please help to solve -- multiply by 2 or divide by 3 - 60 times

Sundari

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A little monkey is playing with his calculator. He starts with the number 12. He multiplies or divides the number by 2 or 3(if possible) 60 times total.which of the following results can he not obtain?

A) 12
B) 18
C) 36
D) 72
E)108

Right answer is option-- C)36.
 
Have you considered the prime factorization of each?
 
Do I have to try Prime factorization on the numbers in answer ?

I am able to do on all numbers resulting 2 and 3.

how that would help?

Please explain.
 
A little monkey is playing with his calculator. He starts with the number 12. He multiplies or divides the number by 2 or 3(if possible) 60 times total.which of the following results can he not obtain?

A) 12
B) 18
C) 36
D) 72
E)108

Right answer is option-- C)36.
I'll give you a hint why you can get 108. You start with 12, then multiply by 3 and then again by 3 which gives you 108. So you used up 2 of the 60 operations. Can you figure out the remaining 58 moves and still get a result of 108?
 
A little monkey is playing with his calculator. He starts with the number 12. He multiplies or divides the number by 2 or 3(if possible) 60 times total.which of the following results can he not obtain?

A) 12
B) 18
C) 36
D) 72
E)108

Right answer is option-- C)36.

The key idea is that you have to do exactly 60 multiplications or divisions. (I missed that at first.)

For example, you can get 12 by multiplying by 2 30 times, and dividing by 2 30 times. (If the number had been 61 instead of 60, you couldn't get 12.) You can get 18 by multiplying by 3, dividing by 2, and then wasting the other 58 operations in a similar way.

Now think about the other numbers. There's more to this than just listing prime factors.
 
Do I have to try Prime factorization on the numbers in answer ?

I am able to do on all numbers resulting 2 and 3.

how that would help?

Please explain.

Given the prime factorization, it is rather simple to determine the minimum number of monkey calculations to get there from 12. 60 is an even number. Think about parity.
 
Oh ya, can understand now how prime factorization is helpful on this problem.

Prime factorization on 12, 18,72,108 gives even number of operations.

number 36 takes odd number of operation.


Thank you everyone for helping.
 
Oh ya, can understand now how prime factorization is helpful on this problem.

Prime factorization on 12, 18,72,108 gives even number of operations.

number 36 takes odd number of operation.


Thank you everyone for helping.
Not clear what you mean by Oh ya, can understand now how prime factorization is helpful on this problem. Prime factorization on 12, 18,72,108 gives even number of operations.

After all 12 = 2*2*3, 18=3*3*2 and 108= 2*2*3*3*3 all have an odd number of factors (operations???)
 
1.12/2=6
2.6/3=2
3.2*3=6
4.6*2=12

Starting from 12 it took 4 operations to get 12 again.

Prime Factorization

12 = 2*6 (Step 1 of prime factorization)
then 6 = 2*3 (Step 2 of prime factorization)
that is two steps of operation.

In similar number 18 takes 2 steps of prime factorization.
number 36 takes 3 steps of prime factorization.
number 72 and 108 takes 4 steps of prime factorization.

the even number of steps gets repeated to attain 12 and then follow required 60 operation.IMG_4099.jpg

so I concluded the answer.

Please let me know that my understanding is right.
 
Oh ya, can understand now how prime factorization is helpful on this problem.

Prime factorization on 12, 18,72,108 gives even number of operations.

number 36 takes odd number of operation.


Thank you everyone for helping.

That's the spirit. Don't let the monkey play with the calculator.
 
1.12/2=6
2.6/3=2
3.2*3=6
4.6*2=12

Starting from 12 it took 4 operations to get 12 again.

Prime Factorization

12 = 2*6 (Step 1 of prime factorization)
then 6 = 2*3 (Step 2 of prime factorization)
that is two steps of operation.

In similar number 18 takes 2 steps of prime factorization.
number 36 takes 3 steps of prime factorization.
number 72 and 108 takes 4 steps of prime factorization.

the even number of steps gets repeated to attain 12 and then follow required 60 operation.View attachment 10671

so I concluded the answer.

Please let me know that my understanding is right.
Well 12 does not need any 'operations' to get to 12 (and 0 is even). 12/2= 6 and 6*2=12, so two operations which is even. Your method to get to 12 also have an even number of operations. The question is will the parity change. You seem to assume that it will not change. Can you prove this?
 
Hi,


Parity is same by all ways of doing the prime factorization.

Think I did it right.

There should be 60 multiplication or division, so I did the steps for number 12 to get back to 12.

whether I answered your question?
Am I right.
 
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