Given that $$0.0001402 \times 10^q < 5^{-2}$$, and $$q$$ is an integer, which of the following is the largest possible value of $$q$$?

Correct.
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Plug in $$q = 2$$:
>$$0.0001402 \times 10^q$$
>$$= 0.0001402 \times 10^2$$.
Shift the decimal point two places to the right:
>$$= 0.01402$$.
Since 0.01402 is less than 0.04, this is a possible answer choice. The next answer choice, $$q=3$$, will result in 0.1402 (after an additional shift of the decimal point to the right), which is greater than 0.04—too big, in fact. Therefore, $$q=2$$ is the greatest possible value for $$q$$, and this answer choice is indeed the correct one.

Incorrect.
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__Plug In__ $$q = 3$$:
>$$0.0001402 \times 10^q < 5^{-2}$$
>$$ 0.0001402 \times 10^3 \stackrel{?}{<} \frac{1}{ 5^2}$$
>$$ 0.1402 \stackrel{?}{<} \frac{1}{25}$$
>$$0.1402 \nless 0.04$$.
Since 0.1402 is *not* less than 0.04, eliminate this answer choice.

Incorrect.
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__Plug In__ $$q = 4$$:
>$$0.0001402 \times 10^q < 5^{-2}$$
>$$0.0001402 \times 10^4 \stackrel{?}{<} \frac{1}{ 5^2}$$
>$$1.402 \stackrel{?}{<} \frac{1}{25}$$
>$$1.402 \nless 0.04$$.
Since 1.402 is *not* less than 0.04, eliminate this answer choice.

Incorrect.
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__Plug In__ $$q= 5$$:
>$$0.0001402 \times 10^q < 5^{-2}$$
>$$0.0001402 \times 10^5 \stackrel{?}{<} \frac{1}{5^2}$$
>$$14.02 \stackrel{?}{<} \frac{1}{25}$$
>$$14.02 \nless 0.04$$.
Since 14.02 is *not* less than 0.04, eliminate this answer choice.

Incorrect.
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The number 1 is indeed a possible value of $$q$$, but it is not the *largest* possible value in which $$0.0001402 \times 10^q < 5^{-2}$$.
Hence, this is not the correct answer. Look for a bigger number that is also possible.

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