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If a, b, c and d are four consecutive integers, and a^b = c^d
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Updated on: 10 Oct 2019, 15:51
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If \(a\), \(b\), \(c\) and \(d\) are four consecutive integers (not necessarily in that order), and \(a^b = c^d\), what is the least possible value of \(a+b+c+d\) ? A) 8 B) 6 C) 2 D) 6 E) 12
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Originally posted by GMATPrepNow on 01 Oct 2019, 08:28.
Last edited by GMATPrepNow on 10 Oct 2019, 15:51, edited 1 time in total.



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Re: If a, b, c and d are four consecutive integers, and a^b = c^d
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01 Oct 2019, 08:34
2^0=1^3 So, 0+1+2+3=6 Option D Posted from my mobile device
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Re: If a, b, c and d are four consecutive integers, and a^b = c^d
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Updated on: 01 Oct 2019, 15:12
integers can be x, x+1 , x+2 & x+3 sum of integers ; 4x+6 ; 4(x+1)+2 answer can be multiple of 4 ; IMO A ; 8 GMATPrepNow wrote: If \(a\), \(b\), \(c\) and \(d\) are four consecutive integers (not necessarily in that order), and \(a^b = c^d\), what is the least possible value of \(a+b+c+d\) ?
A) 8 B) 6 C) 2 D) 6 E) 12
Originally posted by Archit3110 on 01 Oct 2019, 08:51.
Last edited by Archit3110 on 01 Oct 2019, 15:12, edited 1 time in total.



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Re: If a, b, c and d are four consecutive integers, and a^b = c^d
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01 Oct 2019, 10:11
Hint: The correct answer is not D
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Re: If a, b, c and d are four consecutive integers, and a^b = c^d
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01 Oct 2019, 10:16
Is the correct answer B
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Re: If a, b, c and d are four consecutive integers, and a^b = c^d
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01 Oct 2019, 10:37
a=1 b=0 c=1 d=2
a^b=1^0=1
c^d= 1^2= 1
thus 2+1+0+1 = 2
AnsC
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Re: If a, b, c and d are four consecutive integers, and a^b = c^d
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01 Oct 2019, 11:08
GMATPrepNow wrote: If \(a\), \(b\), \(c\) and \(d\) are four consecutive integers (not necessarily in that order), and \(a^b = c^d\), what is the least possible value of \(a+b+c+d\) ?
A) 8 B) 6 C) 2 D) 6 E) 12 This question takes some playing around with numbers. It also helps to recognize the following properties: \(1^k = 1\) for all values of k
\((1)^k = 1\) for all EVEN integer values of k
\(k^0 = 1\) for all nonzero values of k
If \(a = 1\), \(b = 2\), \(c=3\) and \(d = 0\), then the equation \(a^b = c^d\) becomes \((1)^{2} = (3)^0\) Simplify to get: \(1= 1\)....PERFECT! In this case, \(a+b+c+d=(1)+(2)+(3)+0=6\) So, it's possible to get a sum of 6 (answer choice B). HOWEVER, perhaps it's possible to get a sum of 8 (answer choice A) Well, it turns out that we CAN'T get a sum of 8. Here's why: We know that the 4 numbers are CONSECUTIVE INTEGERS. So, if we let x = the smallest integer, then x+1 = the next integer x+2 = the next integer And x+3 = the next integer So, the sum of these 4 consecutive integers = x + (x+1) + (x+2) + (x+3) = 4x + 6 = 4x + 4 + 2 = 4(x+1) + 2 Notice that 4(x+1) is a multiple of 4So, 4(x+1) + 2 is 2 greater than some multiple of 4Since the sum of the four integers must be 2 greater than some multiple of 4, we can eliminate answer choice A, since 8 is a multiple of 4 Answer: B Cheers, Brent
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Re: If a, b, c and d are four consecutive integers, and a^b = c^d
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10 Oct 2019, 10:50
Can someone please post the correct method of solving this question.



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Re: If a, b, c and d are four consecutive integers, and a^b = c^d
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10 Oct 2019, 15:39
sp4182 wrote: Can someone please post the correct method of solving this question. I know the above solutions aren't exactly algorithmic (like many/most GMAT quant questions), but there are still plenty of official questions that require testtakers to find values that meet a certain set of conditions.
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Re: If a, b, c and d are four consecutive integers, and a^b = c^d
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10 Oct 2019, 15:49
Dear Brent GMATPrepNow, If answer is B, why do you mark E under the spoiler? I think there is mistake.



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Re: If a, b, c and d are four consecutive integers, and a^b = c^d
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10 Oct 2019, 15:52
Mo2men wrote: Dear Brent GMATPrepNow, If answer is B, why do you mark E under the spoiler? I think there is mistake. Thanks for pointing that out!! The correct answer is, indeed, B. I changed the OA. Kudos for you!!! Cheers, Brent
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Re: If a, b, c and d are four consecutive integers, and a^b = c^d
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