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# The number 10^30 is divisible for all of the following EXCEPT

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Math Expert
Joined: 02 Sep 2009
Posts: 52902
The number 10^30 is divisible for all of the following EXCEPT  [#permalink]

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12 Jun 2018, 23:03
00:00

Difficulty:

15% (low)

Question Stats:

86% (00:41) correct 14% (01:08) wrong based on 79 sessions

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The number $$10^{30}$$ is divisible for all of the following EXCEPT

A. 250

B. 125

C. 32

D. 16

E. 6

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Posts: 2568
Re: The number 10^30 is divisible for all of the following EXCEPT  [#permalink]

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12 Jun 2018, 23:13
2

Solution

To find:
• Out of the given options, which one does not divide the number $$10^{30}$$

Approach and Working:
We can factorise all the options as well as the given number $$10^{30}$$ to tally the prime factors

• However, if we observe the options, we can see 6 is consists of the prime factors 2 and 3.
• Also, 3 can never divide any number which is in the form of $$10^x$$, where x is a whole number

Hence, the correct answer is option E.

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Re: The number 10^30 is divisible for all of the following EXCEPT  [#permalink]

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12 Jun 2018, 23:15
Bunuel wrote:
The number $$10^{30}$$ is divisible for all of the following EXCEPT

A. 250

B. 125

C. 32

D. 16

E. 6

Let us check each option

A.250 ==> 1000/250 ==> 4

B.125 ==> 1000/125 ==> 8

C.32 ==>100000/32 ==> 3125

D.16 ==> 10000/16 ==> 625

E. 6 ==> Ans

Hence E
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The number 10^30 is divisible for all of the following EXCEPT  [#permalink]

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13 Jun 2018, 01:32
1
We can follow the routine job called prime factorization:
10^30=2^30*5^30

We have to find out which answer options have different prime factors, in our case: 6=2*3

P.S To make this question more tricky, I would lower the 10's power in the stem, for instance: 10^3, dismiss 6 from answer choices and add 80
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Re: The number 10^30 is divisible for all of the following EXCEPT  [#permalink]

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13 Jun 2018, 01:55
A. 1000 is divisible for 250
B. 1000 is divisible for 125
C. 2^5
D. 2^4
E. 6= 3x2

So left E is the correct answer
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Re: The number 10^30 is divisible for all of the following EXCEPT  [#permalink]

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13 Jun 2018, 07:06
Bunuel wrote:
The number $$10^{30}$$ is divisible for all of the following EXCEPT

A. 250

B. 125

C. 32

D. 16

E. 6

Given, 10^{30}. So this number will end with 30 zeros. If we add the digits of 10^{30} we will have 1 only.

Look at answer choice E . 6 = 3*2 . Thus 10^{30} will never ever divisible by E.

Note: Rules of divisibility of 3 is the key to this question .
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The number 10^30 is divisible for all of the following EXCEPT  [#permalink]

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13 Jun 2018, 07:27
Bunuel wrote:
The number $$10^{30}$$ is divisible for all of the following EXCEPT

A. 250
B. 125
C. 32
D. 16
E. 6

Number is devisible by 3, if sum of all digits is divisible by 3.
$$10^{30}=10......00$$ - the sum will be 1, which is not divisible by 3 or any multiple of 3.
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Re: The number 10^30 is divisible for all of the following EXCEPT  [#permalink]

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16 Jun 2018, 09:10
Bunuel wrote:
The number $$10^{30}$$ is divisible for all of the following EXCEPT

A. 250

B. 125

C. 32

D. 16

E. 6

Since 10^30 = 2^30 x 5^30 does not contain any 3’s, we see that 10^30 is not divisible by 6.

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Re: The number 10^30 is divisible for all of the following EXCEPT   [#permalink] 16 Jun 2018, 09:10
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