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# On a certain two-part test, a student must choose one of 4 short essay

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

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10 Feb 2019, 02:01
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Difficulty:

45% (medium)

Question Stats:

56% (01:55) correct 44% (02:09) wrong based on 33 sessions

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

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10 Feb 2019, 02:46
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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
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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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10 Feb 2019, 03:11
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
Joined: 02 Aug 2009
Posts: 7334
Re: On a certain two-part test, a student must choose one of 4 short essay  [#permalink]

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10 Feb 2019, 03:23
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.
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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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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10 Feb 2019, 03:33
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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Re: On a certain two-part test, a student must choose one of 4 short essay  [#permalink]

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10 Feb 2019, 04:33
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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Re: On a certain two-part test, a student must choose one of 4 short essay   [#permalink] 10 Feb 2019, 04:33
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