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Question of the Day - 22nd August, 2009

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quant-master: Senior | Next Rank: 100 Posts; Posts: 74; Joined: Fri Jul 31, 2009 11:38 am; Thanked: 4 times; Followed by:1 members

Question of the Day - 22nd August, 2009

by quant-master » Fri Aug 21, 2009 9:50 am

In a certain game played with red chips and blue chips, each red chip has a point value of X and each blue chip has a point value of Y, where X>Y and X and Y are positive integers. If a player has 5 red chips and 3 blue chips, what is the average (arithmetic mean ) point value of the 8 chips that the player has?

(1) The average point value of one red chip and one blue chip is 5.
(2) The average point value of the 8 chips that the player has is an integer.

OA will be posted in 24hrs time.

Thanks,
Quant-Master

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Source: Beat The GMAT — Data Sufficiency | Fri Aug 21, 2009 9:50 am

pandeyvineet24: Legendary Member; Posts: 527; Joined: Mon Jun 02, 2008 9:14 am; Location: Atlanta; Thanked: 17 times

by pandeyvineet24 » Fri Aug 21, 2009 3:23 pm

Answer should be E.
FIND (5X + 3Y)/8

Stmt1
(X + Y) / 2 =5
INSUFF

Stmt 2
(5X + 3Y)/8 -- INTEGER
INSUFF

Combine both stmts .. not suff
X = 15, Y = 5 or
X = 11, Y = 9

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shanrizvi: Senior | Next Rank: 100 Posts; Posts: 73; Joined: Tue Aug 11, 2009 2:30 am; Thanked: 2 times; GMAT Score:720

by shanrizvi » Sun Aug 23, 2009 3:42 pm

I think it should be C.

Lets summarize all the information first:

X = Point value of a RED chip
Y = Point value of a BLUE chip

X>Y

X and Y are integers.

The player has 5 RED and 3 BLUE chips. What is the average point value of the 8 chips?

Average point value: (5x+3y)/8

Statement 1: The average point value of one red chip and one blue chip is 5.

(X+Y)/2 = 5
X+Y = 10

As X>Y, (X,Y) can be (9,1), (8,2), (7,3) or (6,4). We cannot determine the average point value. Hence, statement 1 is sufficient.

Statement 2: The average point value of the 8 chips that the player has is an integer.

Lets put the values of (X,Y) into the average point value equation and pick the answer for which we get an integer. You only get an integer for (9,1). Hence, Statement 2 is sufficient.

Edit: The answer is C. (I made a typo earlier on and wrote B instead of C)

Last edited by shanrizvi on Mon Aug 24, 2009 6:07 am, edited 1 time in total.

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ranell: Master | Next Rank: 500 Posts; Posts: 224; Joined: Mon May 04, 2009 2:44 pm; Location: Russia, Moscow; Thanked: 10 times; GMAT Score:730

by ranell » Sun Aug 23, 2009 5:54 pm

Answer should be C.
The average value is calculated as (5X+3Y)/8
1 - not sufficient, as we know only the average of X and Y and cannot count the average value of 8 elements given

2 - not sufficient.... the fact that the average number is integer is all that we have

combine these statements with X>Y and will reach the following variants -
X=9, Y =1 - the average number is an integer
X=8, Y =2 - the average number isn't an integer
X=7, Y =3 - the average number isn't an integer
X=6, Y =4 - the average number isn't an integer
X=5, Y =5 and so on is not possible, as X>Y

The answer is definitely C

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srivas: Senior | Next Rank: 100 Posts; Posts: 76; Joined: Fri Dec 26, 2008 8:18 am; Thanked: 3 times

by srivas » Mon Aug 24, 2009 3:54 am

Stmt1
(X + Y) / 2 =5 so X+Y = 10
INSUFF

Stmt 2
(5X + 3Y)/8 -- INTEGER
INSUFF

both combine x=9 & y=1 gives you an integer

Gmat710,, Hyd

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arbiter: Senior | Next Rank: 100 Posts; Posts: 36; Joined: Mon Jun 09, 2008 9:17 am; Thanked: 2 times

by arbiter » Mon Aug 24, 2009 7:41 am

what is the answer ??

Is it A?

arbiter

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pradeepsarathy: Senior | Next Rank: 100 Posts; Posts: 87; Joined: Wed Jul 09, 2008 7:12 am; Location: Secaucus, New Jersey; Thanked: 3 times; Followed by:1 members; GMAT Score:700

by pradeepsarathy » Mon Aug 24, 2009 12:38 pm

IMO C

We are asked to find (5x+3y)/8

Stmt 1 -
(x+y)/2 = 5
x+y = 10
Plug the above stmt in question stem, we get
(2x+30)/8
Insufficient

Stmt 2 -
Insufficient

Stmt 1 and Stmt 2 -
For (2x+30)/8 to be an integer, X can take any of the following values - 1, 5, 9, 13 ...and so on, provided it satisfies the condition x+y =10(from stmt 1)
But given X>Y , this implies, X can take only one value, which is 9

Hence both stmts are necessary.

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mehravikas: Legendary Member; Posts: 1161; Joined: Mon May 12, 2008 2:52 am; Location: Sydney; Thanked: 23 times; Followed by:1 members

by mehravikas » Tue Aug 25, 2009 1:37 am

IMO - C

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oagostinho: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Tue May 19, 2009 2:38 am; Location: Lisbon; Thanked: 1 times

by oagostinho » Tue Aug 25, 2009 7:55 am

Hi,

IMO E, because, (1) and (2) it is not possible to get one specific value!

What do you think?

cheers!

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ershovici: Senior | Next Rank: 100 Posts; Posts: 91; Joined: Tue Aug 25, 2009 7:50 am; Location: Washington DC; Thanked: 2 times; GMAT Score:600

by ershovici » Tue Aug 25, 2009 8:04 am

option 1 alone as option 2 alone is not suffitient
but if we combine both options:
- the summ of 2 integers devided by 2 is 5 - summ is 10
- from this option only 9*5 and 1*3 give an integer.

so the answer is C or 3

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deepak115: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Mon Aug 03, 2009 2:19 pm

by deepak115 » Tue Aug 25, 2009 8:59 am

C - Both Together are Sufficient !

from Stmt I:

(X+Y)/2 = 5

(5X+3Y)/8 = ?

X = 10-Y

(5(10-Y) + 3Y)/8 = ?

(50 - 2Y) / 8 = ?

(25-Y)/4 = ?

from Stmt II:

(25-Y)/4 is Integer, then 25-Y is divisible by 4

or Y = 1,5,9,13,17,21

Since X+Y = 10, Y is either of 1,5,9

But, Also X > Y, so Y = 1

then X = 9

Ave. can now be calculated !

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quant-master: Senior | Next Rank: 100 Posts; Posts: 74; Joined: Fri Jul 31, 2009 11:38 am; Thanked: 4 times; Followed by:1 members