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Updated on: 12 Jul 2019, 08:25
Originally posted by Siddharthjain07 on 12 Jul 2019, 08:07.
Last edited by Bunuel on 12 Jul 2019, 08:25, edited 1 time in total.
Last edited by Bunuel on 12 Jul 2019, 08:25, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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71% (01:32) correct
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N is the product if all integers from 1 to 75. If 10^k is a factor of N , what is the greatest value of k?
A. 5
B. 10
C. 12
D. 18
E. 25
A. 5
B. 10
C. 12
D. 18
E. 25
Gagan0009
Joined: 25 Feb 2019
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Concentration: Marketing, General Management
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Schools: Olin '22 (WA$) Jones '22 (WA$) McDonough '22 (WA) Goizueta "23 (WL) Johnson'23 (WL) Stern '23 (WL)
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GRE 1: Q168 V155
Posts: 27
there is a simple way for that you just need to find the highest power of 5 that can occur in 75! as that would act as a limiting factor.
Highest power of 5 would be around 18.
Answer D
Highest power of 5 would be around 18.
Answer D
12 Jul 2019, 09:02
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Is k an integer? The question needs to tell you that. If k is not an integer, you need logarithms to answer the question, and logs are not tested on the GMAT.
If k is an integer, we just need to count the 5's in 75!. We'll have 15 multiples of 5 if we write out 75! in full, and three of those, 25, 50 and 75, are also multiples of 5^2, so that gives us three additional fives. So 5^18 is a factor of 75!. We have a lot more than eighteen 2's inside 75!, so 10^18 will be a divisor of 75!, and 10^19 will not be, and 18 is the largest integer value of k.
If k is an integer, we just need to count the 5's in 75!. We'll have 15 multiples of 5 if we write out 75! in full, and three of those, 25, 50 and 75, are also multiples of 5^2, so that gives us three additional fives. So 5^18 is a factor of 75!. We have a lot more than eighteen 2's inside 75!, so 10^18 will be a divisor of 75!, and 10^19 will not be, and 18 is the largest integer value of k.
