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# If x=343y, where y is a positive integer, and x/196 is a

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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If x=343y, where y is a positive integer, and x/196 is a  [#permalink]

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23 Jan 2018, 01:11
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Difficulty:

55% (hard)

Question Stats:

63% (02:33) correct 38% (02:00) wrong based on 63 sessions

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[GMAT math practice question]

If $$x=343y$$, where y is a positive integer, and $$\frac{x}{196}$$ is a terminating decimal, what is the smallest possible value of $$y$$?

$$A. 1$$
$$B. 3$$
$$C. 5$$
$$D. 7$$
$$E. 9$$

_________________
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"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: 31 Jul 2017 Posts: 512 Location: Malaysia Schools: INSEAD Jan '19 GMAT 1: 700 Q50 V33 GPA: 3.95 WE: Consulting (Energy and Utilities) If x=343y, where y is a positive integer, and x/196 is a [#permalink] ### Show Tags 23 Jan 2018, 01:27 MathRevolution wrote: [GMAT math practice question] If $$x=343y$$, where y is a positive integer, and $$\frac{x}{196}$$ is a terminating decimal, what is the smallest possible value of $$y$$? $$A. 1$$ $$B. 3$$ $$C. 5$$ $$D. 7$$ $$E. 9$$ Easy question if we think this way - Given, $$x = 7^3y.$$... or$$\frac{x}{49} = 7y$$.... ---> as $$\frac{x}{49*4} = \frac{7y}{4}$$. Now, the samllest possible value will be $$y = 1$$. _________________ If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !! Senior SC Moderator Joined: 22 May 2016 Posts: 3536 If x=343y, where y is a positive integer, and x/196 is a [#permalink] ### Show Tags 23 Jan 2018, 17:53 1 MathRevolution wrote: [GMAT math practice question] If $$x=343y$$, where y is a positive integer, and $$\frac{x}{196}$$ is a terminating decimal, what is the smallest possible value of $$y$$? $$A. 1$$ $$B. 3$$ $$C. 5$$ $$D. 7$$ $$E. 9$$ A terminating decimal will occur only when a fraction, reduced to its lowest terms, contains, in its denominator, only: powers of 2; powers of 5; or powers of 2 and 5 (powers of 10). Find the prime factors of 196: $$2^27^2$$ Thus $$\frac{x}{2*2*7*7}$$ = a terminating decimal To make $$\frac{x}{2*2*7*7}$$ terminate, x must have, at the least, 7*7 as a factor (in order to "cancel" the sevens in the denominator). Assess 343y. When in doubt about numbers that do not conform to common divisibility rules, start by dividing by 7 (then 11, then 13, etc.). x = 343y = 7 * 7 * 7 * y We need only two of those sevens for x in order to create a terminating decimal. But we want to minimize y -- so we maximize x, and "take" all three 7s for x. x = 343 * y x = (7 *7 * 7) * y x = (7 * 7 * 7) = 343 y = 1 Thus $$\frac{x}{196} = \frac{7*7*7}{2*2*7*7} = \frac{7}{4} = 1.75$$ The smallest possible value for y is 1 Answer A _________________ SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here. Choose life. Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2817 Re: If x=343y, where y is a positive integer, and x/196 is a [#permalink] ### Show Tags 24 Jan 2018, 10:34 MathRevolution wrote: [GMAT math practice question] If $$x=343y$$, where y is a positive integer, and $$\frac{x}{196}$$ is a terminating decimal, what is the smallest possible value of $$y$$? $$A. 1$$ $$B. 3$$ $$C. 5$$ $$D. 7$$ $$E. 9$$ We may recall that a fraction will be a terminating decimal when the denominator of its lowest terms has only prime factors of 2 and/or 5. . We see that 196 = 98 x 2 = 49 x 2 x 2 = 7^2 x 2^2 In order for x/196 to be a terminating decimal, the numerator x must contain at least the number 49 = 7^2, thereby canceling out the 7^2 in the denominator.. We see that 343 = 7^3, so if y = 1, x = 343 and thus 343/196 will be a terminating decimal. Answer: A _________________ # Jeffrey Miller Head of GMAT Instruction Jeff@TargetTestPrep.com 122 Reviews 5-star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8001 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x=343y, where y is a positive integer, and x/196 is a [#permalink] ### Show Tags 25 Jan 2018, 04:06 => $$\frac{x}{196} = \frac{(343*y)}{196} = \frac{(7^3*y)}{(14^2)} = \frac{(7^3*y)}{(2^2)(7^2)} = \frac{(7y)}{4}$$ As the denominator has only 2 as a prime factor, it is a terminating decimal, regardless of the value of y. Thus, the smallest possible value of y is 1. Therefore, the answer is A. Answer: A _________________ 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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Joined: 06 Aug 2017
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Re: If x=343y, where y is a positive integer, and x/196 is a  [#permalink]

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25 Jan 2018, 11:23
7y/4 7/4 is a terminating decimal. so y=1
Re: If x=343y, where y is a positive integer, and x/196 is a   [#permalink] 25 Jan 2018, 11:23
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