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

 It is currently 19 Oct 2019, 12:48

### 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

# In the next Cricket World Cup T-20, Team A has decided to score 200

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Aug 2009
Posts: 7984
In the next Cricket World Cup T-20, Team A has decided to score 200  [#permalink]

### Show Tags

04 Apr 2016, 07:15
2
3
00:00

Difficulty:

85% (hard)

Question Stats:

37% (01:51) correct 63% (02:24) wrong based on 84 sessions

### HideShow timer Statistics

In the next Cricket World Cup T-20, Team A has decided to score 200 runs only through 4s and 6s. In how many ways can the Team A score these 200 runs?

A. 13
B. 15
C. 16
D. 17
E. 18

Kudos for BEST and SHORTEST Method..

_________________
Manager
Joined: 08 Aug 2015
Posts: 55
Re: In the next Cricket World Cup T-20, Team A has decided to score 200  [#permalink]

### Show Tags

04 Apr 2016, 07:22
4x + 6y = 200...Sorry, no idea how to solve this. Very interested in the approach though. Nice questions, thanks for posting!
Marshall & McDonough Moderator
Joined: 13 Apr 2015
Posts: 1684
Location: India
Re: In the next Cricket World Cup T-20, Team A has decided to score 200  [#permalink]

### Show Tags

04 Apr 2016, 07:38
3
Team A can score a maximum of 50 fours and a minimum of 2 fours with an interval or spacing of 3 units to accommodate the 6's.

So the number of fours scored forms an AP 2, 5, 8, ... 50 with a common difference of 3.

Number of ways of scoring 200 only through 4's and 6's = (50 - 2)/3 + 1 = 17

Alternate solution: 4x + 6y = 200 --> 2x + 3y = 100

x = (100 - 3y)/2 --> 100 - 3y should be even. This is possible when 3y is even.

There are 17 even multiples of 3 between 0 and 100.

Intern
Joined: 11 Mar 2014
Posts: 23
Schools: HEC Montreal '20
Re: In the next Cricket World Cup T-20, Team A has decided to score 200  [#permalink]

### Show Tags

04 Apr 2016, 10:28
it takes max 34 balls ( 6* 33= 198 +1*4=202) And max 50 balls by hitting only fours all other combinations are in between hence calculating from 34 balls to 50 balls
ans = 17
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4774
Location: India
GPA: 3.5
Re: In the next Cricket World Cup T-20, Team A has decided to score 200  [#permalink]

### Show Tags

04 Apr 2016, 11:26
1
chetan2u wrote:
In the next Cricket World Cup T-20, Team A has decided to score 200 runs only through 4s and 6s. In how many ways can the Team A score these 200 runs?
A. 13
B. 15
C. 16
D. 17
E. 18

Self Made : OA - 2 days
Kudos for BEST and SHORTEST Method..

IMHO the best way has already been posted by Vyshak just expanding a bit -

The point to remember here is that the No of 4s and 6s must be positive whole numbers.

Further as vp101 has put forward the equation - 4x + 6y = 200

Here substitute x for the minimum value that will yield y as a positive real number as below

Attachment:

Runs.PNG [ 4.86 KiB | Viewed 2549 times ]

Scrutinize U will see a pattern of 4s scored increases in a definite manner { 2, 5 , 8 , 11......50 }

Our goal is to maximize 4s ( That will automatically minimize 6s )

So, count the possible number of 4s (The same can also be calculated by AP formula ) as follows -

Attachment:

4s.PNG [ 5.42 KiB | Viewed 2548 times ]

Though a bit lengthy ( my intentions were just to expand the wonderful explanation provided by Vyshak
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Manager
Joined: 14 May 2014
Posts: 52
Location: India
GMAT 1: 680 Q49 V31
GPA: 3.44
Re: In the next Cricket World Cup T-20, Team A has decided to score 200  [#permalink]

### Show Tags

05 Apr 2016, 08:39
chetan2u wrote:
In the next Cricket World Cup T-20, Team A has decided to score 200 runs only through 4s and 6s. In how many ways can the Team A score these 200 runs?
A. 13
B. 15
C. 16
D. 17
E. 18

Self Made : OA - 2 days
Kudos for BEST and SHORTEST Method..

So together we have 200 runs
1st way->200/4=50...which means this score can be attained in 50 balls (22/6 is not divisible so its not the other way)

2nd way-> (2 fours 32 sixes=200runs),(5 fours 30 sixes) and so on
we can see a pattern here for number of sixes 32 sixes then 30 sixes bla bla bla

so 32/2= 16 ways

combining 1st and 2nd we have 16+1=17 ways
Manager
Joined: 01 Jul 2010
Posts: 58
Location: India
GMAT 1: 660 Q43 V38
GPA: 3.4
Re: In the next Cricket World Cup T-20, Team A has decided to score 200  [#permalink]

### Show Tags

05 Apr 2016, 08:55
1
1
For the combination of 4s and 6s take LCM of 4 and 6.
Dividing 200 by 12 we get 16 ways (With 8 as the remainder)

One cannot score 200 with 6s alone , so its 0 way

One can score 200 with 50 4s, so its 1 way

Total possibilities =16+0+1 =17 ways

Ans D
Math Expert
Joined: 02 Aug 2009
Posts: 7984
Re: In the next Cricket World Cup T-20, Team A has decided to score 200  [#permalink]

### Show Tags

05 Apr 2016, 19:59
chetan2u wrote:
In the next Cricket World Cup T-20, Team A has decided to score 200 runs only through 4s and 6s. In how many ways can the Team A score these 200 runs?
A. 13
B. 15
C. 16
D. 17
E. 18

Self Made : OA - 2 days
Kudos for BEST and SHORTEST Method..

Hi,

The equation made is 4x + 6y =200 OR 2x+3y=`100....
FROM 2x + 3y = 100 we can make out y has to be even...
so 3y will be a multiple of 6...

now 100 - multiple of 6 will be div by 2..
How many such numbers are there?
100/6 = 16 numbers..

One more case is when y is 0,
So total 16+1=17 ways

ans D
_________________
Senior Manager
Joined: 13 Oct 2016
Posts: 359
GPA: 3.98
Re: In the next Cricket World Cup T-20, Team A has decided to score 200  [#permalink]

### Show Tags

11 Nov 2016, 06:37
1
1
4x+6y=200

Divide common factor 2

2x+3y=100
3y=100-2x
3y=2(50-x)

y=2n; 50-x=3n => x=50-3n

There is no indication that both 4s and 6s must definitely be used, that means we can use either 4s, or 6s, or 4s and 6s together. So x,y ≥0
From that $$n$$ can take following values:

0, 1, 2 , 3 ….. up to 16 (from 17 $$x$$ becomes negative).

Total number of elements in sequence is 17
Manager
Joined: 17 Feb 2014
Posts: 98
Location: United States (CA)
GMAT 1: 700 Q49 V35
GMAT 2: 740 Q48 V42
WE: Programming (Computer Software)
Re: In the next Cricket World Cup T-20, Team A has decided to score 200  [#permalink]

### Show Tags

12 Nov 2016, 16:41
chetan2u wrote:
In the next Cricket World Cup T-20, Team A has decided to score 200 runs only through 4s and 6s. In how many ways can the Team A score these 200 runs?
A. 13
B. 15
C. 16
D. 17
E. 18

Kudos for BEST and SHORTEST Method..

Not sure why this question has been categorized as "Combinations". All it is asking you is to find out # of pairs of x and y for which the equation $$4x + 6y = 200$$ holds true.

Solution:

We know that x and y have to be non-negative integers.

However, x can not be 0 or 1 as for those values y does not have integer solution (200/6, 196/6 are not integers).

So the minimum value of x for which y has an integer solution is 2 (and corresponding y = 192/6 = 32)

Also note that LCM for (4, 6) is 12, hence every 2 6s can be replaced by 3 4s.

So we increase x by 3 and decrease y by 2 to get the next pair and so on.

1st pair -> (2, 32)
2nd pair -> (5, 30)
3rd pair -> (8, 28)
...
nth pair -> (50, 0)

x => {2, 5, 8, ..., 50}
y => {32, 30, 28, ..., 0}

All we have to do is to use formula for AP on either values of x or values of y to get the value of n.

=> 50 = 2 + 3(n-1) [Last term = 50, First Term = 2; d = 3]
=> n = 17
Intern
Joined: 20 Dec 2014
Posts: 36
Re: In the next Cricket World Cup T-20, Team A has decided to score 200  [#permalink]

### Show Tags

03 Feb 2018, 00:15
raarun wrote:
For the combination of 4s and 6s take LCM of 4 and 6.
Dividing 200 by 12 we get 16 ways (With 8 as the remainder)

One cannot score 200 with 6s alone , so its 0 way

One can score 200 with 50 4s, so its 1 way

Total possibilities =16+0+1 =17 ways

Ans D

Very interesting approach will be trying this on other linear equations problem to see if it works universally,
would you be any chance have further details on this approach?
_________________
Kindly press "+1 Kudos" to appreciate
Director
Joined: 14 Nov 2014
Posts: 599
Location: India
GMAT 1: 700 Q50 V34
GPA: 3.76
Re: In the next Cricket World Cup T-20, Team A has decided to score 200  [#permalink]

### Show Tags

03 Feb 2018, 05:52
solved in this way :
reduce the Eq to : 2x + 3y = 100
now we can have a solution when Y = 0 (only 4 hits ) = 1 , but when x = 0 no solution = 0 ( only 6's )
we can have a integer solution for 2x + 3y = 100 when 3y = even(as 2x will always be even) , that is 3y = 6,12,18.....altogether 16 ways ...
total 16 + 1 = 17
Director
Joined: 31 Jul 2017
Posts: 512
Location: Malaysia
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: In the next Cricket World Cup T-20, Team A has decided to score 200  [#permalink]

### Show Tags

03 Feb 2018, 07:14
chetan2u wrote:
In the next Cricket World Cup T-20, Team A has decided to score 200 runs only through 4s and 6s. In how many ways can the Team A score these 200 runs?

A. 13
B. 15
C. 16
D. 17
E. 18

Kudos for BEST and SHORTEST Method..

Let a be the number of 4's and b be the number of 6's. Here a and b has to non-negative integers.

$$a = 50 - \frac{3b}{2}$$. For a to be positive $$\frac{3b}{2} < 50$$ and b should be even integer.

So, b value will from 0 - 33 and even integer... Total, 17.
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!
Re: In the next Cricket World Cup T-20, Team A has decided to score 200   [#permalink] 03 Feb 2018, 07:14
Display posts from previous: Sort by