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# If y is an integer, is 3^y/10000 > 1

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Re: If y is an integer, is 3^y/10000 > 1 [#permalink]
is the power of 3 from d questn (y/10000)? or the whole of 3^y) / 10000?

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Re: If y is an integer, is 3^y/10000 > 1 [#permalink]
If its the former. then A is sufficienf

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Re: If y is an integer, is 3^y/10000 > 1 [#permalink]
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AkshdeepS wrote:
If y is an integer, is 3^y/10000 > 1?

1. 100/10^y < 0.01

2.$$\sqrt{3y} = 243$$

Source : Barron's GMAT

Are you sure the OA is correct?

Here's what I did:
Given: y is an integer
To find: is $$\frac{3^y}{10000}$$ > 1 Yes/No question

Statement (1): $$\frac{100}{10^y}$$ < 0.01
For this statement to work, y≥5
If y=5, $$\frac{3^5}{10000}$$ < 1 NO
If y=6, $$\frac{3^6}{10000}$$ < 1 NO
We can get YES if y increases.

Statement (2): $$\sqrt{3y} = 243$$
Squaring both the sides, 3y=243*243 => y= 81*243 = some big number and $$\frac{3^y}{10000}$$ > 1 YES as numerator will be greater. SUFFICIENT!

Please recheck the question and OA.
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Re: If y is an integer, is 3^y/10000 > 1 [#permalink]
I'll post how I did it. I hope it will help

The value is $$\frac{3^{y}}{1000} > 1$$ because there's no parenthesis. Exponents are prioritary

$$<=> 3^{y} > 1000$$

(Optionnal Part) :

$$<=> y = \frac{1000}{log(3)}$$ (all the log(x) for every 0 < x < 1 are inferior to 1.

$$<=> y > 1000$$

(1) :

$$\frac{100}{10^y} < 0.01$$

$$<=> 100 < 0.01 * 10^{y}$$

$$<=> \frac{100^{2}}{10^{-3}} < 10^{y}$$

$$<=> 100^{5} < 10^{y}$$

$$<=> 5 < y$$

$$<=> y > 5$$

Which is Sufficient to conclude whether of not the statement is true or false

(2)

$$\sqrt{3y} = 243$$

$$<=> y = \frac{243^{2}}{3}$$

(Optionnal Part) :

$$200^{2} = 4 00 00$$

$$<=> y > 10000$$ (approximately)

Which is Sufficient to conclude whether of not the statement is true or false
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Re: If y is an integer, is 3^y/10000 > 1 [#permalink]
AkshdeepS wrote:
If y is an integer, is 3^y/10000 > 1?

1. 100/3^y < 0.01

2.$$\sqrt{3y} = 243$$

Statement 1 edited. Inconvenience regretted. It was not 10^y but 3^y.

Thank you.

Source : Barron's GMAT

Statement 1 edited.
Re: If y is an integer, is 3^y/10000 > 1 [#permalink]
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