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Senior RC Moderator V
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On a certain two-part test, a student must choose one of 4 short essay  [#permalink]

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3 00:00

Difficulty:   55% (hard)

Question Stats: 60% (02:19) correct 40% (02:20) wrong based on 73 sessions

### HideShow timer Statistics On a certain two-part test, a student must choose one of 4 short essays and one of 2 long essays in Part One, and then choose one of x short essays and one of y long essays in Part Two. If there is a total of 144 different lineups of essays that the student could choose, and the ratio of available long essays to short essays remains constant in both parts of the test, then what is the value of x ?

A. 3
B. 6
C. 8
D. 9
E. 12

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Math Expert V
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Posts: 7764
Re: On a certain two-part test, a student must choose one of 4 short essay  [#permalink]

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1
On a certain two-part test, a student must choose one of 4 short essays and one of 2 long essays in Part One, and then choose one of x short essays and one of y long essays in Part Two. If there is a total of 144 different lineups of essays that the student could choose, and the ratio of available long essays to short essays remains constant in both parts of the test, then what is the value of x ?

A. 3
B. 6
C. 8
D. 9
E. 12

If there is a total of 144 different lineups of essays that the student could choose = 4*2*x*y=144....xy=18

the ratio of available long essays to short essays remains constant in both parts of the test, so x:y=4:2 => 2x=4y...x=2y
xy=(2y)y=18 => $$2y^2=18....y^2=9...y=3$$

Thus x= 18/3=6

B
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Re: On a certain two-part test, a student must choose one of 4 short essay  [#permalink]

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chetan2u wrote:
On a certain two-part test, a student must choose one of 4 short essays and one of 2 long essays in Part One, and then choose one of x short essays and one of y long essays in Part Two. If there is a total of 144 different lineups of essays that the student could choose, and the ratio of available long essays to short essays remains constant in both parts of the test, then what is the value of x ?

A. 3
B. 6
C. 8
D. 9
E. 12

If there is a total of 144 different lineups of essays that the student could choose = 4*2*x*y=144....xy=18

the ratio of available long essays to short essays remains constant in both parts of the test, so x:y=4:2 => 2x=4y...x=2y
xy=(2y)y=18 => $$2y^2=18....y^2=9...y=3$$

Thus x= 18/3=6

B

Hello Chetan sir,

144 lineups = doestnt that mean its the sum of total number of different essays from Part A and B(short n small?

I undertstand from your solution it implies all the different selections from both the parts.

After reading carefully the problem I see,it makes sense:

If there is a total of 144 different lineups of essays that the student could choose

If the question would have omitted the RED part ,how will the solution change.

Will that mean 4+2+x+y= 144??
Math Expert V
Joined: 02 Aug 2009
Posts: 7764
Re: On a certain two-part test, a student must choose one of 4 short essay  [#permalink]

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prabsahi wrote:
chetan2u wrote:
On a certain two-part test, a student must choose one of 4 short essays and one of 2 long essays in Part One, and then choose one of x short essays and one of y long essays in Part Two. If there is a total of 144 different lineups of essays that the student could choose, and the ratio of available long essays to short essays remains constant in both parts of the test, then what is the value of x ?

A. 3
B. 6
C. 8
D. 9
E. 12

If there is a total of 144 different lineups of essays that the student could choose = 4*2*x*y=144....xy=18

the ratio of available long essays to short essays remains constant in both parts of the test, so x:y=4:2 => 2x=4y...x=2y
xy=(2y)y=18 => $$2y^2=18....y^2=9...y=3$$

Thus x= 18/3=6

B

Hello Chetan sir,

144 lineups = doestnt that mean its the sum of total number of different essays from Part A and B(short n small?

I undertstand from your solution it implies all the different selections from both the parts.

After reading carefully the problem I see,it makes sense:

If there is a total of 144 different lineups of essays that the student could choose

If the question would have omitted the RED part ,how will the solution change.

Will that mean 4+2+x+y= 144??

Hi,

I would take different lineups to mean different ways.. The catch here would be different..

If we meant the pool of essay contained 144 essays, then 'there is a total of 144 different lineups of essays' will not fit in. It should be that there are 144 essays lined up to choose from.
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Re: On a certain two-part test, a student must choose one of 4 short essay  [#permalink]

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1
On a certain two-part test, a student must choose one of 4 short essays and one of 2 long essays in Part One, and then choose one of x short essays and one of y long essays in Part Two. If there is a total of 144 different lineups of essays that the student could choose, and the ratio of available long essays to short essays remains constant in both parts of the test, then what is the value of x ?

A. 3
B. 6
C. 8
D. 9
E. 12

different line ups of essay = 144= 4*2*x*y
x*y = 18

given
x=2y
so
2y^2=18
y=3
x= 6
IMO B
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Senior Manager  P
Joined: 09 Jun 2014
Posts: 331
Location: India
Concentration: General Management, Operations
Re: On a certain two-part test, a student must choose one of 4 short essay  [#permalink]

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prabsahi wrote:
chetan2u wrote:
On a certain two-part test, a student must choose one of 4 short essays and one of 2 long essays in Part One, and then choose one of x short essays and one of y long essays in Part Two. If there is a total of 144 different lineups of essays that the student could choose, and the ratio of available long essays to short essays remains constant in both parts of the test, then what is the value of x ?

A. 3
B. 6
C. 8
D. 9
E. 12

If there is a total of 144 different lineups of essays that the student could choose = 4*2*x*y=144....xy=18

the ratio of available long essays to short essays remains constant in both parts of the test, so x:y=4:2 => 2x=4y...x=2y
xy=(2y)y=18 => $$2y^2=18....y^2=9...y=3$$

Thus x= 18/3=6

B

Hello Chetan sir,

144 lineups = doestnt that mean its the sum of total number of different essays from Part A and B(short n small?

I undertstand from your solution it implies all the different selections from both the parts.

After reading carefully the problem I see,it makes sense:

If there is a total of 144 different lineups of essays that the student could choose

If the question would have omitted the RED part ,how will the solution change.

Will that mean 4+2+x+y= 144??

Hi,

I would take different lineups to mean different ways.. The catch here would be different..

If we meant the pool of essay contained 144 essays, then 'there is a total of 144 different lineups of essays' will not fit in. It should be that there are 144 essays lined up to choose from.[/quote]

I got it .Thanks a lot for clarifying.

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Senior Manager  P
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Joined: 05 Feb 2018
Posts: 365
Re: On a certain two-part test, a student must choose one of 4 short essay  [#permalink]

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1) Set up each step:
Part 1 = 4C1 (short) * 2C1 (long) = 8 choices of essays
Part 2 = xC1 (short) * yC1 (long) = xy choice of essays

2) Set up equations:
8xy = 144
Now, we have the ratio S/L = 4/2 so S=2L. It says the ratio of Part 2 is the same so equivalent x=2y

3) Solve equation:
8x(1/2x) = 144
4x² = 144
2x = 12
x = 6 Re: On a certain two-part test, a student must choose one of 4 short essay   [#permalink] 20 Mar 2019, 09:20
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