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# In the 6-digit integer 543, 2xy, x and y are chosen from the digits 0

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42
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In the 6-digit integer 543, 2xy, x and y are chosen from the digits 0  [#permalink]

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15 Jan 2018, 00:30
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Difficulty:

75% (hard)

Question Stats:

49% (02:48) correct 51% (02:31) wrong based on 50 sessions

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[GMAT math practice question]

In the 6-digit integer $$543, 2xy, x$$ and $$y$$ are chosen from the digits $$0, 2, 4, 6$$ and $$8$$. What is the probability that $$543, 2xy$$ is divisible by $$8$$?

$$A. \frac{1}{5}$$
$$B. \frac{6}{25}$$
$$C. \frac{7}{25}$$
$$D. \frac{8}{25}$$
$$E. \frac{9}{25}$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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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" Senior PS Moderator Joined: 26 Feb 2016 Posts: 3332 Location: India GPA: 3.12 In the 6-digit integer 543, 2xy, x and y are chosen from the digits 0 [#permalink] ### Show Tags 15 Jan 2018, 01:53 MathRevolution wrote: [GMAT math practice question] In the 6-digit integer $$543, 2xy, x$$ and $$y$$ are chosen from the digits $$0, 2, 4, 6$$ and $$8$$. What is the probability that $$543, 2xy$$ is divisible by $$8$$? $$A. \frac{1}{5}$$ $$B. \frac{6}{25}$$ $$C. \frac{7}{25}$$ $$D. \frac{8}{25}$$ $$E. \frac{9}{25}$$ In order to solve the question, we must know the rule for divisibility of 8. The rule is as follows: If the last 3 digits are divisible by 8, the number is divisible by 8. Since the last 3 digits are 2xy we need to find out how many of the combinations are divisible by 8. They are 200,208,224,240,248,264,280,288(8 options) The denominator must be the total options possible: 5*5 = 25 Therefore, the probability that $$543, 2xy$$ is divisible by $$8$$ is $$\frac{8}{25}$$(Option D) _________________ You've got what it takes, but it will take everything you've got Manager Joined: 20 Feb 2017 Posts: 88 Location: United States Re: In the 6-digit integer 543, 2xy, x and y are chosen from the digits 0 [#permalink] ### Show Tags 15 Jan 2018, 11:07 1 MathRevolution wrote: [GMAT math practice question] In the 6-digit integer $$543, 2xy, x$$ and $$y$$ are chosen from the digits $$0, 2, 4, 6$$ and $$8$$. What is the probability that $$543, 2xy$$ is divisible by $$8$$? $$A. \frac{1}{5}$$ $$B. \frac{6}{25}$$ $$C. \frac{7}{25}$$ $$D. \frac{8}{25}$$ $$E. \frac{9}{25}$$ Total possible number - xy -> 5X5 = 25 In given question, we have 2xy as 200 is divisible by 8, we just need to worry about xy. (2xy = 200 + xy) So combination with 0,2,4,6,8 divisible by 8 -> 00,08,24,40,48,64,80,88 _________________ ***************************************************************** Kudos are always welcome. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8033 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: In the 6-digit integer 543, 2xy, x and y are chosen from the digits 0 [#permalink] ### Show Tags 17 Jan 2018, 01:05 => An integer with three or more digits is divisible by 8 if and only if its last three digits from a number that is divisible by $$8$$. The values of $$2xy$$ that are divisible by $$8$$ are $$200, 208, 224, 240, 248, 264, 280$$, and $$288$$. The total number of 6-digit integers of the form $$543,2xy$$ is equal to the number of ways of choosing two digits from $$0, 2, 4, 6$$ and $$8$$, which is $$5*5 = 25.$$ Thus, the probability that $$543,2xy$$is divisible by $$8$$ is $$\frac{8}{25}$$ Therefore, the answer is D. Answer: D _________________ 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: In the 6-digit integer 543, 2xy, x and y are chosen from the digits 0   [#permalink] 17 Jan 2018, 01:05
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