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Math Expert V
Joined: 02 Sep 2009
Posts: 59721
A certain rectangular box A, has height of x units, length of y units  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 42% (02:42) correct 58% (02:59) wrong based on 84 sessions

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Fresh GMAT Club Tests' Question:

A certain rectangular box A, has height of x units, length of y units and width of z units, where x, y, and z are positive integers. A second rectangular box B, has each of its dimensions - height, length and width, 50 percent smaller than that of rectangular box A. If the surface ares of rectangular box B is 2.5 unit^2, what is the volume of rectangular box A?

A. 1/4 unit^3
B. 1 unit^3
C. 2 unit^3
D. 4 unit^3
E. 10 unit^3

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 59721
Re: A certain rectangular box A, has height of x units, length of y units  [#permalink]

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Bunuel wrote:

Fresh GMAT Club Tests' Question:

A certain rectangular box A, has height of x units, length of y units and width of z units, where x, y, and z are positive integers. A second rectangular box B, has each of its dimensions - height, length and width, 50 percent smaller than that of rectangular box A. If the surface ares of rectangular box B is 2.5 unit^2, what is the volume of rectangular box A?

A. 1/4 unit^3
B. 1 unit^3
C. 2 unit^3
D. 4 unit^3
E. 10 unit^3

Check other 3-D Geometry Questions in our Special Questions Directory.
_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 59721
Re: A certain rectangular box A, has height of x units, length of y units  [#permalink]

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Bunuel wrote:

Fresh GMAT Club Tests' Question:

A certain rectangular box A, has height of x units, length of y units and width of z units, where x, y, and z are positive integers. A second rectangular box B, has each of its dimensions - height, length and width, 50 percent smaller than that of rectangular box A. If the surface ares of rectangular box B is 2.5 unit^2, what is the volume of rectangular box A?

A. 1/4 unit^3
B. 1 unit^3
C. 2 unit^3
D. 4 unit^3
E. 10 unit^3

_________________
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5483
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
A certain rectangular box A, has height of x units, length of y units  [#permalink]

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1
Bunuel wrote:

Fresh GMAT Club Tests' Question:

A certain rectangular box A, has height of x units, length of y units and width of z units, where x, y, and z are positive integers. A second rectangular box B, has each of its dimensions - height, length and width, 50 percent smaller than that of rectangular box A. If the surface ares of rectangular box B is 2.5 unit^2, what is the volume of rectangular box A?

A. 1/4 unit^3
B. 1 unit^3
C. 2 unit^3
D. 4 unit^3
E. 10 unit^3

sides of box b = x/2,y/2 and z/2

TSA = 2/4(xy+xz+zy)=2.5
or say (xy+xz+zy)= 5

since given that x,y,z are integers
so x=2,y=z=1
so volume would be 2*1*1= 2 IMO c

Originally posted by Archit3110 on 24 Dec 2018, 07:01.
Last edited by Archit3110 on 25 Dec 2018, 01:42, edited 1 time in total.
Senior PS Moderator D
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
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GMAT 1: 740 Q50 V40 GMAT 2: 770 Q51 V42 Re: A certain rectangular box A, has height of x units, length of y units  [#permalink]

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You got the whole solution correct except for the last step which would be 2*1*1 = 2 unit^2

Hence Option (C) is correct.

Best,
Archit3110 wrote:
sides of box b = x/2,y/2 and z/2

TSA = 2/4(xy+xz+zy)=2.5
or say (xy+xz+zy)= 5

since given that x,y,z are integers
so x=2,y=z=1
so volume would be 2*2*1= 4 IMO D

_________________
Regards,

“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5483
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: A certain rectangular box A, has height of x units, length of y units  [#permalink]

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wish you merry xmas.. You got the whole solution correct except for the last step which would be 2*1*1 = 2 unit^2

Hence Option (C) is correct.

Best,
Archit3110 wrote:
sides of box b = x/2,y/2 and z/2

TSA = 2/4(xy+xz+zy)=2.5
or say (xy+xz+zy)= 5

since given that x,y,z are integers
so x=2,y=z=1
so volume would be 2*2*1= 4 IMO D
Director  P
Joined: 24 Nov 2016
Posts: 971
Location: United States
Re: A certain rectangular box A, has height of x units, length of y units  [#permalink]

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Bunuel wrote:

Fresh GMAT Club Tests' Question:

A certain rectangular box A, has height of x units, length of y units and width of z units, where x, y, and z are positive integers. A second rectangular box B, has each of its dimensions - height, length and width, 50 percent smaller than that of rectangular box A. If the surface ares of rectangular box B is 2.5 unit^2, what is the volume of rectangular box A?

A. 1/4 unit^3
B. 1 unit^3
C. 2 unit^3
D. 4 unit^3
E. 10 unit^3

SA of a rectangular box: 2(LW+LH+WH)
V of a rectangular box: LWH

SA of B:
2(0.5*0.5(xy)+0.5*0.5(xz)+0.5*0.5(yz))=2.5
2(0.5*0.5(xy+xz+yz)=2.5
2*1/4(xy+xz+yz)=2.5
(xy+xz+yz)=2.5*2=5
(xy+xz+yz)=(2*1+2*1+1*1)=5
(x,y,z)=(2,1,1)

V of A: xyz=2*1*1=2

Ans (C) Re: A certain rectangular box A, has height of x units, length of y units   [#permalink] 11 Nov 2019, 09:16
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