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# What is the number of multiples of 25 between 5^4 and 5^5, inclusive?

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What is the number of multiples of 25 between 5^4 and 5^5, inclusive? [#permalink]

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10 Feb 2017, 03:05
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Difficulty:

35% (medium)

Question Stats:

73% (00:59) correct 27% (01:46) wrong based on 89 sessions

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What is the number of multiples of 25 between $$5^4$$ and$$5^5$$, inclusive?

A. 75
B. 96
C. 101
D. 121
E. 125

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 5890 Re: What is the number of multiples of 25 between 5^4 and 5^5, inclusive? [#permalink] ### Show Tags 10 Feb 2017, 04:42 MathRevolution wrote: What is the number of multiples of 25 between $$5^4$$ and$$5^5$$, inclusive? A. 75 B. 96 C. 101 D. 121 E. 125 Hi To find answer, convert 5^4 and 5^5 in multiples of 25... $$5^4=25*25.......5^5=25*125$$ So multiples of 25=(125-25)+1=101.... Otherwise answer =$$\frac{5^5-5^4}{25}+1=\frac{25(5^3-5^2)}{25}+1=5^2(5-1)+1=25*4+1=101$$ C _________________ Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html GMAT online Tutor Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 3505 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: What is the number of multiples of 25 between 5^4 and 5^5, inclusive? [#permalink] ### Show Tags 10 Feb 2017, 09:50 MathRevolution wrote: What is the number of multiples of 25 between $$5^4$$ and$$5^5$$, inclusive? A. 75 B. 96 C. 101 D. 121 E. 125 Multiples of $$25 = 5^2$$ Numbers between $$5^4$$ and$$5^5$$ = Numbers between 625 to 3125 There are 2500 numbers... So, Total number of multiples of 25 between 625 to 3125 inclusive = $$\frac{2500}{25} + 1$$ => 100 + 1 Hence, Correct answer must be (C) 101 _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5577 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: What is the number of multiples of 25 between 5^4 and 5^5, inclusive? [#permalink] ### Show Tags 12 Feb 2017, 18:27 ==> The number of multiples become (last-first/n)+1, then you get $$\frac{5^5-5^4}{25}+1=\frac{(5-1)5^4}{25}+1=4(5^2)+1=101$$. Therefore, the answer is C. Answer: C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: What is the number of multiples of 25 between 5^4 and 5^5, inclusive? [#permalink]

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15 Feb 2017, 10:50
MathRevolution wrote:
What is the number of multiples of 25 between $$5^4$$ and$$5^5$$, inclusive?

A. 75
B. 96
C. 101
D. 121
E. 125

We need to determine the number of multiples of 25 between 5^4 = 625 and 5^5 = 3,125.

We can use the following formula:

(largest multiple of 25 in the set - smallest multiple of 25 in the set)/25 + 1

(3125 - 625)/25 + 1 = 2500/25 + 1 = 100 + 1 = 101.

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Re: What is the number of multiples of 25 between 5^4 and 5^5, inclusive? [#permalink]

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11 Jun 2018, 14:19
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Re: What is the number of multiples of 25 between 5^4 and 5^5, inclusive?   [#permalink] 11 Jun 2018, 14:19
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# What is the number of multiples of 25 between 5^4 and 5^5, inclusive?

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