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If x is the product of the integers from 1 to 150, inclusive
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20 Oct 2013, 07:13
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65% (00:36) correct 35% (01:01) wrong based on 1215 sessions
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If x is the product of the integers from 1 to 150, inclusive, and 5^y is a factor of x, what is the greatest possible value of y ? A) 30 B) 34 C) 36 D) 37 E) 39
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Re: If x is the product of the integers from 1 to 150, inclusive
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Re: If x is the product of the integers from 1 to 150, inclusive
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20 Oct 2013, 07:18
bgribble wrote: If x is the product of the integers from 1 to 150, inclusive, and 5^y is a factor of x, what is the greatest possible value of y ?
A) 30 B) 34 C) 36 D) 37 E) 39 It basically asks for the number of 5s in 150! 150/5 + 150/25 + 150/125 = 30 + 6 + 1. Hence 37 Option d)
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Re: If x is the product of the integers from 1 to 150, inclusive
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Re: If x is the product of the integers from 1 to 150, inclusive
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30 Apr 2015, 00:28
bgribble wrote: If x is the product of the integers from 1 to 150, inclusive, and 5^y is a factor of x, what is the greatest possible value of y ?
A) 30 B) 34 C) 36 D) 37 E) 39 total number of 5 is 150/5=30 among 30 there are 25 50 75 100 125 150 contain 1,1,1,1 ,2 , 1 the number of 5 more total 30+7 d very hard
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Re: If x is the product of the integers from 1 to 150, inclusive
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25 Jan 2017, 09:09
1) To paraphrase the question, we need to find all the prime factors 5 of the number 150! 2) 150/5=30; 150/25=6; 150/125=1. The total number of 5's is 30+6+1=37
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Re: If x is the product of the integers from 1 to 150, inclusive
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23 Oct 2017, 07:46
Bunuel wrote: This is same as finding trailing zero  right.



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Re: If x is the product of the integers from 1 to 150, inclusive
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23 Oct 2017, 07:49



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Re: If x is the product of the integers from 1 to 150, inclusive
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23 Oct 2017, 08:11
5^3 < 150 < 5^4 Hence, the total number of 5 in 150!: 150/5^1 + 150/5^2 + 150/5^3 = 30 + 6 + 1 = 37 So, y = 37 Ans: D.
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Re: If x is the product of the integers from 1 to 150, inclusive
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23 Oct 2017, 09:32
bgribble wrote: If x is the product of the integers from 1 to 150, inclusive, and 5^y is a factor of x, what is the greatest possible value of y ?
A) 30 B) 34 C) 36 D) 37 E) 39 It is asking the number of 5 when the multiplication is written in terms of prime factors So, y = [150/5] + [150/25] + [150/125] = 30 + 6 + 1 = 37 Answer D
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If x is the product of the integers from 1 to 150, inclusive
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23 Oct 2017, 10:55
bgribble wrote: If x is the product of the integers from 1 to 150, inclusive, and 5^y is a factor of x, what is the greatest possible value of y ?
A) 30 B) 34 C) 36 D) 37 E) 39 Spelled out a little more: 1) \(x\) = product of integers from 1 to 150 \(x\) = 150 * 149* 148 . . .* 3 * 2 *1: That is, \(x\) = 150! 2) \(5^{y}\) is a factor of 150! What is the greatest possible value of \(y\)? Using \(\frac{150}{5^{y}}\), consider each power \(y\), of 5. Do not worry about remainders. \(\frac{150}{5^1}\) = 30 (5 divides into 150 thirty times) \(\frac{150}{5^2}\) = 6 (25 divides into 150 six times) \(\frac{150}{5^3}\) = 1 (125 divides into 150 only once. Ignore the remainder.) \(5^4 = 625\)  too large to divide into 150 as a factor. 3) Add the results: 30 + 6 + 1 = 37 Answer D Once you know the theory and method, questions such as this one are pretty straightforward. The stats here might indicate that the suggestion below is indispensable. Bunuel wrote: Quote:
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Re: If x is the product of the integers from 1 to 150, inclusive
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14 Mar 2018, 19:11
Hi All, 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: GMAT assassins aren't born, they're made, Rich
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If x is the product of the integers from 1 to 150, inclusive
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26 Mar 2018, 04:01
bgribble wrote: If x is the product of the integers from 1 to 150, inclusive, and 5^y is a factor of x, what is the greatest possible value of y ?
A) 30 B) 34 C) 36 D) 37 E) 39 x is the product of the integers from 1 to 150, inclusive means x = 150! 5^y is a factor of 150! means, \(\frac{150!}{5^y}\) \(= I\), where "I" is an integer We need to calculate the no. of 5s in 150! = \(\frac{150}{5} + \frac{150}{25} + \frac{150}{125}\) = \(30 + 6 + 1\) = \(37\) (D)
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Re: If x is the product of the integers from 1 to 150, inclusive
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27 Mar 2018, 11:34
bgribble wrote: If x is the product of the integers from 1 to 150, inclusive, and 5^y is a factor of x, what is the greatest possible value of y ?
A) 30 B) 34 C) 36 D) 37 E) 39 The product of the integers from 1 to 150, inclusive, is 150!. To determine the number of factors of 5 within 150!, we can use the following shortcut in which we divide 150 by 5, and then divide the quotient of 150/5 by 5 and continue this process until we can no longer get a nonzero integer as the quotient. 150/5 = 30 30/5 = 6 6/5 = 1 (we can ignore the remainder) Since 1/5 does not produce a nonzero quotient, we can stop. The final step is to add up our quotients; that sum represents the number of factors of 5 within 150!. Thus, there are 30 + 6 + 1 = 37 factors of 5 within 150!. Answer: D
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Re: If x is the product of the integers from 1 to 150, inclusive
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03 Apr 2018, 08:35
The answer must be D, i.e. 5 will have a total power of 37 in 150!.
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