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# n ranges over the positive integers between 100 and 200, inclusive. Fi

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7766
GMAT 1: 760 Q51 V42
GPA: 3.82
n ranges over the positive integers between 100 and 200, inclusive. Fi  [#permalink]

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31 Jul 2019, 00:09
1
4
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Difficulty:

45% (medium)

Question Stats:

70% (02:37) correct 30% (02:25) wrong based on 40 sessions

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[GMAT math practice question]

$$n$$ ranges over the positive integers between $$100$$ and $$200,$$ inclusive. Find the number of values of $$7n+2$$ which are multiples of $$5$$

$$A. 18$$

$$B. 20$$

$$C. 22$$

$$D. 24$$

$$E. 26$$

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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 $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Joined: 19 Oct 2018 Posts: 791 Location: India Re: n ranges over the positive integers between 100 and 200, inclusive. Fi [#permalink] ### Show Tags 31 Jul 2019, 02:52 7n+2= 0 mod 5 7n= -2 mod 5= 3 mod 5 n= 4 mod 5 104= 4 mod 5 . . 199= 4 mod 5 total possible values of n= [(199-104)/5]+1=20 MathRevolution wrote: [GMAT math practice question] $$n$$ ranges over the positive integers between $$100$$ and $$200,$$ inclusive. Find the number of values of $$7n+2$$ which are multiples of $$5$$ $$A. 18$$ $$B. 20$$ $$C. 22$$ $$D. 24$$ $$E. 26$$ Intern Joined: 15 Feb 2019 Posts: 4 Re: n ranges over the positive integers between 100 and 200, inclusive. Fi [#permalink] ### Show Tags 01 Aug 2019, 02:27 3 Hi, I'm not sure if my approach is correct but here's how I did it. 7n+2 will be divisible by 5 if 7n has last digit as 3 or 8. There are only two digits (103 and 108) from 100 to 110. So from 100 to 200, there will be 2*10 digits which satisfy this condition. Please correct me if i'm wrong. Would request your input Bunuel . Cheers! Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7766 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: n ranges over the positive integers between 100 and 200, inclusive. Fi [#permalink] ### Show Tags 02 Aug 2019, 02:02 => If $$n = 5k,$$ then $$7n + 2 = 7(5k) + 2 = 5(7k) + 2$$ is not a multiple of $$5.$$ If $$n = 5k+1,$$ then $$7n + 2 = 7(5k+1) + 2 = 5(7k) + 7 + 2 = 5(7k) + 9 = 5(7k+1)+4$$ is not a multiple of $$5.$$ If $$n = 5k+2,$$ then $$7n + 2 = 7(5k+2) + 2 = 5(7k) + 14 + 2 = 5(7k) + 16 = 5(7k+3)+1$$ is not a multiple of $$5.$$ If $$n = 5k+3,$$ then $$7n + 2 = 7(5k+3) + 2 = 5(7k) + 21 + 2 = 5(7k) + 23 = 5(7k+4)+3$$ is not a multiple of $$5.$$ If $$n = 5k+4,$$ then $$7n + 2 = 7(5k+4) + 2 = 5(7k) + 28 + 2 = 5(7k) + 30 = 5(7k+6)$$ is a multiple of $$5.$$ Thus, $$n$$ has remainder $$4$$ when it is divided by $$5.$$ The possible values of $$n$$ are $$104, 109, …, 199.$$ The number of possible values of $$n$$ is $$\frac{(199-104)}{5} + 1 = 20.$$ Therefore, B is the answer. Answer: B _________________ 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$79 for 1 month Online Course"
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Re: n ranges over the positive integers between 100 and 200, inclusive. Fi   [#permalink] 02 Aug 2019, 02:02
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