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# The exponent of a^x is a multiple of 20, what is the minimum p

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Manager
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The exponent of a^x is a multiple of 20, what is the minimum p  [#permalink]

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06 Jun 2018, 16:49
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75% (hard)

Question Stats:

55% (02:12) correct 45% (01:41) wrong based on 159 sessions

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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  [#permalink]

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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

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  [#permalink]

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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

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  [#permalink]

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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  [#permalink]

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07 Jun 2018, 20:10
1
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  [#permalink]

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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  [#permalink]

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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, chetan2u

foryearss - 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  [#permalink]

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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
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  [#permalink]

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07 Jun 2018, 21:17
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
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"
"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  [#permalink]

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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  [#permalink]

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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  [#permalink]

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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.
We don’t need to look at other options as question is asking about minimum value of ( a+x)

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Re: The exponent of a^x is a multiple of 20, what is the minimum p  [#permalink]

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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  [#permalink]

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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  [#permalink]

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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.
We don’t need to look at other options as question is asking about minimum value of ( a+x)

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  [#permalink]

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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.
We don’t need to look at other options as question is asking about minimum value of ( a+x)

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.
2-if 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  [#permalink]

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02 Nov 2018, 07:55
Bunuel
could 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  [#permalink]

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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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Re: The exponent of a^x is a multiple of 20, what is the minimum p &nbs [#permalink] 08 Jan 2019, 11:55
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