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Math Revolution GMAT Instructor
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When a, b and c are consecutive positive even integers such that a>b>c
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21 Jun 2018, 01:45
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[GMAT math practice question] When \(a, b\) and \(c\) are consecutive positive even integers such that \(a>b>c\), which of the following must be an odd integer? \(A. \frac{(ac)}{2}\) \(B. \frac{(ca)}{2}\) \(C. \frac{(a+c)}{2}\) \(D. \frac{(a+c)}{4}\) \(E. \frac{(ac)}{4}\)
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Re: When a, b and c are consecutive positive even integers such that a>b>c
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21 Jun 2018, 02:49
MathRevolution wrote: [GMAT math practice question]
When \(a, b\) and \(c\) are consecutive positive even integers such that \(a>b>c\), which of the following must be an odd integer?
\(A. \frac{(ac)}{2}\) \(B. \frac{(ca)}{2}\) \(C. \frac{(a+c)}{2}\) \(D. \frac{(a+c)}{4}\) \(E. \frac{(ac)}{4}\) Two operations.. 1) ca.. Since they are consecutive positive even integers, and a>b>c, ca or ac will be 4 So it will always leave an EVEN integer when divided by 2.. So eliminate A and B But what about div by 4, (ac)/4=4/4=1, so ODD..C is the answer But let's see the addition 2) a+c It is nothing but 2b.. 2b will be even when div by 2 or 4 when B is multiple of 4, so eliminate C and D Example.. a>b>c => 10>8>6, so 2*8/4=4, even number Ans C
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When a, b and c are consecutive positive even integers such that a>b>c
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21 Jun 2018, 03:27
MathRevolution wrote: [GMAT math practice question]
When \(a, b\) and \(c\) are consecutive positive even integers such that \(a>b>c\), which of the following must be an odd integer?
\(A. \frac{(ac)}{2}\) \(B. \frac{(ca)}{2}\) \(C. \frac{(a+c)}{2}\) \(D. \frac{(a+c)}{4}\) \(E. \frac{(ac)}{4}\) Test a=6, b=4 and c=2 in the five answer choices. Eliminate any answer choice that does not yield an odd integer. A: \(\frac{ac}{2} = \frac{62}{2} = 2\) > Eliminate A. B: \(\frac{ac}{2} = \frac{26}{2} = 2\) > Eliminate B. C: \(\frac{a+c}{2} = \frac{6+2}{2} = 4\) > Eliminate C. D: \(\frac{a+c}{4} = \frac{6+2}{4} = 2\) > Eliminate D.
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Re: When a, b and c are consecutive positive even integers such that a>b>c
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21 Jun 2018, 06:05
MathRevolution wrote: [GMAT math practice question]
When \(a, b\) and \(c\) are consecutive positive even integers such that \(a>b>c\), which of the following must be an odd integer?
\(A. \frac{(ac)}{2}\) \(B. \frac{(ca)}{2}\) \(C. \frac{(a+c)}{2}\) \(D. \frac{(a+c)}{4}\) \(E. \frac{(ac)}{4}\) If a, b and c are consecutive EVEN integers, and a>b>c, then we we know that b is 2 greater than c, and a is 2 greater than bSo, we can write: b = c + 2a = c + 4 Now let's check the answer choices from E to A ASIDE This is one of those questions that require us to check/test each answer choice. In these situations, always check the answer choices from E to A, because the correct answer is typically closer to the bottom than to the top. For more on this strategy, see my article: http://www.gmatprepnow.com/articles/han ... questions  E) (a  c)/4 = [( c + 4 )  (c)]/4 = 4/4 = 1 (ODD!) Answer: E Cheers, Brent
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Re: When a, b and c are consecutive positive even integers such that a>b>c
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21 Jun 2018, 06:39
Solution Given:• a,b and c are consecutive positive even integers and a>b>c. To find:• Among the given options which one is an odd integer. Approach and Working: • Since, a,b and c are consecutive positive integer and a>b>c, a = c+4, b=c+2. Now, let us check every option. A. \(\frac{(a−c)}{2}= \frac{(c+4  c)}{2}= 2\) B. \(\frac{(c−a)}{2}= \frac{(ac)}{2}= 2\) C. \(\frac{(a+c)}{2}= \frac{2c+4}{2}= c+2= b\) D. \(\frac{(a+c)}{4}= \frac{2c+4}{4}= \frac{c}{2+1}\) • If c= 2 then \(\frac{c}{2}+1= 2\) and if c= any other number than 2 then \(\frac{c}{2}+1\)= odd • Hence, we can say if \(\frac{c}{2}+1\) is odd or not. E. \(\frac{(ac)}{4}= \frac{4}{4}= 1\) Hence, the correct answer is option E. Answer: E
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Re: When a, b and c are consecutive positive even integers such that a>b>c
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24 Jun 2018, 17:56
MathRevolution wrote: [GMAT math practice question]
When \(a, b\) and \(c\) are consecutive positive even integers such that \(a>b>c\), which of the following must be an odd integer?
\(A. \frac{(ac)}{2}\) \(B. \frac{(ca)}{2}\) \(C. \frac{(a+c)}{2}\) \(D. \frac{(a+c)}{4}\) \(E. \frac{(ac)}{4}\) We can let c = x, so b = x + 2 and a = x + 4. We see that (a  c)/4 = [(x + 4)  x]/4 = 4/4 = 1, which is an odd integer. Answer: E
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Re: When a, b and c are consecutive positive even integers such that a>b>c
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24 Jun 2018, 19:17
=> Write \(a = 2n + 2, b = 2n\) and \(c = 2n – 2\). We check each of the alternatives. \(A. \frac{( a – c )}{2} = \frac{( 2n + 2 – ( 2n – 2 ) )}{2} = \frac{4}{2} = 2.\) \(B. \frac{( c – a )}{2} = \frac{( 2n – 2 – ( 2n + 2 ) )}{2} = \frac{4}{2} = 2.\) \(C. \frac{( a + c )}{2} = \frac{( 2n + 2 + 2n – 2 )}{2} = \frac{4n}{2} = 2n.\) \(D. \frac{( a + c )}{4} = \frac{( 2n + 2 + 2n – 2 )}{4} = \frac{4n}{4} = n.\) \(E. \frac{( a – c )}{4} = \frac{( 2n + 2 – ( 2n – 2 ) )}{4}= \frac{4}{4} = 1\) Only option E is guaranteed to be odd. Therefore, the answer is E. Answer : E
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Re: When a, b and c are consecutive positive even integers such that a>b>c
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