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# A whole number greater than 1 has remainders of 1 when it is divided b

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6815
GMAT 1: 760 Q51 V42
GPA: 3.82
A whole number greater than 1 has remainders of 1 when it is divided b  [#permalink]

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23 Aug 2018, 01:13
00:00

Difficulty:

25% (medium)

Question Stats:

79% (00:49) correct 21% (01:07) wrong based on 42 sessions

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[Math Revolution GMAT math practice question]

A whole number greater than $$1$$ has remainders of $$1$$ when it is divided by each of the numbers of $$2, 3, 4$$ and $$5$$. What is the smallest such number?

$$A. 31$$
$$B. 51$$
$$C. 61$$
$$D. 91$$
$$E. 121$$

_________________

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 $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Status: Learning stage Joined: 01 Oct 2017 Posts: 950 WE: Supply Chain Management (Energy and Utilities) A whole number greater than 1 has remainders of 1 when it is divided b [#permalink] ### Show Tags 23 Aug 2018, 01:29 MathRevolution wrote: [Math Revolution GMAT math practice question] A whole number greater than $$1$$ has remainders of $$1$$ when it is divided by each of the numbers of $$2, 3, 4$$ and $$5$$. What is the smallest such number? $$A. 31$$ $$B. 51$$ $$C. 61$$ $$D. 91$$ $$E. 121$$ LCM(2,3,4,5)=60 The number can be written in the form 60k+1 so 60k+1 would be the smallest when k=1 So 60k+1=60*1+1=60+1=61 Ans .(C) _________________ Regards, PKN Rise above the storm, you will find the sunshine Retired Moderator Status: Preparing for GMAT Joined: 25 Nov 2015 Posts: 986 Location: India GPA: 3.64 Re: A whole number greater than 1 has remainders of 1 when it is divided b [#permalink] ### Show Tags 23 Aug 2018, 03:23 MathRevolution wrote: [Math Revolution GMAT math practice question] A whole number greater than $$1$$ has remainders of $$1$$ when it is divided by each of the numbers of $$2, 3, 4$$ and $$5$$. What is the smallest such number? $$A. 31$$ $$B. 51$$ $$C. 61$$ $$D. 91$$ $$E. 121$$ Strategy - Test The Answers A - 31 - Rem>1 when divided by 4 B - 51 - Div. by 3 C - 61 - Leaves remainder 1 when div by 2,3,4,5 Answer C. _________________ Please give kudos, if you like my post When the going gets tough, the tough gets going... CEO Joined: 11 Sep 2015 Posts: 3332 Location: Canada Re: A whole number greater than 1 has remainders of 1 when it is divided b [#permalink] ### Show Tags 23 Aug 2018, 07:19 Top Contributor MathRevolution wrote: [Math Revolution GMAT math practice question] A whole number greater than $$1$$ has remainders of $$1$$ when it is divided by each of the numbers of $$2, 3, 4$$ and $$5$$. What is the smallest such number? $$A. 31$$ $$B. 51$$ $$C. 61$$ $$D. 91$$ $$E. 121$$ Let N = the number in question. If N divided by 2 leaves a remainder of 1, then N is 1 greater than some multiple of 2. This means that N - 1 must be a multiple of 2. Likewise, if N divided by 3 leaves a remainder of 1, then N is 1 greater than some multiple of 3. This means that N - 1 must be a multiple of 3. Etc... So, N - 1 must be a multiple of 2, 3, 4 and 5 Since we're looking for the smallest possible value of N, we must find the LEAST common multiple of 2, 3, 4 and 5 The LEAST common multiple of 2, 3, 4 and 5 is 60 So, N - 1 = 60, which means N = 61 Answer: C Cheers, Brent _________________ Test confidently with gmatprepnow.com Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6815 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: A whole number greater than 1 has remainders of 1 when it is divided b [#permalink] ### Show Tags 26 Aug 2018, 17:23 => Let $$x$$ be the smallest number satisfying the original condition. Then $$x – 1$$ is the least common multiple of $$2, 3, 4$$ and $$5$$. So, $$x – 1 = 60.$$ Thus, $$x = 61$$. 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$149 for 3 month Online Course"
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Re: A whole number greater than 1 has remainders of 1 when it is divided b &nbs [#permalink] 26 Aug 2018, 17:23
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