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• ### $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### Free GMAT Strategy Webinar November 17, 2018 November 17, 2018 07:00 AM PST 09:00 AM PST Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. # There are 2 decks of cards. The first deck has a 100 cards labelled...  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Intern Joined: 19 Sep 2014 Posts: 21 Concentration: Finance, Economics GMAT Date: 05-05-2015 There are 2 decks of cards. The first deck has a 100 cards labelled... [#permalink] ### Show Tags 03 Feb 2015, 18:03 2 2 00:00 Difficulty: 55% (hard) Question Stats: 73% (02:47) correct 27% (03:05) wrong based on 157 sessions ### HideShow timer Statistics There are 2 decks of cards. The first deck has a 100 cards labelled with integers from 1 to 100. The second one has 150 cards labelled with integers 101 to 250. If we select one card at random from each deck, what is the probability that numbers on both selected cards will be multiples of 7? A. $$\frac{7}{3000}$$ B. $$\frac{7}{2500}$$ C. $$\frac{7^2}{15000}$$ D. $$\frac{7^2}{7500}$$ E. $$\frac{7^2}{2500}$$ Could someone please explain the answer to this question. It will be much appreciated, thank you Math Expert Joined: 02 Aug 2009 Posts: 7025 There are 2 decks of cards. The first deck has a 100 cards labelled... [#permalink] ### Show Tags 03 Feb 2015, 18:20 3 kdatt1991 wrote: There are 2 decks of cards. The first deck has a 100 cards labelled with integers from 1 to 100. The second one has 150 cards labelled with integers 101 to 250. If we select one card at random from each deck, what is the probability that numbers on both selected cards will be multiples of 7? A. $$\frac{7}{3000}$$ B. $$\frac{7}{2500}$$ C. $$\frac{7^2}{15000}$$ D. $$\frac{7^2}{7500}$$ E. $$\frac{7^2}{2500}$$ Could someone please explain the answer to this question. It will be much appreciated, thank you Hi you have to first find the probability of getting seven in each selection.. there are 14 multiples of seven in 1 to 100... $$\frac{100}{7}=14.3$$... so the probability of picking seven multiple will be $$\frac{14}{100}$$.. similarily there are 21 multiples of seven in 100 to 250... so the probability of picking seven multiple will be $$\frac{21}{150}$$.. therefore getting seven multiple on both occasions will be $$\frac{14}{100}*\frac{21}{150}= \frac{7^2}{2500}$$... ans E pl feel free to ask any query ... _________________ 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 EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12853 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: There are 2 decks of cards. The first deck has a 100 cards labelled... [#permalink] ### Show Tags 03 Feb 2015, 21:26 2 Hi kdatt1991, The key to this question is in finding a quick way to figure out how many multiples of 7 you're dealing with. If you're comfortable doing basic division by hand, the "math" required isn't too bad. I'm going to start by figuring out how many TOTAL multiples of 7 we're dealing with: 250/7 = 35 remainder 5, so we know that there are 35 multiples of 7 in total. NOW we have to figure out how many of those multiples are in the first group of 100 cards... 100/7 = 14 remainder 2, so we know.... 35 TOTAL multiples: There are 14 multiples of 7 in the first deck. There are 21 multiples of 7 in the second deck. Pulling 1 card from both decks, the probability of pulling two multiples of 7 is: (14/100)(21/150) While this might look "scary", you can reduce BOTH fractions before you multiply. The answer choices hint that the product will reduce anyway... (14/100) = 7/50 (21/150) = 7/50 (7/50)(7/50) = (7^2)/2500 Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: There are 2 decks of cards. The first deck has a 100 cards labelled...  [#permalink]

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03 Feb 2015, 21:46
was time consuming to find number of multiples in two intervals

1-100: 98-7/7+1=14

101-250: 245-105/7+1=21

14/100*21/150=2*7*3*7/15000=7^2*6/15000=7^2/2500

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Re: There are 2 decks of cards. The first deck has a 100 cards labelled...  [#permalink]

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03 Feb 2015, 21:57
1
kdatt1991 wrote:
There are 2 decks of cards. The first deck has a 100 cards labelled with integers from 1 to 100. The second one has 150 cards labelled with integers 101 to 250. If we select one card at random from each deck, what is the probability that numbers on both selected cards will be multiples of 7?

A. $$\frac{7}{3000}$$

B. $$\frac{7}{2500}$$

C. $$\frac{7^2}{15000}$$

D. $$\frac{7^2}{7500}$$

E. $$\frac{7^2}{2500}$$

Could someone please explain the answer to this question. It will be much appreciated, thank you

Multiples of 7 in 1 - 100:
7, 14, ..., 98
7*1 to 7*14 (= 98) gives us 14 multiples.

Multiples of 7 in 101 - 250
105, 112, ..., 245
7*15 (=105) to 7*35 (= 245) gives us 35 - 15 + 1 = 21 multiples

Probability of picking a multiple of 7 in both cases = (14/100) * (21/150) = 7^2/2500

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Re: There are 2 decks of cards. The first deck has a 100 cards labelled...  [#permalink]

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12 Oct 2017, 17:06
kdatt1991 wrote:
There are 2 decks of cards. The first deck has a 100 cards labelled with integers from 1 to 100. The second one has 150 cards labelled with integers 101 to 250. If we select one card at random from each deck, what is the probability that numbers on both selected cards will be multiples of 7?

A. $$\frac{7}{3000}$$

B. $$\frac{7}{2500}$$

C. $$\frac{7^2}{15000}$$

D. $$\frac{7^2}{7500}$$

E. $$\frac{7^2}{2500}$$

Let’s determine the number of multiples of 7 from 1 to 100 and from 101 to 250.

From 1 to 100: (Note that the greatest multiple of 7 is 98 and the smallest multiple of 7 is 7.)

(98 - 7)/7+ 1 = 91/7 + 1 = 14

From 101 to 250: (Note that the greatest multiple of 7 is 245 and the smallest multiple of 7 is 105.)

(245 - 105)/7+ 1 = 140/7 + 1 = 21

Thus, the probability of selecting a multiple of 7 in the first set of cards is 14/100, and in the second set it is 21/150. We want the probability that both selected cards will contain multiples of 7, so we multiply the two probabilities to determine the total probability: 14/100 x 21/150 = (14 x 21)/(100 x 150) = (7 x 7)/(50 x 50) = 7^2/2500.

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Re: There are 2 decks of cards. The first deck has a 100 cards labelled... &nbs [#permalink] 12 Oct 2017, 17:06
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