24 Jul 2019, 05:18, edited 1 time in total.
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Re: A perfect square is a number that becomes an integer when square rooti
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Updated on: 10 Apr 2019, 03:32
Bunuel wrote: 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 let assume the values in the light of ratio. A = 1 B = 2 C = 3. option C and D give us integer after square rooting the sum. plug  2, 4 , 6. D is the best answer.
Originally posted by KSBGC on 10 Apr 2019, 00:57.
Last edited by KSBGC on 10 Apr 2019, 03:32, edited 1 time in total.



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Re: A perfect square is a number that becomes an integer when square rooti
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10 Apr 2019, 01:08
Should be D. Assume a, b, and c to be 1, 2, & 3 respectively. Option C and D fit perfectly. Then assume a, b, and c to be 2, 4, & 6 Only option D makes sense. Posted from my mobile device
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Re: A perfect square is a number that becomes an integer when square rooti
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10 Apr 2019, 01:16
Let the values of A,B And C be X,2x,3x respectively...
Plug in these values to find out. Only option D turns out to be 16x^2.. which is 4^2*x^2.. which is a perfect square....
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Re: A perfect square is a number that becomes an integer when square rooti
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10 Apr 2019, 03:17
Bunuel wrote: 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 IMO D ; ratio 1:2:3 so let a,b,c be 1,2,3 test value in D we get = 16 and √ sum of 3A^2 + B^2 + C^2 = 4 IMO D



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Re: A perfect square is a number that becomes an integer when square rooti
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10 Apr 2019, 06:28
Bunuel is there any other method to solve this? Or we need to solve it just by plugging in numbers? I took over 2mins to solve it that way. Posted from my mobile device



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Re: A perfect square is a number that becomes an integer when square rooti
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10 Apr 2019, 08:55
sumi747 wrote: Bunuel is there any other method to solve this? Or we need to solve it just by plugging in numbers? I took over 2mins to solve it that way. Posted from my mobile device If you just use x,2x,3x it's really fast and can be done under a minute
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Re: A perfect square is a number that becomes an integer when square rooti
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13 Apr 2019, 18:32
Bunuel wrote: 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 We can let A = x, B = 2x and C = 3x for some integer x. Let’s analyze each answer choice. We have: A) A + B + C = x + 2x + 3x = 6x is not necessarily a perfect square. B) A^2 + B^2 + C^2 = x^2 + 4x^2 + 9x^2 = 13x^2 is not necessarily a perfect square. C) A^3 + B^3 + C^3 = x^3 + 8x^3 + 27x^3 = 36x^3 is not necessarily a perfect square. D) 3A^2 + B^2 + C^2 = 3x^2 + 4x^2 + 9x^2 = 16x^2 IS a perfect square since 16x^2 = (4x)^2. Answer: D
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Re: A perfect square is a number that becomes an integer when square rooti
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