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Math Revolution GMAT Instructor
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What is the number of multiples of 5 between 5^3 and 5^4,inclusive?
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28 May 2017, 23:59
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What is the number of multiples of 5 between 5^3 and 5^4,inclusive? A. 85 B. 97 C. 101 D. 111 E. 123
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Re: What is the number of multiples of 5 between 5^3 and 5^4,inclusive?
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29 May 2017, 00:23
From 5^3 (125) to 5^4 (625) inclusive, we have: 125, 130, 135, ....., 625
Or: 5*25, 5*26, 5*27, ...., 5*125 We have to now count integers from 25 to 125.. = 125  25 + 1 = 101
Hence answer is C



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Re: What is the number of multiples of 5 between 5^3 and 5^4,inclusive?
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29 May 2017, 01:45
MathRevolution wrote: What is the number of multiples of 5 between 5^3 and 5^4,inclusive?
A. 85 B. 97 C. 101 D. 111 E. 123 5^3 = 125 5^4 = 625 So we have to find number of multiples of 5 between 125 and 625 inclusive. Every 5th term from 125 will be a multiple of 5, thus the series become: 125, 130, 135 ...... 625. It is an Arithmetic Progression (AP) with common difference of 5 Thus using nth term formula: nth term = a + (n  1)*d where a = 1st term and d = common difference 125 + (n1)*5 = 625 (n1)*5 = 500 n1=100 n=101 Answer = Option C Regards Anugrah



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Re: What is the number of multiples of 5 between 5^3 and 5^4,inclusive?
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29 May 2017, 01:54
MathRevolution wrote: What is the number of multiples of 5 between 5^3 and 5^4,inclusive?
A. 85 B. 97 C. 101 D. 111 E. 123 No. of multiples of 5 from 1 to 5^4 = 625/5 = 125 No. of multiples of 5 from 1 to 124(we took 124 since , we need to consider 125 in the multiples count) = [124/5] = 24 SO total number of multiples of 5 between 5^3 and 5^4 = 12524 = 101..
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What is the number of multiples of 5 between 5^3 and 5^4,inclusive?
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30 May 2017, 08:33
MathRevolution wrote: What is the number of multiples of 5 between 5^3 and 5^4,inclusive?
A. 85 B. 97 C. 101 D. 111 E. 123 To find number of multiples in a given range, inclusive : [(Last term  first term) / INCREMENT] + 1 1. Last term  first term: Last term is 5^4 = 625 First term is 5^3 = 125 625  125 = 500 2. Divide 500 by increment 5 500 / 5 = 100, not done yet ==> 3. Add 1. 100 + 1 = 101 Answer C
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Re: What is the number of multiples of 5 between 5^3 and 5^4,inclusive?
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31 May 2017, 00:54
==> You get(〖5^〗^4〖5^〗^3)/5+1=(〖5^〗^3 (51))/5+1=5^2(4)+1=101. The answer is C. Answer: C
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Re: What is the number of multiples of 5 between 5^3 and 5^4,inclusive?
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11 Jul 2017, 22:17
MathRevolution wrote: What is the number of multiples of 5 between 5^3 and 5^4,inclusive?
A. 85 B. 97 C. 101 D. 111 E. 123 The world "inclusive" just means including the beginning and ending points of the sequence (5^3, 5^4) simply use the formula 5^45^3/5 + 1 = 101 If we wanted to find the number of multiples of 4 between say 4^3 and 4^4, inclusive then again 4^44^3/4 + 1 And we could still use this formula if the question read how many multiples of five are between 121 and 626 5^45^3/5 + 1



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Re: What is the number of multiples of 5 between 5^3 and 5^4,inclusive?
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16 Jul 2017, 00:24
Here you go 5^4=625 5^3=125 subtract small from large power result==500(now divide it by 5 since we have to know multiple of 5 only) 100 now add 1 so Answer will be 101



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Re: What is the number of multiples of 5 between 5^3 and 5^4,inclusive?
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19 Jul 2017, 08:20
We can also try it as series in AP 625=125+(n1)5 500=(n1)5 100=n1 n=101 C
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Re: What is the number of multiples of 5 between 5^3 and 5^4,inclusive?
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25 Jul 2017, 10:53
MathRevolution wrote: What is the number of multiples of 5 between 5^3 and 5^4,inclusive?
A. 85 B. 97 C. 101 D. 111 E. 123 From the integers 5^3 to 5^4 inclusive, 5^4 is the largest multiple of 5 and 5^3 is the smallest multiple of 5; thus, the number of multiples of 5 between them is: (5^4  5^3)/5 + 1 = 5^3(5  1)/5 + 1 = 5^2(4) + 1 = 101 Alternate Solution: We see that we are really being asked to determine the number of multiples of 5 between 5^3 = 125 and 5^4 = 625. This is an evenly spaced set, and so we can use the following formula: (greatest multiple of 5 – smallest multiple of 5)/5 + 1 = (625 – 125)/5 + 1 = 500/5 + 1 = 101. Answer: C
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Re: What is the number of multiples of 5 between 5^3 and 5^4,inclusive?
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