Last visit was: 21 Nov 2024, 11:35 It is currently 21 Nov 2024, 11:35

Close

GRE Prep 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 GRE 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
Verbal Expert
Joined: 18 Apr 2015
Posts: 30001
Own Kudos [?]: 36335 [1]
Given Kudos: 25926
Send PM
Verbal Expert
Joined: 18 Apr 2015
Posts: 30001
Own Kudos [?]: 36335 [0]
Given Kudos: 25926
Send PM
avatar
Intern
Intern
Joined: 31 May 2024
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 0
Send PM
Verbal Expert
Joined: 18 Apr 2015
Posts: 30001
Own Kudos [?]: 36335 [0]
Given Kudos: 25926
Send PM
M = {6, 5, 4, 3, 2} T = { 2, 1, 0, 1, 2, 3, 4, . . .n}, n is a [#permalink]
Expert Reply
Since the product of the two integers should be negative, we need to select a positive integer from one set and a negative integer from the other set.

Since set M has all terms negative, we need to select the positive integer from set T.

Set T has (n + 3) terms, of which, n are positive.

Number of ways of selecting a negative integer from set \(M = C^5_1 = 5 \)

Number of ways of selecting a positive integer from set \(T =C^n_1 =n\)

Thus, number of favorable cases = 5 x n.

Total number of cases = (# of ways of selecting an integer from set M) x (# of ways of selecting an integer from set T)


\(= C^5_1 \times C^{n+3}_1 = 5 x (n + 3) \)

Thus, required probability


Number of favorable cases/Total number of cases

\(\frac{5n}{5(n+3)}\)

\(\frac{n}{n+3}\)

Thus, we have:

\(\frac{n}{n+3}>\frac{3}{5}\)

\(5n>3n+9\)

\(n>\frac{9}{2}=4.5\)

Among the options, the eligible values for n are 5, 7, 8, and 9.
The correct answers are options B, C, D and E.
Prep Club for GRE Bot
M = {6, 5, 4, 3, 2} T = { 2, 1, 0, 1, 2, 3, 4, . . .n}, n is a [#permalink]
Moderators:
GRE Instructor
83 posts
GRE Forum Moderator
37 posts
Moderator
1111 posts
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne