GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Oct 2019, 13:19 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  Given a positive number N, when N is rounded by a certain method (for

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Senior Manager  G
Joined: 04 Sep 2017
Posts: 291
Given a positive number N, when N is rounded by a certain method (for  [#permalink]

Show Tags

6 00:00

Difficulty:   95% (hard)

Question Stats: 22% (02:28) correct 78% (02:32) wrong based on 32 sessions

HideShow timer Statistics

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

Show Tags

1
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
_________________
Director  D
Joined: 19 Oct 2018
Posts: 985
Location: India
Re: Given a positive number N, when N is rounded by a certain method (for  [#permalink]

Show Tags

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
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  