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

 It is currently 13 Oct 2019, 23:55 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.  M70-20

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

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58335

Show Tags 00:00

Difficulty:   65% (hard)

Question Stats: 24% (00:32) correct 76% (01:04) wrong based on 29 sessions

HideShow timer Statistics

$$a$$ and $$b$$ are integers. $$[x]$$ is an integer less than or equal to $$x$$. Is $$[\frac{a}{b}] \geq {1}$$?

(1) $$ab = 64$$

(2) $$a=b^2$$

_________________

Originally posted by Bunuel on 03 Sep 2018, 05:01.
Last edited by Bunuel on 16 Oct 2018, 02:16, edited 3 times in total.
Math Expert V
Joined: 02 Sep 2009
Posts: 58335

Show Tags

Official Solution:

We’ll go for LOGICAL because there is a logic to understanding the operator.

Since $$[\frac{a}{b}]$$ is defined as an integer either equal to or less than $$\frac{a}{b}$$, no possible value of $$(a,b)$$ can ever make $$[\frac{a}{b}]$$ necessarily greater than any integer. This means a definitive answer to the question stem, if there is sufficient information, can only be ‘NO!’ – when $$[\frac{a}{b}] < {1}$$. This would be the case if $$b$$ is greater than $$a$$. (1) gives us no such information, and (2) gives us the opposite: the greater integer $$b$$ is, integer $$a$$ becomes even greater. Thus, combining the two we’ll still get $$a > b$$. Therefore, (E) is correct.

_________________
Intern  B
Joined: 08 Dec 2017
Posts: 8

Show Tags

someone please give mathematical solution
Manager  B
Joined: 12 Mar 2018
Posts: 110

Show Tags

if u combine two, b^3=64 then b=4. and a=16, thus sufficient. Am I wrong?
Director  D
Joined: 08 Jun 2013
Posts: 544
Location: France
Schools: INSEAD Jan '19
GMAT 1: 200 Q1 V1 GPA: 3.82
WE: Consulting (Other)

Show Tags

Bunuel wrote:
Official Solution:

We’ll go for LOGICAL because there is a logic to understanding the operator.

Since $$[\frac{a}{b}]$$ is defined as an integer either equal to or less than $$\frac{a}{b}$$, no possible value of $$(a,b)$$ can ever make $$[\frac{a}{b}]$$ necessarily greater than any integer. This means a definitive answer to the question stem, if there is sufficient information, can only be ‘NO!’ – when $$[\frac{a}{b}] < {1}$$. This would be the case if $$b$$ is greater than $$a$$. (1) gives us no such information, and (2) gives us the opposite: the greater integer $$b$$ is, integer $$a$$ becomes even greater. Thus, combining the two we’ll still get $$a > b$$. Therefore, (E) is correct.

Hello chetan2u Bunuel

OS above is not clear to me...

Can you explain with some other approach...

I find OA dubious....

Thanks.
_________________
Everything will fall into place…

There is perfect timing for
everything and everyone.
Never doubt, But Work on
improving yourself,
Keep the faith and
Stay ready. When it’s
It will all make sense.
Math Expert V
Joined: 02 Aug 2009
Posts: 7953

Show Tags

3
1
Bunuel wrote:
$$a$$ and $$b$$ are integers. $$[x]$$ is an integer less than or equal to $$x$$. Is $$[\frac{a}{b}] \geq {1}$$?

(1) $$ab = 64$$

(2) $$a=b^2$$

Harshgmat
Yes the question is a bit confusing because we have been dealing with such questions with a bit different wordings.

Had it been $$[x]$$ is the GREATEST integer less than or equal to $$x$$, the answer would be YES. Because a/B would be 4 and thus >1.

However here GREATEST is missing, so the value could be anything but not greater than a/B..
So if a/b=4, [a/b] can be 4,3,2,1,0,-1,-2.....
So it could be any integer as shown above and $$\frac{a}{b}\leq{4}$$

The difference is the word GREATEST not being there.

Hope it helps.
_________________
Director  D
Joined: 08 Jun 2013
Posts: 544
Location: France
Schools: INSEAD Jan '19
GMAT 1: 200 Q1 V1 GPA: 3.82
WE: Consulting (Other)

Show Tags

chetan2u wrote:
Bunuel wrote:
$$a$$ and $$b$$ are integers. $$[x]$$ is an integer less than or equal to $$x$$. Is $$[\frac{a}{b}] \geq {1}$$?

(1) $$ab = 64$$

(2) $$a=b^2$$

Harshgmat
Yes the question is a bit confusing because we have been dealing with such questions with a bit different wordings.

Had it been $$[x]$$ is the GREATEST integer less than or equal to $$x$$, the answer would be YES. Because a/B would be 4 and thus >1.

However here GREATEST is missing, so the value could be anything but not greater than a/B..
So if a/b=4, [a/b] can be 4,3,2,1,0,-1,-2.....
So it could be any integer as shown above and $$\frac{a}{b}\leq{4}$$

The difference is the word GREATEST not being there.

Hope it helps.

chetan2u

Yes it is helpful.

Thanks. Kudos.

Posted from my mobile device
_________________
Everything will fall into place…

There is perfect timing for
everything and everyone.
Never doubt, But Work on
improving yourself,
Keep the faith and
Stay ready. When it’s
It will all make sense. Re: M70-20   [#permalink] 18 Dec 2018, 20:23
Display posts from previous: Sort by

M70-20

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

Moderators: chetan2u, Bunuel

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