GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 14 Oct 2019, 18:33

### 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

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

# If p and q are two distinct numbers chosen from the set ..............

Author Message
TAGS:

### Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3074
If p and q are two distinct numbers chosen from the set ..............  [#permalink]

### Show Tags

30 Jan 2019, 01:43
00:00

Difficulty:

55% (hard)

Question Stats:

44% (01:37) correct 56% (02:42) wrong based on 42 sessions

### HideShow timer Statistics

If p and q are two distinct numbers chosen from the set {-4,-3, -2, -1, 0, 1, 2, 3, 4, 5}. Find the probability that p * q is a prime number.

A. $$\frac{1}{30}$$

B. $$\frac{1}{15}$$

C. $$\frac{1}{9}$$

D. $$\frac{2}{15}$$

E. $$\frac{2}{9}$$

_________________
Intern
Joined: 17 Jan 2019
Posts: 6
Re: If p and q are two distinct numbers chosen from the set ..............  [#permalink]

### Show Tags

30 Jan 2019, 02:07
1
prime factors in the set: -3, -2, 2, 3, 5
Each product with 1 or -1 is also prime.
5*2/10C2=10/45=2/9→(E)

Posted from my mobile device
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4987
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
If p and q are two distinct numbers chosen from the set ..............  [#permalink]

### Show Tags

Updated on: 01 Feb 2019, 09:21
prime no are +ve integer value (2,3,5)
2,3,5 can be formed ( -3,-1) ,( -2,-1), ( 1,2), ( 1,3),(1,5) ; total 5 pairs p*q can be 2 ways; 5*2 = 10

total pairs = 5 and p*q = 10c2
5/10c2 ; 5/45
=1/9
IMOC

EgmatQuantExpert wrote:
If p and q are two distinct numbers chosen from the set {-4,-3, -2, -1, 0, 1, 2, 3, 4, 5}. Find the probability that p * q is a prime number.

A. $$\frac{1}{30}$$

B. $$\frac{1}{15}$$

C. $$\frac{1}{9}$$

D. $$\frac{2}{15}$$

E. $$\frac{2}{9}$$

_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.

Originally posted by Archit3110 on 30 Jan 2019, 07:04.
Last edited by Archit3110 on 01 Feb 2019, 09:21, edited 1 time in total.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3074
Re: If p and q are two distinct numbers chosen from the set ..............  [#permalink]

### Show Tags

01 Feb 2019, 01:57
1
1

Solution

Given:
• A set of 10 integers, {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5}
• p and q are two distinct integers chosen from the given set

To find:
• The probability that p * q is a prime number

Approach and Working:
The total number of ways of choosing two distinct integers from a set of 10 elements = $$^{10}C_2 = 45$$

Now, for p * q to be prime, one of them must be ±1 and the other must be = ± a prime number.
• Thus, the possible cases are {-1, -2}, {-1, -3}, {1, 2}, {1, 3}, {1, 5}

Therefore, probability = $$\frac{5}{45} = \frac{1}{9}$$

Hence the correct answer is Option C.

_________________
Re: If p and q are two distinct numbers chosen from the set ..............   [#permalink] 01 Feb 2019, 01:57
Display posts from previous: Sort by