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# If x is an integer, is 3^x less than 500?

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Re: If x is an integer, is 3^x less than 500? [#permalink]
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for both the value of x in statement 2 i.e -6 and 6, statement 3x<500 is yes. Then why isnt the answer b?

I see. we are interpreting the question differently. The main statement is 3x in the question not 3 RAISED TO THE POWER X.

If 3x, in that case answer is b otherwise its c.

It's $$3^x$$, NOT $$3x$$. That's what the first post says as well as my solution above.
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If x is an integer, is 3^x less than 500? [#permalink]
Bunuel wrote:
If x is an integer, is 3^x less than 500?

Since $$3^6=729>500$$ and $$3^5=243<500$$, then the question basically asks whether x is an integer less than 6 (5, 4, 3, 2, 1, 0, -1, ...).

(1) 4^(x–1) < 4^x – 120;

$$\frac{4^x}{4}<4^x-120$$;

$$120<\frac{3}{4}*4^x$$;

$$160<4^x$$;

x is an integer greater than 3: 4, 5, 6, 7, ... Not sufficient.

(2) x^2 = 36 --> $$x=6$$ or $$x=-6$$. Not sufficient.

(1)+(2) From above $$x=6$$, thus the answer to the question is NO. Sufficient.

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Hope it helps.

Can you please elaborate the steps for statement 1?
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If x is an integer, is 3^x less than 500? [#permalink]
AmanMatta wrote:
Can you please elaborate the steps for statement 1?

$$4^{(x–1)} < 4^x – 120$$;

$$\frac{4^x}{4}<4^x-120$$;

Add 120 to both sides: $$\frac{4^x}{4}+120<4^x$$;

Subtract 4^x/4 from both sides: $$20<4^x-\frac{4^x}{4}$$;

$$120<\frac{3}{4}*4^x$$;

Multiply by 4/3: $$160<4^x$$;

x is an integer greater than 3: 4, 5, 6, 7, ... Not sufficient.
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Re: If x is an integer, is 3^x less than 500? [#permalink]
Bunuel - can you explain to me how did 4^(x–1) become 4x/4?
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Re: If x is an integer, is 3^x less than 500? [#permalink]
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anindhya25 wrote:
Bunuel - can you explain to me how did 4^(x–1) become 4x/4?

$$4^{(x–1)}=4^x*4^{-1}= 4^x*\frac{1}{4}=\frac{4^x}{4}$$
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If x is an integer, is 3^x less than 500? [#permalink]
Bunuel wrote:
If x is an integer, is 3^x less than 500?

Since $$3^6=729>500$$ and $$3^5=243<500$$, then the question basically asks whether x is an integer less than 6 (5, 4, 3, 2, 1, 0, -1, ...).

(1) 4^(x–1) < 4^x – 120;

$$\frac{4^x}{4}<4^x-120$$;

$$120<\frac{3}{4}*4^x$$;

$$160<4^x$$;

x is an integer greater than 3: 4, 5, 6, 7, ... Not sufficient.

(2) x^2 = 36 --> $$x=6$$ or $$x=-6$$. Not sufficient.

(1)+(2) From above $$x=6$$, thus the answer to the question is NO. Sufficient.

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Hope it helps.

3^(-6) is also less than 500 no?
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Re: If x is an integer, is 3^x less than 500? [#permalink]
Chanovski wrote:
Bunuel wrote:
If x is an integer, is 3^x less than 500?

Since $$3^6=729>500$$ and $$3^5=243<500$$, then the question basically asks whether x is an integer less than 6 (5, 4, 3, 2, 1, 0, -1, ...).

(1) 4^(x–1) < 4^x – 120;

$$\frac{4^x}{4}<4^x-120$$;

$$120<\frac{3}{4}*4^x$$;

$$160<4^x$$;

x is an integer greater than 3: 4, 5, 6, 7, ... Not sufficient.

(2) x^2 = 36 --> $$x=6$$ or $$x=-6$$. Not sufficient.

(1)+(2) From above $$x=6$$, thus the answer to the question is NO. Sufficient.

Similar questions to practice:
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https://gmatclub.com/forum/is-4-x-5-3x- ... 86765.html
https://gmatclub.com/forum/is-5-x-134898.html
https://gmatclub.com/forum/is-3-x-134968.html

Hope it helps.

3^(-6) is also less than 500 no?

Yes, 3^(-6) = 1/3^6, which is less than 1.
Re: If x is an integer, is 3^x less than 500? [#permalink]
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