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If q, r, and s are consecutive even integers and q < r < s, which of t [#permalink]
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21 Oct 2014, 09:21
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58% (01:59) correct 42% (01:45) wrong based on 218 sessions
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Re: If q, r, and s are consecutive even integers and q < r < s, which of t [#permalink]
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21 Oct 2014, 19:00
s > r > q are consecutive even integers Testing for \(s^2  r^2  q^2\) I: For s = 0, r = 2, q = 4,\(s^2  r^2  q^2 = 20\) II: For s = 2, r = 0, q = 2\(s^2  r^2  q^2 = 0\) III: For s = 4, r = 2, q = 0\(s^2  r^2  q^2 = 12\) Step II & Step III have consecutive representation of values of s, r, q. No other combination is possible. 8 cannot be the answer as for value of s = 6 & above, the resultant would be greater than 12 Answer = C
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Re: If q, r, and s are consecutive even integers and q < r < s, which of t [#permalink]
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30 Dec 2014, 12:03
This is fine, but is there an approach that is not based on trial and error? Because, on first site, I don't see why 8 would be the value.. And I guess there should be, otherwise there is not much point in this question. Anyone can plug in numbers and test them.. Am I missing anything?



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Re: If q, r, and s are consecutive even integers and q < r < s, which of t [#permalink]
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31 Dec 2014, 03:45
If we changed the all 3 variables to one variable ( for example r ) we see that : s= r+2 and q= r2 . so we should replace these equations in the main equation and we get this equation: s^2  r^2 q^2= (r+2)^2  R^2 (r2)^2 = 8rr^2 so If we replaced any even integer in this new equation we see that ONLY 8 can not obtain. If we replace 10 we get 8 (10)  (10)^2 = 20 so option A is ruled out If we replace 4 we get 32 16 = 16 etc So the only 8 can not the answer so option c.....



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If q, r, and s are consecutive even integers and q < r < s, which of t [#permalink]
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31 Dec 2014, 14:25
my approach was: take s=r2 and q=r+2 =>s^2r^2q^2=(r2)^2r^2(r+2)^2 by solving we will have r(r+8) when r =2, value is 20 when r= 2, value is 12 when r= 0, value is 0 when r=4, value is 16 so remaining option is C:8
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Re: If q, r, and s are consecutive even integers and q < r < s, which of t [#permalink]
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08 Aug 2015, 02:29
Let the possible outcome of the equation be c.
Assuming the three numbers to be (r2), r & (r+2), and substituting in the equation we get the equation as
8rr^2 = c
Now multiplying by 1 we get
r^28r=(c)
which becomes
r^28r+c=0
The determinant of this quadratic equation is thus:
644*c
now we compute the determinant for each of the options. The value of c which does not give a perfect square as the determinant will make the roots irrational and hence is not a valid answer: a. c=20 gives D=144 > Rational roots b. c=0 gives D=64 > Rational roots c. c=8 gives D=32 > Irrational roots d. c=12 gives D=16 > Rational roots e. c=16 gives D=0 > Rational roots
Hence 8 cannot be the value of the expression.
Answer is C.



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Re: If q, r, and s are consecutive even integers and q < r < s, which of t [#permalink]
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19 Aug 2016, 23:17
a more simple method would be using the quadratic equation.Since the numbers are consecutive
s=n+2 q=n r=n2
after substituting the values we get
n^2 +4+4nn^2n^24n+4n which will be 8nn^2
equate the values to this equation to get value of n.



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If q, r, and s are consecutive even integers and q < r < s, which of t [#permalink]
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01 Nov 2016, 06:03
Let’s denote consecutive even integers as follows: 2x, 2x+2, 2x+4 As to the question we have following:
\((2x+4)^2(2x+2)^2(2x)^2\) by simplifying this expression we’ll get: \(4x^2+8x+12\)
Now we need to put above polynomial into correspondence to our question choices and find out if resultant expression has integer solutions or, read it other way, can it be factorized or not.
a) \(4x^2+8x+12=20\) \(4x^2+8x+32=0\) \(4(x4)(x+2)=0\) Yes.
b) \(4x^2+8x+12=0\) \(4(x3)(x+1)=0\) Yes.
c) \(4x^2+8x+12=8\) \(4(x22x1)=0\) This polynomial does not have integer roots.
d) \(4x^2+8x+12=12\) \(4x(x+2)=0\) Yes.
e) \(4x^2+8x+12=16\) \(4(x1)^2=0\) Yes.
Answer C.



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Re: If q, r, and s are consecutive even integers and q < r < s, which of t [#permalink]
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08 Apr 2018, 11:12
Hi All, We're told that Q, R and S are consecutive EVEN integers, so we're restricted there (notice that the prompt does NOT say anything about the 3 values being positive though). While this question might look a bit complex, you can "brute force" this question quickly by following the instructions and TESTing values. Using these values, here are the results (note that we're looking for what CANNOT be the value): 0, 2, 4 = 16  4  0 = 12 Eliminate D 2, 4, 6 = 36  16  4 = 16 Eliminate E 2, 0, 2 = 4  0  4 = 0 Eliminate B 4, 2, 0 = 0  4  16 = 20 Eliminate A Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: If q, r, and s are consecutive even integers and q < r < s, which of t
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