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# When 2 numbers are selected from the integers from 1 to 21 inclusive,

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6619
GMAT 1: 760 Q51 V42
GPA: 3.82
When 2 numbers are selected from the integers from 1 to 21 inclusive,  [#permalink]

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30 Jul 2018, 23:43
00:00

Difficulty:

25% (medium)

Question Stats:

77% (01:37) correct 23% (01:31) wrong based on 39 sessions

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[Math Revolution GMAT math practice question]

When $$2$$ numbers are selected from the integers from $$1$$ to $$21$$ inclusive, what is the probability that the $$2$$ selected numbers are prime numbers?

$$A. \frac{2}{15}$$
$$B. \frac{1}{5}$$
$$C. \frac{1}{3}$$
$$D. \frac{4}{15}$$
$$E. \frac{2}{5}$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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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: 7099 Re: When 2 numbers are selected from the integers from 1 to 21 inclusive, [#permalink] ### Show Tags 31 Jul 2018, 00:00 MathRevolution wrote: [Math Revolution GMAT math practice question] When $$2$$ numbers are selected from the integers from $$1$$ to $$21$$ inclusive, what is the probability that the $$2$$ selected numbers are prime numbers? $$A. \frac{2}{15}$$ $$B. \frac{1}{5}$$ $$C. \frac{1}{3}$$ $$D. \frac{4}{15}$$ $$E. \frac{2}{5}$$ Prime numbers till 21 - 2, 3, 5, 7, 11, 13 17 19 so 8 of them.. Total ways to select 2 out of 21..=21*20 Probability=8*7/21*20=2/15 A _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Director Joined: 20 Feb 2015 Posts: 796 Concentration: Strategy, General Management Re: When 2 numbers are selected from the integers from 1 to 21 inclusive, [#permalink] ### Show Tags 31 Jul 2018, 00:03 1 MathRevolution wrote: [Math Revolution GMAT math practice question] When $$2$$ numbers are selected from the integers from $$1$$ to $$21$$ inclusive, what is the probability that the $$2$$ selected numbers are prime numbers? $$A. \frac{2}{15}$$ $$B. \frac{1}{5}$$ $$C. \frac{1}{3}$$ $$D. \frac{4}{15}$$ $$E. \frac{2}{5}$$ 1 is not a prime number prime numbers between 1 and 21(inclusive) = 2,3,5,7,11,13,17,19=8 2 out of 8 can be selected in 8c2 ways = 28 2 out of 21 can be selected in 21c2 ways =210 probability of selecting 2 primes = 28/210=2/15 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6619 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: When 2 numbers are selected from the integers from 1 to 21 inclusive, [#permalink] ### Show Tags 02 Aug 2018, 01:20 => There are $$8$$ prime numbers between $$1$$ and $$21$$, inclusive: $$2, 3, 5, 7, 11, 13, 17$$ and $$19$$. So, there are 8C2 ways of selecting $$2$$ numbers from these $$8$$ prime numbers. There are 21C2 ways of selecting $$2$$ numbers from the $$21$$ numbers from $$1$$ to $$21$$, inclusive. Thus, the probability that the $$2$$ selected numbers are prime numbers is 8C2 / 21C2 = ( 8*7 / 1*2) / ( 21*20 / 1*2 ) = 8*7 / 21*20 = 2/15. 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$99 for 3 month Online Course"
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Re: When 2 numbers are selected from the integers from 1 to 21 inclusive, &nbs [#permalink] 02 Aug 2018, 01:20
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