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If x is the product of numbers 1 through 150....
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fourteenstix
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theCodeToGMAT
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To find "y" we need power of 5 in 150!
so,
150/5 = 30
30/5 = 6
6/5 = 1
1/5 = 0
Answer = 30 + 6 + 1 = 37
so,
150/5 = 30
30/5 = 6
6/5 = 1
1/5 = 0
Answer = 30 + 6 + 1 = 37
R A H U L
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Hi fourteenstix,
Since we're multiplying a big string of numbers together, this question comes down to "prime factorization"....we need to "find" all of the 5s that exist in this string of numbers. As a hint, some numbers have MORE THAN one 5 in them.
To start, we know that there are 30 multiples of 5 in the string from 1 to 150, so that's 30 5s right there.
Now, we need to think about numbers that have more than one 5 in them....
5, 10, 15....these all have just one 5
25, 50, 75, 100, 150...these all have TWO 5s; we already counted one of the 5s in each, so we have to now add the other one to the total = +5 more
125....this has THREE 5s; we already counted one of the 5s, so we have to now add the other two to the total = +2 more
30 + 5 + 2 = 37 fives.
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
Since we're multiplying a big string of numbers together, this question comes down to "prime factorization"....we need to "find" all of the 5s that exist in this string of numbers. As a hint, some numbers have MORE THAN one 5 in them.
To start, we know that there are 30 multiples of 5 in the string from 1 to 150, so that's 30 5s right there.
Now, we need to think about numbers that have more than one 5 in them....
5, 10, 15....these all have just one 5
25, 50, 75, 100, 150...these all have TWO 5s; we already counted one of the 5s in each, so we have to now add the other one to the total = +5 more
125....this has THREE 5s; we already counted one of the 5s, so we have to now add the other two to the total = +2 more
30 + 5 + 2 = 37 fives.
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
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helen.xia@mbawatch
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The product of 1 to 150 can be written as 150!. To find how many 5's can be divided into 150! I listed all the numbers in the 150! pattern that are divisible by 5:
5, 10, 15, 20.....150
going over those number the first time, there are 30 numbers.
Of those 30 numbers, 25, 50, 75, 100, and 150 are divisible by 5 twice. 125 is divisible by 5 three times.
Therefore: 30 + 5 + 2 = 37.
I guess I don't have the best approach to this problem..can you confirm the answer?
5, 10, 15, 20.....150
going over those number the first time, there are 30 numbers.
Of those 30 numbers, 25, 50, 75, 100, and 150 are divisible by 5 twice. 125 is divisible by 5 three times.
Therefore: 30 + 5 + 2 = 37.
I guess I don't have the best approach to this problem..can you confirm the answer?
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GMATGuruNY
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x = 150!.
5^y = the number of 5's that can be divided into x.
Count how many times EACH POWER OF 5 can be divided into 150:
150/5¹ = 30.
The calculation above indicates that 150! includes 30 multiples of 5¹.
Each multiple of 5¹ supplies at least one 5.
150/5² = 150/25 = 6.
The calculation above indicates that 150! includes 6 multiples of 5², each of which supplies an additional 5.
150/5³ = 150/125 = 1.
The calculation above indicates that 150! includes one multiple of 5³, supplying one more 5.
Thus, the maximum number of 5's that can be divided into x = 30+6+1 = 37.
The correct answer is D.
A similar problem:
https://www.beatthegmat.com/product-of-t ... 94247.html
5^y = the number of 5's that can be divided into x.
Count how many times EACH POWER OF 5 can be divided into 150:
150/5¹ = 30.
The calculation above indicates that 150! includes 30 multiples of 5¹.
Each multiple of 5¹ supplies at least one 5.
150/5² = 150/25 = 6.
The calculation above indicates that 150! includes 6 multiples of 5², each of which supplies an additional 5.
150/5³ = 150/125 = 1.
The calculation above indicates that 150! includes one multiple of 5³, supplying one more 5.
Thus, the maximum number of 5's that can be divided into x = 30+6+1 = 37.
The correct answer is D.
A similar problem:
https://www.beatthegmat.com/product-of-t ... 94247.html
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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rahul.sehgal@btgchampion
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theCodeToGMAT wrote:To find "y" we need power of 5 in 150!
so,
150/5 = 30
30/5 = 6
6/5 = 1
1/5 = 0
Answer = 30 + 6 + 1 = 37
Can you help me understand how you did this ? I mean, why you divide this way ? I might be missing a trick here.
Best Regards,
Rahul Sehgal
Rahul Sehgal
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theCodeToGMAT
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Refer the Mitch's solution above your post.. the method is exactly the same..rahulsehgal wrote:
Can you help me understand how you did this ? I mean, why you divide this way ? I might be missing a trick here.
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gmattesttaker2
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Hello Rich,[email protected] wrote:Hi fourteenstix,
Since we're multiplying a big string of numbers together, this question comes down to "prime factorization"....we need to "find" all of the 5s that exist in this string of numbers. As a hint, some numbers have MORE THAN one 5 in them.
To start, we know that there are 30 multiples of 5 in the string from 1 to 150, so that's 30 5s right there.
Now, we need to think about numbers that have more than one 5 in them....
5, 10, 15....these all have just one 5
25, 50, 75, 100, 150...these all have TWO 5s; we already counted one of the 5s in each, so we have to now add the other one to the total = +5 more
125....this has THREE 5s; we already counted one of the 5s, so we have to now add the other two to the total = +2 more
30 + 5 + 2 = 37 fives.
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
Thanks for the explanation. Here:
we have 30 5's.5, 10, 15....these all have just one 5
I have tried to understand this as follows:
For 25, 50, 75, 100, 125, 150 we have one more 5 in each. Hence, we have 6 5's here.
For 125, we have one more 5.
Hence, total = 30 + 6 + 1 = 37
Is this correct?
Thanks a lot for your help.
Best Regards,
Sri
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Hi Sri,
Yes, your way of organizing this question is correct. One of the "design elements" of most GMAT questions is that they can be solved in a variety of ways (even the "math" can be done in more than one way). This design rewards flexible thinkers; it also means that you won't necessarily get "stuck" if you're not sure how to solve a particular question - there's more than 1 way to the solution, so try to do something.
GMAT assassins aren't born, they're made,
Rich
Yes, your way of organizing this question is correct. One of the "design elements" of most GMAT questions is that they can be solved in a variety of ways (even the "math" can be done in more than one way). This design rewards flexible thinkers; it also means that you won't necessarily get "stuck" if you're not sure how to solve a particular question - there's more than 1 way to the solution, so try to do something.
GMAT assassins aren't born, they're made,
Rich
