Let U = 2*2004^2005, V = 2004^2005, W = 2003*2004^2004, X = 2*2004^200

Question

Let:

U = 2*2004^{2005} ,

V = 2004^{2005} ,

W = 2003*2004^{2004} ,

X = 2*2004^{2004} ,

Y = 2004^{2004} ,

Z = 2004^{2003} .

Which of the following is the largest?

(A) U - V
(B) V - W
(C) W - X
(D) X - Y
(E) Y - Z

Archit3110 · Answer

solving for all the given options we observe option A is the largest
2004^2005 * 1 
IMO A

GMATWhizTeam · Answer

Solution:  
We will have to solve every option manually and check which one is the largest.

Option A:  U- V

U- V = 2*2004^{2005} – 2004^{2005} = 2004^{2005}(2-1) = 2004^{2005}

Option B:  V – W

V- W = 2004^{2005} – 2003*2004^{2004} =2004^{2004}(2004 – 2003) = 2004^{2004}

Option C:  W – X

W-X = 2003*2004^{2004} – 2* 2004^{2004} = 2004^{2004} (2003-2) = 2001*2004^{2004}

Option D:  X-Y

X-Y = 2*2004^{2004} – 2004^{2004} = 2004^{2004}(2-1) = 2004^{2004}

Option E:  Y -Z

Y-Z =2004^{2004} - 2004^{2003} = 2004^{2003}(2004-1) = 2003*2004^{2003}

• We can see that;

o  U-V > W- X > V-W=X-Y>Y-Z

Hence, the correct answer is  Option A.

gracex · Answer

I found the answer with a shortcut, not sure if it works all the time though

I intuitively assumed that the answer would have the largest value as the first value in the subtraction. I first compared all of the choices with U, then found that no option is bigger than U, thus I eliminated all of the options that began with something other than "U-", then I double-checked my answer and went with A

bumpbot · Answer

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Let U = 22004^2005, V = 2004^2005, W = 20032004^2004, X = 2*2004^200

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