A certain rectangular box A, has height of x units, length of y units

Question

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

M37-06

Bunuel · Accepted Answer

Official Solution:

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 area of rectangular box B is 2.5  unit^2 , what is the volume of rectangular box A?

A.  \frac{1}{4} \ unit^3 
B.  1 \ unit^3 
C.  2 \ unit^3 
D.  4 \ unit^3 
E.  10 \ unit^3

We need to find  Volume_A=xyz , while given that  Surface \ area_B = 2*(\frac{x}{2}*\frac{y}{2} +\frac{x}{2}*\frac{z}{2}+\frac{y}{2}*\frac{z}{2})=2.5 .
 
Simplify  2*(\frac{x}{2}*\frac{y}{2} +\frac{x}{2}*\frac{z}{2}+\frac{y}{2}*\frac{z}{2})=2.5 :
 
 xy+xz+yz=5 
 
Recall that we are given that  x ,  y , and  z  are positive integers. 5 is small enough number to quickly get by testing numbers that  (x, y, z) =(2, 1, 1)  in any order. 
 
 Volume_A=xyz=2 .

Answer: C

Bunuel · Answer

Check other  3-D Geometry Questions  in our  Special Questions Directory .

Bunuel · Answer

Par of  GMAT CLUB'S New Year's Quantitative Challenge Set

Archit3110 · Answer

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

Gladiator59 · Answer

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,
Gladi

Archit3110 · Answer

Thanks Gladiator59 wish you merry xmas..

exc4libur · Answer

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)

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

A certain rectangular box A, has height of x units, length of y units

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A certain rectangular box A, has height of x units, length of y units

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards