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

 It is currently 20 Oct 2019, 14:29 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.  Jean puts N identical cubes, the sides of which are 1 inch

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

Hide Tags

Board of Directors D
Joined: 01 Sep 2010
Posts: 3405
Jean puts N identical cubes, the sides of which are 1 inch  [#permalink]

Show Tags

4
25 00:00

Difficulty:   95% (hard)

Question Stats: 44% (02:33) correct 56% (02:14) wrong based on 399 sessions

HideShow timer Statistics

Jean puts N identical cubes, the sides of which are 1 inch long, inside a rectangular box, each side of which is longer than 1 inch, such that the box is completely filled with no gaps and no cubes left over. What is N?

(1) 56 < N < 63
(2) N is a multiple of 3.

In the explanation of this problem I can't figure out why " To be able to put N cubes into a rectangular box with no gaps and no left-over cubes, you must have the following equality: N = length × width × height. Moreover, if the length, width, and height are all greater than 1, then it must be true that N is the product of at least 3 primes. If N is itself prime or the product of just 2 primes (unique or not), then the condition fails.

So you can rephrase the question this way: is N the product of at least 3 primes?
"

Can you help me ?? the key of this problem is just this process of thought....... Thanks

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 58434
Re: Jean puts N identical cubes, the sides of which are 1 inch  [#permalink]

Show Tags

7
8
Jean puts N identical cubes, the sides of which are 1 inch long, inside a rectangular box, each side of which is longer than 1 inch, such that the box is completely filled with no gaps and no cubes left over. What is N?

Notice that, since the volume of each cube is 1 inch^3, then the volume of N cubes (the volume of the rectangular box) is N inch^3. For example if there are 10 cubes, then the volume of the rectangular box (total volume of 10 cubes) is 10 inch^3. Next, we are told that the length, the width and the height of the rectangular box is longer than 1 inch and there are no gaps when all cubes are put in the box, so the length, the width and the height of the rectangular box are integers more than one: 2, 3, 4, ... Thus each dimension of the rectangular box must have at least one prime in it, so the volume (length*width*height) must be the product of at least 3 primes (not necessarily distinct primes).

(1) 56 < N < 63. N could be 57, 58, 59, 60, 61, or 62. Analyze each case:

57=3*19 --> just two primes. Discard.
58=2*29 --> just two primes. Discard.
59 --> prime itself. Discard.
60=2^2*3*5 --> the product of 4 primes. OK. For example, the the length, the width and the height of the cube cold be 2, by 6, by 5.
61 --> prime itself. Discard.
62=2*31 --> just two primes. Discard.

As we can see, N can only be 60. Sufficient.

(2) N is a multiple of 3. Multiple values of N are possible so that it to be a multiple of 3 AND the product of at least 3 primes, for example 27 or 60. Not sufficient.

Hope it's clear.
_________________
General Discussion
Board of Directors D
Joined: 01 Sep 2010
Posts: 3405
Re: Jean puts N identical cubes, the sides of which are 1 inch  [#permalink]

Show Tags

First of all thanks for editing my question in an appropiate manner.

Secondly is clear. I should infer a lot on this question. I always have the doubt that these kind of questions are too convoluted for the exam.

Anyway, thanks _________________
Manager  Joined: 25 Jun 2012
Posts: 61
Location: India
WE: General Management (Energy and Utilities)
Re: Jean puts N identical cubes, the sides of which are 1 inch  [#permalink]

Show Tags

great solution buenel..!!!

I didt consider while solving that Rectangular box must have integer value for its L,B &H.

I went unnecessarily on jumping to fractional values..!!

Poor of me...
Senior Manager  Joined: 28 Jul 2011
Posts: 310
Location: United States
Concentration: International Business, General Management
GPA: 3.86
WE: Accounting (Commercial Banking)
Re: Jean puts N identical cubes, the sides of which are 1 inch  [#permalink]

Show Tags

Bunuel wrote:
Jean puts N identical cubes, the sides of which are 1 inch long, inside a rectangular box, each side of which is longer than 1 inch, such that the box is completely filled with no gaps and no cubes left over. What is N?

Notice that, since the volume of each cube is 1 inch^3, then the volume of N cubes (the volume of the rectangular box) is N inch^3. For example if there are 10 cubes, then the volume of the rectangular box (total volume of 10 cubes) is 10 inch^3. Next, we are told that the length, the width and the height of the rectangular box is longer than 1 inch and there are no gaps when all cubes are put in the box, so the length, the width and the height of the rectangular box are integers more than one: 2, 3, 4, ... Thus each dimension of the rectangular box must have at least one prime in it, so the volume (length*width*height) must be the product of at least 3 primes (not necessarily distinct primes).

(1) 56 < N < 63. N could be 57, 58, 59, 60, 61, or 62. Analyze each case:

57=3*19 --> just two primes. Discard.
58=2*29 --> just two primes. Discard.
59 --> prime itself. Discard.
60=2^2*3*5 --> the product of 4 primes. OK. For example, the the length, the width and the height of the cube cold be 2, by 6, by 5.
61 --> prime itself. Discard.
62=2*31 --> just two primes. Discard.

As we can see, N can only be 60. Sufficient.

(2) N is a multiple of 3. Multiple values of N are possible so that it to be a multiple of 3 AND the product of at least 3 primes, for example 27 or 60. Not sufficient.

Hope it's clear.

Hi Bunnel,

The question says "each side of which is longer than 1 inch" so the lengths of each sides can even be "2, 2, 2, or 3,3,3" may i know why you took the lenghts as "2,3,4"

Regards
Srinath
Math Expert V
Joined: 02 Sep 2009
Posts: 58434
Re: Jean puts N identical cubes, the sides of which are 1 inch  [#permalink]

Show Tags

1
1
kotela wrote:
Bunuel wrote:
Jean puts N identical cubes, the sides of which are 1 inch long, inside a rectangular box, each side of which is longer than 1 inch, such that the box is completely filled with no gaps and no cubes left over. What is N?

Notice that, since the volume of each cube is 1 inch^3, then the volume of N cubes (the volume of the rectangular box) is N inch^3. For example if there are 10 cubes, then the volume of the rectangular box (total volume of 10 cubes) is 10 inch^3. Next, we are told that the length, the width and the height of the rectangular box is longer than 1 inch and there are no gaps when all cubes are put in the box, so the length, the width and the height of the rectangular box are integers more than one: 2, 3, 4, ... Thus each dimension of the rectangular box must have at least one prime in it, so the volume (length*width*height) must be the product of at least 3 primes (not necessarily distinct primes).

(1) 56 < N < 63. N could be 57, 58, 59, 60, 61, or 62. Analyze each case:

57=3*19 --> just two primes. Discard.
58=2*29 --> just two primes. Discard.
59 --> prime itself. Discard.
60=2^2*3*5 --> the product of 4 primes. OK. For example, the the length, the width and the height of the cube cold be 2, by 6, by 5.
61 --> prime itself. Discard.
62=2*31 --> just two primes. Discard.

As we can see, N can only be 60. Sufficient.

(2) N is a multiple of 3. Multiple values of N are possible so that it to be a multiple of 3 AND the product of at least 3 primes, for example 27 or 60. Not sufficient.

Hope it's clear.

Hi Bunnel,

The question says "each side of which is longer than 1 inch" so the lengths of each sides can even be "2, 2, 2, or 3,3,3" may i know why you took the lenghts as "2,3,4"

Regards
Srinath

I said that "the length, the width and the height of the rectangular box are integers more than one: 2, 3, 4, ... " So, yes, each dimension can be 2 or 3, for example .
_________________
Senior Manager  Joined: 28 Jul 2011
Posts: 310
Location: United States
Concentration: International Business, General Management
GPA: 3.86
WE: Accounting (Commercial Banking)
Re: Jean puts N identical cubes, the sides of which are 1 inch  [#permalink]

Show Tags

Bunuel wrote:
kotela wrote:
Bunuel wrote:
Jean puts N identical cubes, the sides of which are 1 inch long, inside a rectangular box, each side of which is longer than 1 inch, such that the box is completely filled with no gaps and no cubes left over. What is N?

Notice that, since the volume of each cube is 1 inch^3, then the volume of N cubes (the volume of the rectangular box) is N inch^3. For example if there are 10 cubes, then the volume of the rectangular box (total volume of 10 cubes) is 10 inch^3. Next, we are told that the length, the width and the height of the rectangular box is longer than 1 inch and there are no gaps when all cubes are put in the box, so the length, the width and the height of the rectangular box are integers more than one: 2, 3, 4, ... Thus each dimension of the rectangular box must have at least one prime in it, so the volume (length*width*height) must be the product of at least 3 primes (not necessarily distinct primes).

(1) 56 < N < 63. N could be 57, 58, 59, 60, 61, or 62. Analyze each case:

57=3*19 --> just two primes. Discard.
58=2*29 --> just two primes. Discard.
59 --> prime itself. Discard.
60=2^2*3*5 --> the product of 4 primes. OK. For example, the the length, the width and the height of the cube cold be 2, by 6, by 5.
61 --> prime itself. Discard.
62=2*31 --> just two primes. Discard.

As we can see, N can only be 60. Sufficient.

(2) N is a multiple of 3. Multiple values of N are possible so that it to be a multiple of 3 AND the product of at least 3 primes, for example 27 or 60. Not sufficient.

Hope it's clear.

Hi Bunnel,

The question says "each side of which is longer than 1 inch" so the lengths of each sides can even be "2, 2, 2, or 3,3,3" may i know why you took the lenghts as "2,3,4"

Regards
Srinath

I said that "the length, the width and the height of the rectangular box are integers more than one: 2, 3, 4, ... " So, yes, each dimension can be 2 or 3, for example .

Thanks Bunnel got it....
_________________
+1 Kudos If found helpful..
CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: Jean puts N identical cubes, the sides of which are 1 inch  [#permalink]

Show Tags

2
1
carcass wrote:
Jean puts N identical cubes, the sides of which are 1 inch long, inside a rectangular box, each side of which is longer than 1 inch, such that the box is completely filled with no gaps and no cubes left over. What is N?

(1) 56 < N < 63
(2) N is a multiple of 3.

In the explanation of this problem I can't figure out why " To be able to put N cubes into a rectangular box with no gaps and no left-over cubes, you must have the following equality: N = length × width × height. Moreover, if the length, width, and height are all greater than 1, then it must be true that N is the product of at least 3 primes. If N is itself prime or the product of just 2 primes (unique or not), then the condition fails.

So you can rephrase the question this way: is N the product of at least 3 primes?
"

Can you help me ?? the key of this problem is just this process of thought....... Thanks

Please check the explanation in attachment
Attachments

File comment: www.GMATinsight.com 5.jpg [ 127.01 KiB | Viewed 2560 times ]

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Intern  B
Joined: 21 Mar 2017
Posts: 49
Re: Jean puts N identical cubes, the sides of which are 1 inch  [#permalink]

Show Tags

Bunuel wrote:
Jean puts N identical cubes, the sides of which are 1 inch long, inside a rectangular box, each side of which is longer than 1 inch, such that the box is completely filled with no gaps and no cubes left over. What is N?

Notice that, since the volume of each cube is 1 inch^3, then the volume of N cubes (the volume of the rectangular box) is N inch^3. For example if there are 10 cubes, then the volume of the rectangular box (total volume of 10 cubes) is 10 inch^3. Next, we are told that the length, the width and the height of the rectangular box is longer than 1 inch and there are no gaps when all cubes are put in the box, so the length, the width and the height of the rectangular box are integers more than one: 2, 3, 4, ... Thus each dimension of the rectangular box must have at least one prime in it, so the volume (length*width*height) must be the product of at least 3 primes (not necessarily distinct primes).

(1) 56 < N < 63. N could be 57, 58, 59, 60, 61, or 62. Analyze each case:

57=3*19 --> just two primes. Discard.
58=2*29 --> just two primes. Discard.
59 --> prime itself. Discard.
60=2^2*3*5 --> the product of 4 primes. OK. For example, the the length, the width and the height of the cube cold be 2, by 6, by 5.
61 --> prime itself. Discard.
62=2*31 --> just two primes. Discard.

As we can see, N can only be 60. Sufficient.

(2) N is a multiple of 3. Multiple values of N are possible so that it to be a multiple of 3 AND the product of at least 3 primes, for example 27 or 60. Not sufficient.

Hope it's clear.

I don't understand the highlighted part. Help me plz! How this part can be deduced??
Senior Manager  G
Joined: 06 Jul 2016
Posts: 358
Location: Singapore
Concentration: Strategy, Finance
Re: Jean puts N identical cubes, the sides of which are 1 inch  [#permalink]

Show Tags

rma26 wrote:
Bunuel wrote:
Jean puts N identical cubes, the sides of which are 1 inch long, inside a rectangular box, each side of which is longer than 1 inch, such that the box is completely filled with no gaps and no cubes left over. What is N?

Notice that, since the volume of each cube is 1 inch^3, then the volume of N cubes (the volume of the rectangular box) is N inch^3. For example if there are 10 cubes, then the volume of the rectangular box (total volume of 10 cubes) is 10 inch^3. Next, we are told that the length, the width and the height of the rectangular box is longer than 1 inch and there are no gaps when all cubes are put in the box, so the length, the width and the height of the rectangular box are integers more than one: 2, 3, 4, ... Thus each dimension of the rectangular box must have at least one prime in it, so the volume (length*width*height) must be the product of at least 3 primes (not necessarily distinct primes).

(1) 56 < N < 63. N could be 57, 58, 59, 60, 61, or 62. Analyze each case:

57=3*19 --> just two primes. Discard.
58=2*29 --> just two primes. Discard.
59 --> prime itself. Discard.
60=2^2*3*5 --> the product of 4 primes. OK. For example, the the length, the width and the height of the cube cold be 2, by 6, by 5.
61 --> prime itself. Discard.
62=2*31 --> just two primes. Discard.

As we can see, N can only be 60. Sufficient.

(2) N is a multiple of 3. Multiple values of N are possible so that it to be a multiple of 3 AND the product of at least 3 primes, for example 27 or 60. Not sufficient.

Hope it's clear.

I don't understand the highlighted part. Help me plz! How this part can be deduced??

The question stem states that the sides of the rectangular box are greater than 1. This means the sides can be 2, or 3, or 4, etc.
So when we calculate the volume, it'll be 2*2*2, or 3*3*3, or 4*4*4, etc.
=> the volume of the rectangular box will be a multiple of 3 prime numbers. They could be the same prime number, or distinct prime numbers.

1) 56 < N < 63
All sides are greater than 1, so any value of N with 1 as a multiple will be discarded.
57 = 1*3*19 -> OUT
58 = 1*2*29 -> OUT
59 = 1*59 -> OUT
60 = $$2^2$$*3*5 -> Keep
61 = 1*61 -> OUT
62 = 1*2*31 -> OUT

N = 60. Sufficient.

2) N = 3a
N could be 27 = $$3^3$$, or 60 = $$2^2$$*3*5
2 values, hence, insufficient.

A is the answer.
_________________
Put in the work, and that dream score is yours!
Intern  B
Joined: 21 Mar 2017
Posts: 49
Re: Jean puts N identical cubes, the sides of which are 1 inch  [#permalink]

Show Tags

Didn't get it! Oh! May be as 2 is the smallest prime, he said so.
Senior Manager  G
Joined: 06 Jul 2016
Posts: 358
Location: Singapore
Concentration: Strategy, Finance
Jean puts N identical cubes, the sides of which are 1 inch  [#permalink]

Show Tags

2
rma26 wrote:
Didn't get it! Oh! May be as 2 is the smallest prime, he said so.

Primes are numbers that are divisible by 1, and itself.
And all numbers are made up of prime numbers.

4 = $$2^2$$ -> made up of 1 prime number 2.
12 = $$2^2$$*3 -> made up of 2 prime numbers 2 and 3.

The question stem states that the rectangular box has side lengths >1.

Volume of box = l*b*h
=> l,b,h > 1
So any value l,b,h take will consist of prime numbers.

Does this help?
_________________
Put in the work, and that dream score is yours!
Intern  B
Joined: 21 Mar 2017
Posts: 49
Jean puts N identical cubes, the sides of which are 1 inch  [#permalink]

Show Tags

Yes! I thought so ,as I wrote in my last post. Thank you!

***********************
Don't forget to give kudos!!   Non-Human User Joined: 09 Sep 2013
Posts: 13316
Re: Jean puts N identical cubes, the sides of which are 1 inch  [#permalink]

Show Tags

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: Jean puts N identical cubes, the sides of which are 1 inch   [#permalink] 03 Nov 2018, 04:30
Display posts from previous: Sort by

Jean puts N identical cubes, the sides of which are 1 inch

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

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