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If a and b are integers and (2^a)(3^b) is a factor of 100^40, what is

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If a and b are integers and (2^a)(3^b) is a factor of 100^40, what is  [#permalink]

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New post 28 Apr 2016, 16:59
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

62% (01:19) correct 38% (01:51) wrong based on 167 sessions

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Re: If a and b are integers and (2^a)(3^b) is a factor of 100^40, what is  [#permalink]

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New post 29 Apr 2016, 00:05
1
2
Bunuel wrote:
If a and b are integers and (2^a)(3^b) is a factor of 100^40, what is the largest possible value of ab?

A. 0
B. 5
C. 20
D. 40
E. 80


(2^a)(3^b) is a factor of 100^40
We need to find the largest possible value of ab.

We know that 100 = 2^2*5^2
Therefore 100^40 will have no powers of 3 in it.
Hence in (2^a)(3^b), b has to 0

Therefore value of ab = 0

Correct Option: A
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Re: If a and b are integers and (2^a)(3^b) is a factor of 100^40, what is  [#permalink]

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New post 29 Apr 2016, 10:15
100 has prime factors 2 and 5 so exponent of prime factor will be 0
thus irrespective of value of exponent value of 2 ab wil always be 0

ans: A
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Re: If a and b are integers and (2^a)(3^b) is a factor of 100^40, what is  [#permalink]

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New post 29 Apr 2016, 12:59
1
Bunuel wrote:
If a and b are integers and (2^a)(3^b) is a factor of 100^40, what is the largest possible value of ab?

A. 0
B. 5
C. 20
D. 40
E. 80


Good one from Bunuel as usual

\(100^{40}\) = \(10^{80}\)

\(10^{80}\) = \({2*5}^{80}\)

From the above you get a = 80 ; but what about b ?

There is no 3 in 100^40 , so b will be 0

hence ab = 80*0 =>0

Answer will be (A)
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Re: If a and b are integers and (2^a)(3^b) is a factor of 100^40, what is  [#permalink]

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New post 05 Feb 2019, 16:23
Bunuel wrote:
If a and b are integers and (2^a)(3^b) is a factor of 100^40, what is the largest possible value of ab?

A. 0
B. 5
C. 20
D. 40
E. 80


I am so careless.. ended up choosing E.

There are 80 multiples of 2 in 100^40 and 0 multiples of 3

so 0 * 80 = 0. i need to make sure I am answering the question!!!!
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Re: If a and b are integers and (2^a)(3^b) is a factor of 100^40, what is  [#permalink]

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New post 11 Jun 2019, 02:14
(100)^40 = { (2)^2 * (5)^2 }^40 = ( 2^80 * 5^80)

Given,

2^a * 3^b is a factor of (100)^40 (= ( 2^80 * 5^80)). This is possible for a=80 and b=0.

Hence, a*b = 80*0 = 0

Answer: A
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Re: If a and b are integers and (2^a)(3^b) is a factor of 100^40, what is   [#permalink] 11 Jun 2019, 02:14
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