GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 24 May 2020, 21:42

### 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

# Set A contains three different positive odd integers and two

Author Message
TAGS:

### Hide Tags

Current Student
Joined: 18 Jul 2013
Posts: 73
Location: Italy
GMAT 1: 600 Q42 V31
GMAT 2: 700 Q48 V38
GPA: 3.75
Set A contains three different positive odd integers and two  [#permalink]

### Show Tags

03 Aug 2014, 11:05
2
12
00:00

Difficulty:

25% (medium)

Question Stats:

75% (02:05) correct 25% (02:07) wrong based on 259 sessions

### HideShow timer Statistics

Set A contains three different positive odd integers and two different positive even integers; set B contains two different positive odd integers and three different positive even integers. If one integer from set A and one integer from set B are chosen at random, what is the probability that the product of the chosen integers is even?

(A) 6/25
(B) 2/5
(C) 1/2
(D) 3/5
(E) 19/25
Intern
Joined: 19 Oct 2013
Posts: 7
GMAT Date: 09-17-2014
GPA: 2.93
WE: Information Technology (Computer Software)
Re: Set A contains three different positive odd integers and two  [#permalink]

### Show Tags

03 Aug 2014, 11:33
7
oss198 wrote:
Set A contains three different positive odd integers and two different positive even integers; set B contains two different positive odd integers and three different positive even integers. If one integer from set A and one integer from set B are chosen at random, what is the probability that the product of the chosen integers is even?

(A) 6/25
(B) 2/5
(C) 1/2
(D) 3/5
(E) 19/25

My approach- probability of product even(P(E)) = 1- probability of product odd(P(O))

Odd product is possible only when an integer picked from both sets is odd, so..

P(O) = (3c1* 2c1)/5c1*5c1
= 6/25
P(E) = 1-6/25 = 19/25.

Hope it helps
##### General Discussion
Manager
Joined: 24 Mar 2010
Posts: 71
Re: Set A contains three different positive odd integers and two  [#permalink]

### Show Tags

09 Aug 2014, 00:43
3
oss198 wrote:
Set A contains three different positive odd integers and two different positive even integers; set B contains two different positive odd integers and three different positive even integers. If one integer from set A and one integer from set B are chosen at random, what is the probability that the product of the chosen integers is even?

(A) 6/25
(B) 2/5
(C) 1/2
(D) 3/5
(E) 19/25

Another approach:

P (product of 2 chosen integers is even) = P(E&E) + P(E&O) + P (O&E) = 2/5*3/5 + 2/5*2/5 + 3/5*3/5 = 19/25
_________________
Start to fall in love with GMAT <3
Tutor
Joined: 20 Apr 2012
Posts: 98
Location: Ukraine
GMAT 1: 690 Q51 V31
GMAT 2: 730 Q51 V38
WE: Education (Education)
Re: Set A contains three different positive odd integers and two  [#permalink]

### Show Tags

10 Aug 2014, 00:42
3
1
Three approaches:
1. Backward (the shortest)
P(product even)=1-P(product odd)=1-P(odd from A)*P(odd from B)=1-3/5*2/5=19/25

2. The previous post
P (product of 2 chosen integers is even) = P(E&E) + P(E&O) + P (O&E) = 2/5*3/5 + 2/5*2/5 + 3/5*3/5 = 19/25

3. Using formula for overlapping sets
P(even from A or even from B)=P(even from A)+P(even from B)-P(even from A and even from B)=2/5+3/5-2/5*3/5=19/25
VP
Joined: 27 May 2012
Posts: 1029
Re: Set A contains three different positive odd integers and two  [#permalink]

### Show Tags

20 Mar 2018, 07:24
oss198 wrote:
Set A contains three different positive odd integers and two different positive even integers; set B contains two different positive odd integers and three different positive even integers. If one integer from set A and one integer from set B are chosen at random, what is the probability that the product of the chosen integers is even?

(A) 6/25
(B) 2/5
(C) 1/2
(D) 3/5
(E) 19/25

Actually what this question means is that all the elements are unique both within set A and also with respect to set B

Consider the following scenarios:
Scenario 1:
Set A :{ 1,3,5,2,4} Set B: {1,3,2,4,6} Here all the elements within a set are unique BUT are NOT unique with respect to the other set.
Required probability : $$\frac{3}{5}$$

Scenario 2:
Set A :{ 1,3,5,4,6} Set B: {7,9,8,10,12} Here all the elements within a set are unique AND are also unique with respect to the other set.
Required probability : $$\frac{19}{25}$$
_________________
- Stne
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3367
Re: Set A contains three different positive odd integers and two  [#permalink]

### Show Tags

25 Mar 2018, 10:39

Solution

If the multiplication of two integers has to be even, then at least 1 integer between the two must be even.

Thus, we can calculate the probability of the product of two integers, one from set A and another from set B, to be even in two ways.

P(A-even) * P (B- odd) + P(A-odd) * P (B- even) + P(A-even) * P (B- even), OR,
1- P (A- odd) * P (B- odd)

Surely, the 2nd method needs very little calculation.
• P (A- odd) = $$\frac{3}{5}$$
• P (B- odd) = $$\frac{2}{5}$$
• 1- P (A- odd) * P (B- odd) = 1- ($$\frac{3}{5}$$) * ($$\frac{2}{5}$$) = $$\frac{19}{25}$$

_________________
Senior SC Moderator
Joined: 22 May 2016
Posts: 3847
Set A contains three different positive odd integers and two  [#permalink]

### Show Tags

25 Mar 2018, 14:03
oss198 wrote:
Set A contains three different positive odd integers and two different positive even integers; set B contains two different positive odd integers and three different positive even integers. If one integer from set A and one integer from set B are chosen at random, what is the probability that the product of the chosen integers is even?

(A) 6/25
(B) 2/5
(C) 1/2
(D) 3/5
(E) 19/25

Calculating the probability of getting an odd product seems easier.

Only one combination yields odd: odd * odd

P(odd) from set A = $$\frac{3}{5}$$

P(odd) from set B =$$\frac{2}{5}$$

$$\frac{3}{5}*\frac{2}{5}=\frac{6}{25}$$

The products are either even or odd. Probability of an even or odd product = 1, so

P(even) = 1 - P(odd)
$$\frac{25}{25}-\frac{6}{25}=\frac{19}{25}$$

_________________
Visit SC Butler, here! Get two SC questions to practice, whose links you can find by date.

Our lives begin to end the day we become silent about things that matter. -- Dr. Martin Luther King, Jr.
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2799
Re: Set A contains three different positive odd integers and two  [#permalink]

### Show Tags

05 Apr 2018, 10:04
oss198 wrote:
Set A contains three different positive odd integers and two different positive even integers; set B contains two different positive odd integers and three different positive even integers. If one integer from set A and one integer from set B are chosen at random, what is the probability that the product of the chosen integers is even?

(A) 6/25
(B) 2/5
(C) 1/2
(D) 3/5
(E) 19/25

We can use the formula:

1 - P(odd product) = P(even product)

We may recall that odd x odd = odd.

P(odd from set A) = 3/5

P(odd from set B) = 2/5

P(odd product) = 3/5 x 2/5 = 6/25

P(even product) = 1 - 6/25 = 19/25

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com
202 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User
Joined: 09 Sep 2013
Posts: 14968
Re: Set A contains three different positive odd integers and two  [#permalink]

### Show Tags

05 Apr 2019, 15:41
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Set A contains three different positive odd integers and two   [#permalink] 05 Apr 2019, 15:41