If $x = \frac{1}{2^2} \cdot 3^2 \cdot 4^2 \cdot 5^2$ is expressed as a decimal, how many distinct nonzero digits will $x$ have?

Correct answer marked below

One

Correct

Two

Three

Seven

Ten

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Explanation

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Comments

NicolásMay 29

Wait, is this really 655-705? I feel like most people would just multiply it out and count digits, which isn't that hard. Am I missing a trick here?

MedhaviJun 12

Yeah, the trap is counting digits of the product before converting to decimal. That's what got me.

UtkarshJun 8

Thanks for this one. I almost picked (B) because I miscounted the distinct nonzero digits in 144. Gotta remember "distinct" means no repeats!

AptiJun 22

Same! I counted 1,4,4 and thought two, then realized it's only 1 and 4. Easy to rush.

KshitizJul 5

Can someone break down the simplification? I got 2^2=4 and 4^2=16, but I'm not seeing how that helps avoid big multiplication with 3^2 and 5^2.

RajeshJul 17

Alternatively, rewrite 4^2 as (2^2)^2 = 2^4, then 2^4/2^2 = 2^2. That's what clicked for me.

TanveerAug 28

This one took me a minute because I started multiplying everything and got a huge number. The decimal part is what makes it tricky.

What this question tests

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

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

If x=122⋅32⋅42⋅52x = \frac{1}{2^2} \cdot 3^2 \cdot 4^2 \cdot 5^2x=221​⋅32⋅42⋅52 is expressed as a decimal, how many distinct nonzero digits will xxx have?