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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## If there are fewer than 8 zeroes between the decimal point ##### This topic has 1 expert reply and 1 member reply ### Top Member ## If there are fewer than 8 zeroes between the decimal point ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult If there are fewer than 8 zeroes between the decimal point and the first nonzero digit in the decimal expansion of (t/1000)^4, which of the following numbers could be the value of t? I. 3 II. 5 III. 9 A) None B) I only C) II only D) III only E) II and III OA A Source: Official Guide ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2950 messages Followed by: 19 members Upvotes: 43 BTGmoderatorDC wrote: If there are fewer than 8 zeroes between the decimal point and the first nonzero digit in the decimal expansion of (t/1000)^4, which of the following numbers could be the value of t? I. 3 II. 5 III. 9 A) None B) I only C) II only D) III only E) II and III OA A Source: Official Guide If t = 1, then (1/1000)^4 = (1/10^3)^4 = 1/10^12. Therefore, the decimal expansion would have 12 decimal places, with the last (rightmost) digit being a 1. That is, there are 11 zeros between the decimal point and the last digit 1. For any of the given t values, 3, 5 and 9, it will not change the number of decimal places; however, it may change the number of zeros between the decimal point and the first nonzero digit. If t = 3, then t^4 = 3^4 = 81. So 81 will occupy the last two of the 12 decimal places; that means there are 10 zeros between the decimal point and the first nonzero digit 8. If t = 5, then t^5 = 5^4 = 625. So 625 will occupy the last three of the 12 decimal places; that means there are 9 zeros between the decimal point and the first nonzero digit 6. If t = 9, then t^5 = 9^4 = 6561. So 6561 will occupy the last four of the 12 decimal places; that means there are 8 zeros between the decimal point and the first nonzero digit 6. Since we are looking for fewer than 8 zeros between the decimal point and the first nonzero digit, none of the given t values will make this happen. Answer: A ### Top Member Legendary Member Joined 29 Oct 2017 Posted: 1023 messages Followed by: 4 members Let's try as follows: $$\left(\frac{t}{1000}\right)^4=\left(\frac{t}{10^3}\right)^4=\frac{t^4}{10^{12}}$$ $$10^{12}$$ will move decimal point to the left $$12$$ times. If we test $$9 \Rightarrow 9^4 = 6561$$ or $$0,6 \cdot 10^4$$ So $$4-12=8$$. Therefore, the correct answer is __A__ • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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