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

 It is currently 15 Oct 2018, 15:01

### 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

# Cody, an avid basketball player, will always wear one or more of the

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49858
Cody, an avid basketball player, will always wear one or more of the  [#permalink]

### Show Tags

25 Dec 2017, 01:37
00:00

Difficulty:

35% (medium)

Question Stats:

66% (01:19) correct 34% (01:44) wrong based on 39 sessions

### HideShow timer Statistics

Cody, an avid basketball player, will always wear one or more of the following articles of "lucky" clothing to play basketball: an old sweatband, a pair of black tube socks, an old jersey, or his mother's basketball shorts. If Cody is getting dressed to play basketball, how many different combinations of these articles of clothing are possible? (Assume the order of the clothing does not matter.)

A. 256
B. 24
C. 15
D. 12
E. 4

_________________
examPAL Representative
Joined: 07 Dec 2017
Posts: 704
Re: Cody, an avid basketball player, will always wear one or more of the  [#permalink]

### Show Tags

25 Dec 2017, 02:20
Bunuel wrote:
Cody, an avid basketball player, will always wear one or more of the following articles of "lucky" clothing to play basketball: an old sweatband, a pair of black tube socks, an old jersey, or his mother's basketball shorts. If Cody is getting dressed to play basketball, how many different combinations of these articles of clothing are possible? (Assume the order of the clothing does not matter.)

A. 256
B. 24
C. 15
D. 12
E. 4

The difficulty of combinatorial questions is usually in understanding how to do the calculation.
This requires an understanding of the underlying logic, e.g a Logical approach.

Cody has 4 items of clothing and he must choose at least 1 of them.
The simplest way to solve this question is to look at each item of clothing separately and ask 'Will Cody take it?'
That is - he can take or not take the sweatband - 2 options.
He can take or not take the socks - 2 options.
He can take or not take the jersey - 2 options and the same for the shorts - 2 options.
Each of these decisions is independent so multiplying all our options we hav 2*2*2*2 = 16 options.
Since Cody must take at least one item then the option where he takes nothing is impossible so there a total of 16 - 1 = 15 options.

**A different solution would be to just brute force list all the options.
This works because there are only 4 items so there aren't too many different choices.
This approach is very good to avoid wasting time if you tend to get stuck on abstract questions.
_________________

Watch free GMAT tutorials in Math, Verbal, IR, and AWA.

GMAT test takers: Watch now the GMAC interview with the people who write the GMAT test!
We discussed the chances of improving a GMAT score; how important the first questions on the test are; what to do if you don’t have enough time to complete a whole section; and more.

You can watch all the action from the interview here.

BSchool Forum Moderator
Joined: 28 Mar 2017
Posts: 1160
Location: India
GMAT 1: 730 Q49 V41
GPA: 4
Cody, an avid basketball player, will always wear one or more of the  [#permalink]

### Show Tags

25 Dec 2017, 04:00
Bunuel wrote:
Cody, an avid basketball player, will always wear one or more of the following articles of "lucky" clothing to play basketball: an old sweatband, a pair of black tube socks, an old jersey, or his mother's basketball shorts. If Cody is getting dressed to play basketball, how many different combinations of these articles of clothing are possible? (Assume the order of the clothing does not matter.)

A. 256
B. 24
C. 15
D. 12
E. 4

We have 4 items and Cody wears atleast one of them. Thus possible combinations are as follows:
$$4C4$$ + $$4C3$$ + $$4C2$$ + $$4C1$$ = 1+4+6+4 =15
_________________

Kudos if my post helps!

Long And A Fruitful Journey - V21 to V41; If I can, So Can You!!

Preparing for RC my way

My study resources:
1. Useful Formulae, Concepts and Tricks-Quant
2. e-GMAT's ALL SC Compilation
3. LSAT RC compilation
4. Actual LSAT CR collection by Broal
5. QOTD RC (Carcass)
6. Challange OG RC
7. GMAT Prep Challenge RC

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2063
Re: Cody, an avid basketball player, will always wear one or more of the  [#permalink]

### Show Tags

25 Dec 2017, 05:37

Solution

Given :
• Cody can wear one or more of the following articles :
o Old Seatband
o Pair of Black Tube Socks
o Old Jersey

Find:

• We need to find, in how many ways can he get dressed to play basketball.

Approach:

• There are four possible cases:
o Cody wears only one article: 4C1 = 4
o Cody wears two articles: 4C2 = 6
o Cody wears three articles = 4C3 = 4
o Cody wears all the four articles = 4C4 = 1
• Thus, total ways in which Cody can dressed to play basketball = 4 + 6 + 4 + 1 = 15 ways

Thus, the correct answer is Option C.

Thanks,
Saquib
Quant Expert
e-GMAT
_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2063
Re: Cody, an avid basketball player, will always wear one or more of the  [#permalink]

### Show Tags

25 Dec 2017, 05:39

Method 2:

Approach:

While choosing any of the articles, there are two possibilities :
• Either Cody will choose the article OR
• He will not choose to wear it.

o Thus, we can conclude that there are two ways in which an articles may be selected or not selected.

• While dressing up, he may choose or not choose to wear the old seatband in 2 ways
• While dressing up, he may choose or not choose to wear the Pair of Black Tube Socks in 2 ways
• While dressing up, he may choose or not choose to wear the old jersey in 2 ways
• While dressing up, he may choose or not choose to wear the basket ball in 2 ways

o Thus, the total ways to select or not select the 4 items = 2 * 2 * 2 * 2 = 16
o Note: There is only one way in which we do not select any of the items and we need to remove that case from the total cases, because Cody is going to wear atleast one or more of the articles.

• Thus, the total number of ways in which Cody can get dressed to play basketball = 16 – 1 = 15 ways.

Thus, the correct answer is Option C.
_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Re: Cody, an avid basketball player, will always wear one or more of the &nbs [#permalink] 25 Dec 2017, 05:39
Display posts from previous: Sort by

# Cody, an avid basketball player, will always wear one or more of the

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.