Last visit was: 24 Jul 2024, 15:02 It is currently 24 Jul 2024, 15:02
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
User avatar
Intern
Intern
Joined: 19 Sep 2014
Posts: 19
Own Kudos [?]: 176 [12]
Given Kudos: 7
Concentration: Finance, Economics
GMAT Date: 05-05-2015
Send PM
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11485
Own Kudos [?]: 34585 [3]
Given Kudos: 325
Send PM
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11797 [3]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Senior Manager
Senior Manager
Joined: 23 Jan 2013
Posts: 424
Own Kudos [?]: 269 [0]
Given Kudos: 43
Schools: Cambridge'16
Re: There are 2 decks of cards. The first deck has a 100 cards labelled... [#permalink]
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

E
Tutor
Joined: 16 Oct 2010
Posts: 15148
Own Kudos [?]: 66848 [1]
Given Kudos: 436
Location: Pune, India
Send PM
Re: There are 2 decks of cards. The first deck has a 100 cards labelled... [#permalink]
1
Kudos
Expert Reply
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

Answer (E)
Target Test Prep Representative
Joined: 04 Mar 2011
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Posts: 3036
Own Kudos [?]: 6626 [0]
Given Kudos: 1646
Send PM
Re: There are 2 decks of cards. The first deck has a 100 cards labelled... [#permalink]
Expert Reply
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.

Answer: E
Manager
Manager
Joined: 29 Aug 2023
Posts: 141
Own Kudos [?]: 69 [0]
Given Kudos: 13
Send PM
Re: There are 2 decks of cards. The first deck has a 100 cards labelled... [#permalink]
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 multiples of 7

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 multiples of 7

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.

Now, 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.

Answer: E
GMAT Club Bot
Re: There are 2 decks of cards. The first deck has a 100 cards labelled... [#permalink]
Moderator:
Math Expert
94609 posts