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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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Math Expert
Joined: 02 Sep 2009
Posts: 52938
If a and b are integers and (2^a)(3^b) is a factor of 100^40, what is  [#permalink]

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28 Apr 2016, 15:59
00:00

Difficulty:

45% (medium)

Question Stats:

61% (01:20) correct 39% (01:52) wrong based on 100 sessions

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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

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Joined: 06 Nov 2014
Posts: 1877
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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28 Apr 2016, 23:05
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
Manager
Joined: 07 May 2015
Posts: 175
Location: India
GMAT 1: 660 Q48 V31
GPA: 3
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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29 Apr 2016, 09:15
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
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4383
Location: India
GPA: 3.5
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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29 Apr 2016, 11:59
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

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Thanks and Regards

Abhishek....

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Manager
Joined: 22 Sep 2018
Posts: 243
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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05 Feb 2019, 15:23
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!!!!
Re: If a and b are integers and (2^a)(3^b) is a factor of 100^40, what is   [#permalink] 05 Feb 2019, 15:23
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