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

 It is currently 12 Dec 2018, 03:59

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
Your Progress

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

Events & Promotions

Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• The winning strategy for 700+ on the GMAT

December 13, 2018

December 13, 2018

08:00 AM PST

09:00 AM PST

What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
• GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

December 14, 2018

December 14, 2018

09:00 AM PST

10:00 AM PST

10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.

A certain clock marks every hour by striking a number of tim

 post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
Intern
Joined: 15 Feb 2010
Posts: 8
A certain clock marks every hour by striking a number of tim  [#permalink]

Show Tags

23 Mar 2010, 14:29
17
00:00

Difficulty:

(N/A)

Question Stats:

79% (01:28) correct 21% (01:05) wrong based on 98 sessions

HideShow timer Statistics

110. A certain clock marks every hour by striking a number of times qual to the hour, and the time required for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stroke and the end of the last stroke is 22 secs. At 12:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?

A. 72
B. 50
C. 48
D. 46
E. 44

157. A certain right triangle has sides of length x, y, z, where x < y< z. If the area of this triangular region is 1, which of the following indicates all of the possible values of y?

A. $$y> \sqrt{2}$$
B. $$\frac{\sqrt{3}}{2} < y< \sqrt{2}$$
C. $$\frac{\sqrt{2}}{3} < y < \frac{\sqrt{3}}{2}$$
D. $$\frac{\sqrt{2}}{4} <y < \frac{\sqrt{2}}{3}$$
E. $$y < \frac{\sqrt{3}}{4}$$

160. If n is a positive integer and N^2 is divisible by 72, then the largest positive integer that must divide N is

A. 6
B. 12
C. 24
D. 36
E. 48

MODERATOR: Please post one question per topic and please check the following links for writing math symbols:
questions-about-posting-84537.html
writing-mathematical-symbols-in-posts-72468.html

ALL OG13 QUESTIONS WITH SOLUTIONS ARE HERE: the-official-guide-quantitative-question-directory-143450.html
Manager
Joined: 26 May 2005
Posts: 189
Re: OG quantitative #110, 157, 169  [#permalink]

Show Tags

23 Mar 2010, 14:36
1
aramjung wrote:
110. A certain clock marks every hour by striking a number of times qual to the hour, and the time required for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stroke and the end of the last stroke is 22 secs. At 12:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?

A. 72 B. 50 C. 48 D. 46 E. 44

at 6, the number of strokes will be 6 and the number of time interval between strokes will be 5, for a total of 11 - so each one is 2 sec. at 12, number of strokes will be 12 and the number of time intervals will be 11 for a total of 23
total time = 23 * 2 = 46

D
Math Expert
Joined: 02 Sep 2009
Posts: 51123
Re: OG quantitative #110, 157, 169  [#permalink]

Show Tags

23 Mar 2010, 14:51
2
2
A certain right triangle has sides of length x, y, z, where x < y< z. If the area of this triangular region is 1, which of the following indicates all of the possible values of y?

The area of the triangle is $$\frac{xy}{2}=1$$ ($$x<y<z$$ means that hypotenuse is $$z$$) --> $$x=\frac{2}{y}$$. As $$x<y$$, then $$\frac{2}{y}<y$$ --> $$2<y^2$$ --> $$\sqrt{2}<y$$.

Also note that max value of $$y$$ is not limited at all. For example $$y$$ can be $$1,000,000$$ and in this case $$\frac{xy}{2}=\frac{x*1,000,000}{2}=1$$ --> $$x=\frac{2}{1,000,000}$$.

Answer: A.

Hope it helps.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 51123
Re: OG quantitative #110, 157, 169  [#permalink]

Show Tags

23 Mar 2010, 14:52
4
4
If n is a positive integer and N^2 is divisible by 72, then the largest positive integer that must divide N is

A. 6
B. 12
C. 24
D. 36
E. 48

The largest positive integer that must divide $$n$$, means for lowest value of $$n$$ which satisfies the given statement in the stem. The lowest square of integer, which is multiple of $$72$$ is $$144$$ --> $$n^2=144$$ --> $$n=12$$. Largest factor of $$12$$ is $$12$$.

OR:

Given: $$72k=n^2$$, where $$k$$ is an integer $$\geq1$$ (as $$n$$ is positive).

$$72k=n^2$$ --> $$n=6\sqrt{2k}$$, as $$n$$ is an integer $$\sqrt{2k}$$, also must be an integer. The lowest value of $$k$$, for which $$\sqrt{2k}$$ is an integer is when $$k=2$$ --> $$\sqrt{2k}=\sqrt{4}=2$$ --> $$n=6\sqrt{2k}=6*2=12$$

Answer: B.
_________________
Intern
Joined: 15 Feb 2010
Posts: 8
Re: OG quantitative #110, 157, 169  [#permalink]

Show Tags

25 Mar 2010, 14:33
110 i dont understand what the interval means
does it mean the how many strokes to get to the 6th stroke not counting the beginning.

157. i need more questions like this, i'm not quite conveying it. i need elementary explanations with pictures

sorry!
thank you!
Senior Manager
Joined: 19 Nov 2007
Posts: 399
Re: OG quantitative #110, 157, 169  [#permalink]

Show Tags

25 Mar 2010, 16:15
Bunuel wrote:
If n is a positive integer and N^2 is divisible by 72, then the largest positive integer that must divide N is

A. 6
B. 12
C. 24
D. 36
E. 48

The largest positive integer that must divide $$n$$, means for lowest value of $$n$$ which satisfies the given statement in the stem. The lowest square of integer, which is multiple of $$72$$ is $$144$$ --> $$n^2=144$$ --> $$n=12$$. Largest factor of $$12$$ is $$12$$.

OR:

Given: $$72k=n^2$$, where $$k$$ is an integer $$\geq1$$ (as $$n$$ is positive).

$$72k=n^2$$ --> $$n=6\sqrt{2k}$$, as $$n$$ is an integer $$\sqrt{2k}$$, also must be an integer. The lowest value of $$k$$, for which $$\sqrt{2k}$$ is an integer is when $$k=2$$ --> $$\sqrt{2k}=\sqrt{4}=2$$ --> $$n=6\sqrt{2k}=6*2=12$$

Answer: B.

Bunuel,
48^2 is also divisible by 72. Why can't 48 be N ?
_________________

-Underline your question. It takes only a few seconds!
-Search before you post.

Manager
Joined: 20 Mar 2010
Posts: 78
Re: OG quantitative #110, 157, 169  [#permalink]

Show Tags

25 Mar 2010, 17:00
4
2
aramjung wrote:
110 i dont understand what the interval means
does it mean the how many strokes to get to the 6th stroke not counting the beginning.

157. i need more questions like this, i'm not quite conveying it. i need elementary explanations with pictures

sorry!
thank you!

Interval is the time delay between each stroke which is equal to the time required for stroke . The 22 seconds includes the time from the beginning of the first stroke till the end of the 6th stroke including the gap time in between.

If let's say S is the time for each stroke and I is the interval time in between
S+I+S+I+S+I+S+I+S+I+S =22sec
But S=I
11S =11I=22 and S=I=2 seconds

At 12:00 clock strikes 12 times and there will be 11 intervals in total between the 12 strokes so total time will be (12+11)*2 = 46

Hope this helps

Thanks
_________________

___________________________________
Please give me kudos if you like my post

Manager
Joined: 20 Mar 2010
Posts: 78
Re: OG quantitative #110, 157, 169  [#permalink]

Show Tags

25 Mar 2010, 17:13
1
vscid wrote:
Bunuel wrote:
If n is a positive integer and N^2 is divisible by 72, then the largest positive integer that must divide N is

A. 6
B. 12
C. 24
D. 36
E. 48

The largest positive integer that must divide $$n$$, means for lowest value of $$n$$ which satisfies the given statement in the stem. The lowest square of integer, which is multiple of $$72$$ is $$144$$ --> $$n^2=144$$ --> $$n=12$$. Largest factor of $$12$$ is $$12$$.

OR:

Given: $$72k=n^2$$, where $$k$$ is an integer $$\geq1$$ (as $$n$$ is positive).

$$72k=n^2$$ --> $$n=6\sqrt{2k}$$, as $$n$$ is an integer $$\sqrt{2k}$$, also must be an integer. The lowest value of $$k$$, for which $$\sqrt{2k}$$ is an integer is when $$k=2$$ --> $$\sqrt{2k}=\sqrt{4}=2$$ --> $$n=6\sqrt{2k}=6*2=12$$

Answer: B.

Bunuel,
48^2 is also divisible by 72. Why can't 48 be N ?

The question is about the largest integer that must divide n. With the known information we can only say that n is divisible by 12 irrespective of the value of k. 36 and 48 also can divide n but they are dependent on k value being a multiple of 18 and 32 respectively. But since we don't know k value 12 is the largest that must divide n

Thanks
_________________

___________________________________
Please give me kudos if you like my post

Intern
Joined: 29 Oct 2009
Posts: 44
Re: OG quantitative #110, 157, 169  [#permalink]

Show Tags

25 Mar 2010, 23:43
110. A certain clock marks every hour by striking a number of times qual to the hour, and the time required for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stroke and the end of the last stroke is 22 secs. At 12:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?

solution:- at 6'o clock there will be 6 strokes, now will we find number of intervals between these 6 strokes which will be one less than total strokes i.e.5

now given in ques is

"the time required for a stroke is exactly equal to the time interval between strokes."

so total time lapsed for 1stroke (x) at 6 o clock comes out to be

(6strokes+5 interval)x = 22
x=2

now at 12o clock, there will be 12 strokes and 11 intervals i.e. total 23

so total time lapse will be 23*2=46 secs
Math Expert
Joined: 02 Sep 2009
Posts: 51123
Re: A certain clock marks every hour by striking a number of tim  [#permalink]

Show Tags

29 Oct 2013, 23:00
ALL OG13 QUESTIONS WITH SOLUTIONS ARE HERE: the-official-guide-quantitative-question-directory-143450.html
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 9130
Re: A certain clock marks every hour by striking a number of tim  [#permalink]

Show Tags

08 Aug 2018, 00:11
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: A certain clock marks every hour by striking a number of tim &nbs [#permalink] 08 Aug 2018, 00:11
Display posts from previous: Sort by

A certain clock marks every hour by striking a number of tim

 post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.