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The exponent of a^x is a multiple of 20, what is the minimum p
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06 Jun 2018, 16:49
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The exponent of \(a^{x}\) is a multiple of 20, what is the minimum possible value of (a + x), if a is a factor of x? ( a & x are positive integers) A. 10 B. 15 C. 20 D. 40 E. 50
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The exponent of a^x is a multiple of 20, what is the minimum p
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06 Jun 2018, 17:22
Quote: The exponent of axax is a multiple of 20, what is the minimum possible value of (a + x), if a is a factor of x? (a & x are positive integers)
A. 10
B. 15
C. 20
D. 40
E. 50 it is not an easy question : let me try : a ^x is a factor of 20 a^x = 2^2 . 5 .y where y is an integer a is a factor of x so x=a.k where k is an integer a^a.k = 2^2 . 5 y now a cannot be <10 because we have 2s and a 5 in the right side a should at least be 10 10^10*1 =10^10 is the least possible value for a^x (a=10 , x=10 ) so the least possible value for (x+a) is 20 Answer : C I would say that the level of this question is >700 What do you think ?



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The exponent of a^x is a multiple of 20, what is the minimum p
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07 Jun 2018, 19:27
GMATSkilled wrote: The exponent of \(a^{x}\) is a multiple of 20, what is the minimum possible value of (a + x), if a is a factor of x? (a & x are positive integers)
A. 10
B. 15
C. 20
D. 40
E. 50 foryearss, I wonder about this part: You wrote Quote: x=10 The prompt says: The exponent of \(a^{x}\) is a multiple of 20\(x\) must be a positive integer. The first positive multiple of 20 is 20. How can \(x=10\)?
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Re: The exponent of a^x is a multiple of 20, what is the minimum p
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07 Jun 2018, 19:54
Quote: The prompt says: The exponent of axax is a multiple of 20
xx must be a positive integer. The first positive multiple of 20 is 20.
How can x=10x=10? the whole exponent is a multiple of 20 , not x and i put a^x = 20 . y (20 is a factor of a^x ) (and y is what ever the rest of a^x could be ) a^x = 2^2 . 5 . y now i want to start trying values for a can a be 2 for example ? no why ? because 2^(what ever ) will produce a number that only has 2s as factors . I want to produce a number that has both 2s and at least one 5 as factors . can a be 3 ? no for the same reason , also a cannot be 4,5,6,7,8,9 now we reach 10 . a can be 10 , yes we can produce a number that has both 2s and 5 when raised to a power . but what power of 10 ? we are interested in the least possible value . if a=10 and x=a.k ( a is a factor of x ) then x is at least 10 so a^x =10^10 and that is a multiple of 20



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Re: The exponent of a^x is a multiple of 20, what is the minimum p
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07 Jun 2018, 20:10
GMATSkilled wrote: The exponent of \(a^{x}\) is a multiple of 20, what is the minimum possible value of (a + x), if a is a factor of x? (a & x are positive integers)
A. 10
B. 15
C. 20
D. 40
E. 50 exponent clearly means the power.. if it meant \(a^x\), you did not require to mention exponent, it would have been simply a^x is a multiple of 20.. so if i take x as 20, the lowest factor of 20 will be 1.. so \(a^x=1^{20}\), +x=1+20=21..
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The exponent of a^x is a multiple of 20, what is the minimum p
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07 Jun 2018, 20:22
Quote: exponent clearly means the power.. if it meant axax, you did not require to mention exponent, it would have been simply a^x is a multiple of 20..
so if i take x as 20, the lowest factor of 20 will be 1.. so ax=120ax=120, +x=1+20=21.. Oh , i have misunderstood the question ... but why not saying x is a multiple of 20 ..



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The exponent of a^x is a multiple of 20, what is the minimum p
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07 Jun 2018, 20:43
chetan2u wrote: GMATSkilled wrote: Theexponent of \(a^{x}\) is a multiple of 20, what is the minimum possible value of (a + x), if a is a factor of x? (a & x are positive integers)
A. 10
B. 15
C. 20
D. 40
E. 50 exponent clearly means the power.. if it meant \(a^x\), you did not require to mention exponent, it would have been simply a^x is a multiple of 20.. so if i take x as 20, the lowest factor of 20 will be 1.. so \(a^x=1^{20}\), +x=1+20=21.. ... which is the answer I got. Thanks, chetan2uforyearss  at least you gave it a shot. Quote: but why not saying x is a multiple of 20 .. Maybe I misunderstand your statement, but . . . the prompt DOES say that \(x\), which = the exponent of \(a^{x}\), is a multiple of 20
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Re: The exponent of a^x is a multiple of 20, what is the minimum p
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07 Jun 2018, 21:00
Quote: he prompt DOES say that xx, which = the exponent of axax, is a multiple of 20 i meant why not saying : x is a multiple of 20 instead of : the exponent of a^x is a multiple of 20 Anyway , so now what is the answer ? 21 is not an option



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Re: The exponent of a^x is a multiple of 20, what is the minimum p
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07 Jun 2018, 21:17
foryearss wrote: Quote: he prompt DOES say that xx, which = the exponent of axax, is a multiple of 20 i meant why not saying : x is a multiple of 20 instead of : the exponent of a^x is a multiple of 20 Anyway , so now what is the answer ? 21 is not an option The question is flawed or the answers are wrong. You ask why the question does NOT say "x is a multiple of 20" instead of "the exponent of a^x is a multiple of 20." I did not write the question. I have no idea why the author wrote the question as s/he did. GMATSkilled  what is the OE?
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The exponent of a^x is a multiple of 20, what is the minimum p
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08 Jun 2018, 01:02
\(10^{10}\) making it 10 + 10 = 20. Therefore option C is the correct answer.
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Re: The exponent of a^x is a multiple of 20, what is the minimum p
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30 Oct 2018, 05:57
CAMANISHPARMAR wrote: \(10^{10}\) making it 10 + 10 = 20. Therefore option C is the correct answer. How is it possible ?? As question stem just said that Exponent which is "x" is a multiple of 20. 10 is not a multiple of 20. Please explain.



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Re: The exponent of a^x is a multiple of 20, what is the minimum p
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30 Oct 2018, 06:15
Given: i) a^x is multiple of 20: Means unit digit must be Zero. ii) a is a factor of x means a< x or a= x, a cant be greater than x iii) both a and x is positive integer.
we need to find minimum value of (a+x). look at the options with above results: A: 10 no value of a and x can result to unit digit zero. ( multiple of 20) eliminate B: 15 only 10^5 (a^x) can give unit digit zero but , condition 2 didn’t match a has to be less than or equal to x. Eliminate C: 20 10^10 (a^x) can give unit digit zero as well as a is equal to x. Correct answer. We don’t need to look at other options as question is asking about minimum value of ( a+x)
Correct answer C.



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Re: The exponent of a^x is a multiple of 20, what is the minimum p
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30 Oct 2018, 06:17
garvitbh11 wrote: CAMANISHPARMAR wrote: \(10^{10}\) making it 10 + 10 = 20. Therefore option C is the correct answer. How is it possible ?? As question stem just said that Exponent which is "x" is a multiple of 20. 10 is not a multiple of 20. Please explain. you misread the question, given a^x is multiple of 20.



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Re: The exponent of a^x is a multiple of 20, what is the minimum p
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30 Oct 2018, 08:05
vishalkazone wrote: garvitbh11 wrote: CAMANISHPARMAR wrote: \(10^{10}\) making it 10 + 10 = 20. Therefore option C is the correct answer. How is it possible ?? As question stem just said that Exponent which is "x" is a multiple of 20. 10 is not a multiple of 20. Please explain. you misread the question, given a^x is multiple of 20. Yes! I agree vishalkazone explanation. garvitbh11  I hope your doubt is cleared by @ vishalkazone 's explanation. Please feel free to revert in case if you need further clarifications.
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The exponent of a^x is a multiple of 20, what is the minimum p
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30 Oct 2018, 12:44
GMATSkilled wrote: The exponent of \(a^{x}\) (=a^x) is a multiple of 20, what is the minimum possible value of (a + x), if a is a factor of x? (a & x are positive integers) vishalkazone wrote: Given: i) a^x is multiple of 20: Means unit digit must be Zero. ii) a is a factor of x means a< x or a= x, a cant be greater than x iii) both a and x is positive integer.
we need to find minimum value of (a+x). look at the options with above results: A: 10 no value of a and x can result to unit digit zero. ( multiple of 20) eliminate B: 15 only 10^5 (a^x) can give unit digit zero but , condition 2 didn’t match a has to be less than or equal to x. Eliminate C: 20 10^10 (a^x) can give unit digit zero as well as a is equal to x. Correct answer. We don’t need to look at other options as question is asking about minimum value of ( a+x)
Correct answer C. vishalkazone , please explain what this reference means or why it is inserted: the exponent OF a^x [is a multiple of 20] a is not the exponent. a is the base. \(a^{x}\) is not the exponent. \(a^{x}\) is the term. "The exponent" is x It appears that you omitted the reference or ignored it: Quote: Given: a^x is multiple of 20: Mathematical workarounds and elision do not answer the question, "If the question intends to target the entire term 'a^x,' then what is the point of mentioning the exponent (x)?" I don't think anyone has answered that question.
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Re: The exponent of a^x is a multiple of 20, what is the minimum p
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30 Oct 2018, 18:28
generis wrote: GMATSkilled wrote: The exponent of \(a^{x}\) (=a^x) is a multiple of 20, what is the minimum possible value of (a + x), if a is a factor of x? (a & x are positive integers) vishalkazone wrote: Given: i) a^x is multiple of 20: Means unit digit must be Zero. ii) a is a factor of x means a< x or a= x, a cant be greater than x iii) both a and x is positive integer.
we need to find minimum value of (a+x). look at the options with above results: A: 10 no value of a and x can result to unit digit zero. ( multiple of 20) eliminate B: 15 only 10^5 (a^x) can give unit digit zero but , condition 2 didn’t match a has to be less than or equal to x. Eliminate C: 20 10^10 (a^x) can give unit digit zero as well as a is equal to x. Correct answer. We don’t need to look at other options as question is asking about minimum value of ( a+x)
Correct answer C. vishalkazone , please explain what this reference means or why it is inserted: the exponent OF a^x [is a multiple of 20] a is not the exponent. a is the base. \(a^{x}\) is not the exponent. \(a^{x}\) is the term. "The exponent" is x It appears that you omitted the reference or ignored it: Quote: Given: a^x is multiple of 20: Mathematical workarounds and elision do not answer the question, "If the question intends to target the entire term 'a^x,' then what is the point of mentioning the exponent (x)?" I don't think anyone has answered that question. Many be this can be cleared by question originator, but in my opinion there are two cases: 1 a^x is already exponent so no need to mention exponent. 2if it means x is multiple of 20, then it should be written as : exponent of a is multiple of 20, not exponent of a^x is multiple of 20.



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Re: The exponent of a^x is a multiple of 20, what is the minimum p
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02 Nov 2018, 07:55
Bunuelcould you prove an answer to this question?



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Re: The exponent of a^x is a multiple of 20, what is the minimum p
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08 Jan 2019, 11:55
GMATSkilled wrote: The exponent of \(a^{x}\) is a multiple of 20, what is the minimum possible value of (a + x), if a is a factor of x? (a & x are positive integers)
A. 10
B. 15
C. 20
D. 40
E. 50 Yes , there seems to be a small typo in the question, the question should state The exponent \(a^x\)is a multiple of 20 rather than: The exponent of \(a^x\). The term of is creating all the confusion.
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