Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 : GMAT Data Sufficiency (DS)
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# Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35

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Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 [#permalink]

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21 Jun 2011, 23:22
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Is x > 10^10 ?

(1) x > 2^34

(2) x = 2^35

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-x-10-10-1-x-2-34-2-x-127881.html
[Reveal] Spoiler: OA
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Re: Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 [#permalink]

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21 Jun 2011, 23:44
Now we're asked if x > 2^10 * 5^10

(1) says :

x > 2^34

x > 2^10 * 2^24

Because 2^24 > 5^10

So x > 10^10

Sufficient

(2)

x = 2^35 = 2^10 * 2^25

Because 2^25 > 5^10

So x > 10^10

Sufficient

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Re: Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 [#permalink]

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21 Jun 2011, 23:52
subhashghosh wrote:
Now we're asked if x > 2^10 * 5^10

(1) says :

x > 2^34

x > 2^10 * 2^24

Because 2^24 > 5^10

So x > 10^10

Sufficient

(2)

x = 2^35 = 2^10 * 2^25

Because 2^25 > 5^10

So x > 10^10

Sufficient

How did you come up with 2^24 > 5^10???

Did you manually calculate..its tedious to calculate in the exam ...or you know it by heart?
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Re: Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 [#permalink]

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21 Jun 2011, 23:55
2^24 > 5^10 is quite obvious, you can't calculate it without a computer (Btw, I didn't do so). You can reckon that the number of exponents is so big ( > twice that of RHS) that LHS will be > RHS.
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Re: Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 [#permalink]

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21 Jun 2011, 23:58
subhashghosh wrote:
2^24 > 5^10 is quite obvious, you can't calculate it without a computer (Btw, I didn't do so). You can reckon that the number of exponents is so big ( > twice that of RHS) that LHS will be > RHS.

so its more of intuition...i wanted to be sure thats why i asked...i used intuition too but i am scared to do so and would like to confirm
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Re: Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 [#permalink]

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22 Jun 2011, 00:07
I think with huge difference in exponents, it should not be very uncertain.
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Re: Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 [#permalink]

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22 Jun 2011, 00:57
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subhashghosh wrote:
2^24 > 5^10 is quite obvious, you can't calculate it without a computer (Btw, I didn't do so). You can reckon that the number of exponents is so big ( > twice that of RHS) that LHS will be > RHS.

I don't consider that inequality to be obvious at all. If instead you were asked if 2^22 > 5^10 was true, you would be misled if you simply compared the exponents. 2^22 = (2^11)^2 = (2048)^2, whereas 5^10 = (5^5)^2 = (3125)^2, so 5^10 is certainly bigger than 2^22.

I'm not sure there's a convenient way to answer the question in the original post unless you notice that one power of 2, namely 2^10, is very close to a power of 10. Since 2^10 = 1024, then we have:

x > 2^34 = (2^4)(2^10)^3 = 16*(1024)^3 > 16*(10^3)^3 = 16*(10^9) > 10*10^9 = 10^10

so x > 10^10, and Statement 1 is sufficient. It's such a specialized 'trick' that we need here that I don't consider the question particularly valuable to study - you are extremely unlikely to need to do anything similar on the actual GMAT.

Statement 2 is clearly sufficient without doing any work: we know the value of x, so we can compare it to any number at all.

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Re: Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 [#permalink]

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22 Jun 2011, 02:28
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siddhans wrote:
Is x > 10^10 ?

(1) x > 2^34

(2) x = 2^35

x> 1000*1000*1000*10

1.
x> 1024*1024*1024*16
Sufficient.

2.
x= 1024*1024*1024*32
Sufficient.

Ans: "D"
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Re: Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 [#permalink]

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22 Jun 2011, 03:06
fluke wrote:
siddhans wrote:
Is x > 10^10 ?

(1) x > 2^34

(2) x = 2^35

x> 1000*1000*1000*10

1.
x> 1024*1024*1024*16
Sufficient.

2.
x= 1024*1024*1024*32
Sufficient.

Ans: "D"

I agree with fluke,
easiest way of doing this is to think in terms of 2^10.
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Re: Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 [#permalink]

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Re: Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 [#permalink]

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04 Oct 2014, 03:32
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Is x > 10^10 ?

(1) x > 2^34 --> we should compare $$2^{34}$$ and $$10^{10}$$ --> take the square root from both: we should compare $$2^{17}$$ and $$10^5=100,000$$. Now, $$2^{17}=2^{10}*2^7=1,024*128>100,000$$. Sufficient.

OR: $$2^{34}=(2^{10})^{3.4}=(1,024)^{3.4}>(10^3)^{3.4}=10^{(3*3.4)}=10^{10.2}>10^{10}$$.

(2) x = 2^35. Since we have the exact numerical value of x we should be able compare it to 10^10 and answer the question. It really doesn't matter whether 2^35>10^10, the main point is that we have sufficient information to get the answer. Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-x-10-10-1-x-2-34-2-x-127881.html
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Re: Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35   [#permalink] 04 Oct 2014, 03:32
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