x=2^30 ,y=3^20,z=6^10
which of the following is closest to xyz
a)(x-1)yz b)x(y-1)z c)xy(z-1) d)can't be determined

• The question is trying to test the reasoning of which number is the biggest number.
  
  Lets consider the following example, to understand that.
  
  Assume a multiplicatin like 19 * 3,
  If I change, 3 to 2 the effect will be much bigger, because it is affecting the other bigger multiple
  If I change 19 to 18, the effect is much smaller.
  
  So, of the three values, if we can subtract 1 from the biggest value, the effect will be smaller,.
  
  So, the entire question is about finding the biggest number
  
  To find the highest,
  
  3^20 can be written as (3^4) ^ 5 which is (81)^5, this is bigger than 2^30, which can be written as (2^6)^5 that is 64 ^ 5
  (81)^5 is also bigger than 6^ 10 which can be written as (36)^5
  
  So, 3^20 is the biggest number and the effect will be smaller when we subtract one from it.
  
  As the effect is smaler that number is closer to XYZ.
  
  So, x(y-1)z is the answer
  option B is the answer
• 11 years agoHelpfull: Yes(76) No(2)
• x=2^30=8^10
  y=3^20=9^10
  z=6^10=6^10
  
  as we observe the value of y is maximum among the all the three values
  in The product xyz subtracting '1' from x,y,z will cause a slight change in the product
  
  for example : 4*5*6=120
  now (4-1)*5*6=90
  4*(5-1)*6=96
  4*5*(6-1)=100
  
  so from the example we can conclude that reducing one from the maximum component will result in less change (closely resembles the actual product)
  
  so reducing 1 from y will be closer to xyz
  
  Thank you
• 11 years agoHelpfull: Yes(20) No(0)
• sorry for last answer
  in options a,b,c
  yz,zx,xy is subtracted from xyz respectively,so result will be closest to xyz
  when smallest of xy,yz,zx is subtracted from xyz
  xy is greatest & zx is lowest
  hence x(y-1)z is closest to xyz
  option(b)
  
• 11 years agoHelpfull: Yes(18) No(2)
• ANS is option:b
  X=2^30=(2^3)^10=8^10
  Y=3^20=(3^2)^10=9^10
  Z=6^10 =6^10
  so X=8,y=9,z=6
  condition XYZ=?(close equal to) xyz=8*9*6=432
  a)(x-1)yz=xyz-yz=432-54=378
  b)x(y-1)z=xyz-z=432-6=426
  c)xy(z-1)=xyz-xy=432-72=360
  so 426 is closet to 432 so ans is :b
• 10 years agoHelpfull: Yes(6) No(0)
• X has the highest power while z has the lowest power...so xyz-yz is greater than other 2 options...so its closer to xyz
• 11 years agoHelpfull: Yes(3) No(1)
• i think ans is (d)can't be determined
  as in options a,b,c
  yz,zx,xy is subtracted from xyz respectively,so result cant be closest to xyz
  as x,y,z are large,values of xy,yz,zx is not so small.
• 11 years agoHelpfull: Yes(2) No(6)
• otion is b
  let us take 2^3 3^2 6^1
  then by option verification b is correct........
• 11 years agoHelpfull: Yes(2) No(0)
• if we solve it then we get xyz=(2^40)*(3^30)
  now let
  xy=(2^30)*(3^20)=a
  yz=(2^10)*(3^30)=b
  xz=(2^40)*(3^10)=c
  now if we compare a and c,then we get
  a=c*{(3^10)/(2^10)}
  here factor {(3^10)/(2^10)} is greater than 1 so we get a>c
  
  similarly when we compare b and c then we get
  b=c*{(3^20)/(2^30)}=c*{(9^10)/(8^10)}
  here factor {(9^10)/(8^10)} is greater than 1 so we get b>c
  
  hence c i.e. xz is smallest among all of them.
• 11 years agoHelpfull: Yes(1) No(0)
• ANS b) is for sure
• 10 years agoHelpfull: Yes(1) No(0)
• shud be
  (b)
• 11 years agoHelpfull: Yes(0) No(1)
• ans is b, which is xyz-xz..
  reason is xz have lowest value than yz and xy.
• 11 years agoHelpfull: Yes(0) No(0)
• xy=2^30*3^20;
  yz=3^20*(3^10*2^10)=3^30*2^10;
  xz=2^30*(3^10*2^10)=3^10*2^40;
  i think xz is smaller than remaining ones.so option b is the answer
• 11 years agoHelpfull: Yes(0) No(0)
• a) (x-1)yz
  
• 11 years agoHelpfull: Yes(0) No(0)
• if we watch crfully thn we cn say dt y>x>z .... so if we minus 1 from z dn d chng of d multipliction is little bit... so ansr should be c.
  
• 11 years agoHelpfull: Yes(0) No(0)
• The value which having the highest when we decrease by 1 then the change before and after will be in the less percentage so that 2nd option is correct answer.....
  
• 11 years agoHelpfull: Yes(0) No(0)
• we have to find smallest one among yz,xz,xy
  
  now yz=3^20.2^10.3^10=2^10.3^30=2^10.(3^3)^10=2^10.27^10=54^10;
  (as 6^10=3^10.2^10)
  xz=2^30.2^10.3^10=2^40.3^10=(2^4)^10.3^10=16^10.3^10=48^10;
  xy=2^30.3^20=(2^3)^10.(3^2)^10=8^10.9^10=72^10;
  
  so xz is smallest
  so b is the correct ans
• 10 years agoHelpfull: Yes(0) No(0)
• xyz-min(xy,yz,zx)
  is near about xyz
  min(xy,yz,zx)=zx
  xyz-zx will be near about xyz
  so option b is correct
• 10 years agoHelpfull: Yes(0) No(0)
• why everyone apply long process
  its simple
  x=2^30= 8^10
  y=3^20=9^10
  z=6^10
  so in x,y,z
  y is big so if we substract 1 in y
  does'nt matter lot
  so option is B is corect
• 8 years agoHelpfull: Yes(0) No(0)