Let:
$U = 2 \cdot 2004^{2005}$ ,
$V = 2004^{2005}$ ,
$W = 2003 \cdot 2004^{2004}$ ,
$X = 2 \cdot 2004^{2004}$ ,
$Y = 2004^{2004}$ ,
$Z = 2004^{2003}$ .
Which of the following is the largest?

Answer Choices

Correct answer marked below

U - V

Correct

V - W

W - X

X - Y

Y - Z

See the full step-by-step explanation

You can see the correct answer above. Sign in for free to unlock the complete worked solution.

Track your performance and improve

Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.

Start for free Sign in

Explanation

Unlock the full explanation

Create a free account to reveal the correct answer, see the step-by-step explanation, and start tracking your GMAT progress.

Create free account Sign in

Comments

EugenioJul 12

Took me a sec to see that factoring out powers of 2004 makes this way easier. Once I rewrote everything in terms of 2004^2003, it was just comparing coefficients. D is definitely the trap answer if you don't simplify.

AdvitiyaJul 14

Exactly! I almost picked D because it looked bigger, but then I realized W - X simplifies to 2002*2004^2004 which is way larger than X - Y.

AptiJul 22

Yep, factoring is key. I did it a bit differently but got the same result. The exponents scared me at first but it's just arithmetic.

SathwikaAug 15

Is there a quick way to compare B and C without fully expanding? I got B = 2003*2004^2004 and C = 2001*2004^2004, so B is larger. But then I compared B with A and got confused.

PratikAug 23

For A: U - V = (2*2004^2005) - 2004^2005 = 2004^2005 = 2004*2004^2004. So A is 2004*2004^2004, B is 2003*2004^2004, so A > B. Then compare A with the others.

ShivamAug 24

This one was tricky but doable. I liked that all the differences have a common factor of 2004^2003. Made the comparison straightforward after that. Good practice for exponent manipulation.

InêsJul 5

Wait, I got A as the largest. Let me check: A = 2004^2005, B = (2004-1)*2004^2004 = 2003*2004^2004, so A = 2004*2004^2004. So A > B. C = (2003*2004 - 2)*2004^2003? Hmm, maybe I need to redo. But I'm pretty sure A is bigger than B, C, D, E. Can someone confirm?

RonJul 16

Yes, A is correct. C simplifies to (2003*2004 - 2)*2004^2003 = (2003*2004 - 2)*2004^2003, which is less than 2004*2004^2004 because 2003*2004 - 2 = 2004^2 - 2004 - 2? Actually, 2003*2004 = 2004^2 - 2004, so minus 2 gives 2004^2 - 2006, which is less than 2004^2. So A is larger.

What this question tests

What it tests

Your fluency with the order of operations, fractions, decimals, and basic number sense — the foundation every quant question leans on.

Common trap

Applying the order of operations out of sequence or rounding intermediate values before the final step.