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# Given a positive number N, when N is rounded by a certain method (for

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Joined: 04 Sep 2017
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Given a positive number N, when N is rounded by a certain method (for  [#permalink]

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21 Sep 2019, 19:14
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22% (02:28) correct 78% (02:32) wrong based on 32 sessions

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Given a positive number N, when N is rounded by a certain method (for convenience, call it Method Y), the result is $$10^n$$ if and only if n is an integer and $$5*10^{n − 1} ≤ N < 5*10^n$$. In a certain gas sample, there are, when rounded by Method Y, $$10^{21}$$ molecules of $$H_2$$ and also $$10^{21}$$ molecules of $$O_2$$. When rounded by Method Y, what is the combined number of $$H_2$$ and $$O_2$$ molecules in the gas sample?

(1) The number of $$H_2$$ molecules and the number of $$O_2$$ molecules are each less than $$3*10^{21}$$.
(2) The number of $$H_2$$ molecules is more than twice the number of $$O_2$$ molecules.

DS36141.01
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Joined: 02 Aug 2009
Posts: 8004
Re: Given a positive number N, when N is rounded by a certain method (for  [#permalink]

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22 Sep 2019, 07:05
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1
Given a positive number N, when N is rounded by a certain method (for convenience, call it Method Y), the result is $$10^n$$ if and only if n is an integer and $$5*10^{n − 1} ≤ N < 5*10^n$$. In a certain gas sample, there are, when rounded by Method Y, $$10^{21}$$ molecules of $$H_2$$ and also $$10^{21}$$ molecules of $$O_2$$. When rounded by Method Y, what is the combined number of $$H_2$$ and $$O_2$$ molecules in the gas sample?

This means RANGE of both $$H_2$$ and $$O_2$$ will be $$5*10{21-1}<10^{21}<5*10^{21}$$

(1) The number of $$H_2$$ molecules and the number of $$O_2$$ molecules are each less than $$3*10^{21}$$.
We know the range of both as $$5*10{21-1}<10^{21}<5*10^{21}$$.
If both are less than $$2.5*10^{21}$$, answer will be $$10^{21}$$ as the TOTAL will always be less than $$5*{21}$$.
But if both are, say, $$2.6*10^{21}$$, then total is $$5.2^{21}$$, which will get rounded off to $$10^{22}$$.
Insufficient

(2) The number of $$H_2$$ molecules is more than twice the number of $$O_2$$ molecules.
Again various possibilities..
If $$H_2$$ molecules = $$2.6*10^{21}$$ and $$O_2$$ molecules=$$1.3^{21}$$....total will become $$3.9^{21}$$, rounded off to $$10^{21}$$.
But if $$H_2$$ molecules = $$4.8*10^{21}$$ and $$O_2$$ molecules=$$2.4^{21}$$....total will become $$7.2^{21}$$, rounded off to $$10^{22}$$.
Insuff

Combined..
Let us take the MAX value of $$H_2$$ ~ or just less than $$3*10^{21}$$, so max value of $$O_2$$ will be just less than $$1.5*10^{21}$$.
Total = $$4.5*10^{21}$$, rounded off to 10^21..
Thus answer will always be $$10^{21}$$

C
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Re: Given a positive number N, when N is rounded by a certain method (for  [#permalink]

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18 Oct 2019, 15:16
1
$$5*10^{20} ≤ N_h < 5*10^{21}$$
$$5*10^{20} ≤ N_o < 5*10^{21}$$

Statement 1-
$$5*10^{20} ≤ N_h < 3*10^{21}$$......(1)

$$5*10^{20} ≤ N_o < 3*10^{21}$$......(2)

Combining (1) and (2), wen can get the range of $$N_h$$+$$N_o$$.

$$10^{21} ≤ N_h+N_o < 6*10^{21}$$

Case 1- If $$10^{21} ≤ N_h+N_o < 5*10^{21}$$
$$N_h$$+$$N_o$$is rounded off to $$10^{21}$$

Case 2- $$5*10^{21} ≤ N_h+N_o < 6*10^{21}$$
$$N_h$$+$$N_o$$ is rounded off to $$10^{22}$$

Insufficient

Statement 2-
$$10^{21} ≤ N_h < 5*10^{21}$$......(1)

$$0.5*10^{21} ≤ N_o < 2.5*10^{21}$$......(2)

Hence,

$$1.5*10^{21} ≤ N_h+N_o < 7.5*10^{21}$$

Case 1- If $$1.5*10^{21} ≤ N_h+N_o < 5*10^{21}$$
$$N_h$$+$$N_o$$ is rounded off to $$10^{21}$$

Case 2- $$5*10^{21} ≤ N_h+N_o < 7.5*10^{21}$$
$$N_h$$+$$N_o$$ is rounded off to $$10^{22}$$

Insufficient

Combining both statements

$$10^{21} ≤ N_h < 3*10^{21}$$......(1)

$$0.5*10^{21} ≤ N_o < 1.5*10^{21}$$......(2)

$$1.5*10^{21} ≤ N_h+N_o < 4.5*10^{21}$$

Hence, $$N_h$$+$$N_o$$ rounded off to $$10^{21}$$

Sufficient

gmatt1476 wrote:
Given a positive number N, when N is rounded by a certain method (for convenience, call it Method Y), the result is $$10^n$$ if and only if n is an integer and $$5*10^{n − 1} ≤ N < 5*10^n$$. In a certain gas sample, there are, when rounded by Method Y, $$10^{21}$$ molecules of $$H_2$$ and also $$10^{21}$$ molecules of $$O_2$$. When rounded by Method Y, what is the combined number of $$H_2$$ and $$O_2$$ molecules in the gas sample?

(1) The number of $$H_2$$ molecules and the number of $$O_2$$ molecules are each less than $$3*10^{21}$$.
(2) The number of $$H_2$$ molecules is more than twice the number of $$O_2$$ molecules.

DS36141.01
Re: Given a positive number N, when N is rounded by a certain method (for   [#permalink] 18 Oct 2019, 15:16
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# Given a positive number N, when N is rounded by a certain method (for

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