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

It is currently 21 Jul 2018, 12:15

Close

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

M05-22

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

Hide Tags

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47168
M05-22  [#permalink]

Show Tags

New post 16 Sep 2014, 00:25
2
4
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

61% (00:54) correct 39% (01:06) wrong based on 202 sessions

HideShow timer Statistics

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47168
M05-22  [#permalink]

Show Tags

New post 16 Sep 2014, 00:25
Official Solution:

If x is a positive integer, is x divisible by 15?

(1) \(x\) is a multiple of 10. If \(x=10\) then the answer is NO but if \(x=30\) then the answer is YES. Not sufficient.

(2) \(x^2\) is a multiple of 12. The least perfect square which is a multiple of 12 is 36. Hence, the least value of \(x\) is 6 and in this case the answer is NO, but if for example \(x=12*15\) then the answer is YES. Not sufficient.

Notice that from this statement we can deduce that \(x\) must be a multiple of 3 (else how can this prime appear in \(x^2\)?).

(1)+(2) \(x\) is a multiple of both 10 and 3, hence it's a multiple of 30, so \(x\) must be divisible by 15. Sufficient.


Answer: C
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Current Student
User avatar
Joined: 06 Mar 2014
Posts: 257
Location: India
GMAT Date: 04-30-2015
Reviews Badge
Re: M05-22  [#permalink]

Show Tags

New post 27 Sep 2014, 13:20
Bunuel wrote:
Official Solution:


(1) \(x\) is a multiple of 10. If \(x=10\) then the answer is NO but if \(x=30\) then the answer is YES. Not sufficient.

(2) \(x^2\) is a multiple of 12. The least perfect square which is a multiple of 12 is 36. Hence, the least value of \(x\) is 6 and in this case the answer is NO, but if for example \(x=12*15\) then the answer is YES. Not sufficient.

Notice that from this statement we can deduce that \(x\) must be a multiple of 3 (else how can this prime appear in \(x^2\)?).

(1)+(2) \(x\) is a multiple of both 10 and 3, hence it's a multiple of 30, so \(x\) must be divisible by 15. Sufficient.


Answer: C



I couldn't follow the highlighted portion actually.

I seem to find DS Questions with given statements such as below one little difficult/time consuming:
1) x multiple of 55
2) x^3 multiple of 110

Please suggest if there are any familiar types your aware of.

Would be really grateful.
Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47168
Re: M05-22  [#permalink]

Show Tags

New post 27 Sep 2014, 13:45
2
2
earnit wrote:
Bunuel wrote:
Official Solution:


(1) \(x\) is a multiple of 10. If \(x=10\) then the answer is NO but if \(x=30\) then the answer is YES. Not sufficient.

(2) \(x^2\) is a multiple of 12. The least perfect square which is a multiple of 12 is 36. Hence, the least value of \(x\) is 6 and in this case the answer is NO, but if for example \(x=12*15\) then the answer is YES. Not sufficient.

Notice that from this statement we can deduce that \(x\) must be a multiple of 3 (else how can this prime appear in \(x^2\)?).

(1)+(2) \(x\) is a multiple of both 10 and 3, hence it's a multiple of 30, so \(x\) must be divisible by 15. Sufficient.


Answer: C



I couldn't follow the highlighted portion actually.

I seem to find DS Questions with given statements such as below one little difficult/time consuming:
1) x multiple of 55
2) x^3 multiple of 110

Please suggest if there are any familiar types your aware of.

Would be really grateful.


Important thing to know when solving this problem is that exponentiation does not "produce" primes. For example, for integer x if x^(positive integer) is divisible by 3, then x must be divisible by 3. How else would 3 appear in x^(positive integer)?

We are given that \(x^2\), where x is an integer, is a multiple of 12 = 2^2*3.This means that x must be a multiple of both 2 and 3. If they weren't how can x^2 have these primes?

Similar questions to practice:
if-x-is-an-integer-is-x-3-divisible-by-165973.html
how-many-different-prime-numbers-are-factors-of-the-positive-126744.html
if-n-2-n-yields-an-integer-greater-than-0-is-n-divisible-by-126648.html
if-k-is-a-positive-integer-is-k-the-square-of-an-integer-55987.html
if-k-is-a-positive-integer-how-many-different-prime-numbers-95585.html
if-n-is-the-integer-whether-30-is-a-factor-of-n-126572.html
if-x-is-an-integer-is-x-2-1-x-5-an-even-number-104275.html

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Current Student
User avatar
Joined: 06 Mar 2014
Posts: 257
Location: India
GMAT Date: 04-30-2015
Reviews Badge
Re: M05-22  [#permalink]

Show Tags

New post 27 Sep 2014, 13:56
Bunuel wrote:
earnit wrote:
Bunuel wrote:
Official Solution:


(1) \(x\) is a multiple of 10. If \(x=10\) then the answer is NO but if \(x=30\) then the answer is YES. Not sufficient.

(2) \(x^2\) is a multiple of 12. The least perfect square which is a multiple of 12 is 36. Hence, the least value of \(x\) is 6 and in this case the answer is NO, but if for example \(x=12*15\) then the answer is YES. Not sufficient.

Notice that from this statement we can deduce that \(x\) must be a multiple of 3 (else how can this prime appear in \(x^2\)?).

(1)+(2) \(x\) is a multiple of both 10 and 3, hence it's a multiple of 30, so \(x\) must be divisible by 15. Sufficient.


Answer: C



I couldn't follow the highlighted portion actually.

I seem to find DS Questions with given statements such as below one little difficult/time consuming:
1) x multiple of 55
2) x^3 multiple of 110

Please suggest if there are any familiar types your aware of.

Would be really grateful.


Important thing to know when solving this problem is that exponentiation does not "produce" primes. For example, for integer x if x^(positive integer) is divisible by 3, then x must be divisible by 3. How else would 3 appear in x^(positive integer)?

We are given that \(x^2\), where x is an integer, is a multiple of 12 = 2^2*3.This means that x must be a multiple of both 2 and 3. If they weren't how can x^2 have these primes?

Similar questions to practice:
if-x-is-an-integer-is-x-3-divisible-by-165973.html
how-many-different-prime-numbers-are-factors-of-the-positive-126744.html
if-n-2-n-yields-an-integer-greater-than-0-is-n-divisible-by-126648.html
if-k-is-a-positive-integer-is-k-the-square-of-an-integer-55987.html
if-k-is-a-positive-integer-how-many-different-prime-numbers-95585.html
if-n-is-the-integer-whether-30-is-a-factor-of-n-126572.html
if-x-is-an-integer-is-x-2-1-x-5-an-even-number-104275.html

Hope it helps.


THANKS a ton.
Really appreciate it.
:)
Intern
Intern
avatar
B
Joined: 17 May 2015
Posts: 30
M05-22  [#permalink]

Show Tags

New post 17 Sep 2015, 08:24
Need great help , I don't understand why (2) can give both yes and no answer , many thanks
My understanding:
(2)X2 can be 36 or 144 which is x=6 or 12
Both are not divisible by 15
Many thsnks
Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47168
Re: M05-22  [#permalink]

Show Tags

New post 18 Sep 2015, 09:17
1
1 KUDOS received
Intern
Intern
avatar
B
Joined: 11 Jan 2015
Posts: 34
GMAT ToolKit User
Re: M05-22  [#permalink]

Show Tags

New post 28 Jun 2016, 20:17
1
Plz let me know if my approach is correct:

In order to know if x is divisible by 15, x has to contain at least the prime factors of \(15\) -> \((3*5)\).

From (1): We only know that x is similar to \(x*2*5\) ->\(x\) could be three. Not sufficient.

From (2): We only know that \(x^2\) is similar to \(x*x*2*2*3\) -> One of the \(x\) could be \(5\). Not sufficient.

From (1) + (2): We know that \(x\) contains at least one 3 and one 5 what makes it divisible by \(15\) -> \((3*5)\). Sufficient
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47168
Re: M05-22  [#permalink]

Show Tags

New post 29 Jun 2016, 00:29
paddy41 wrote:
Plz let me know if my approach is correct:

In order to know if x is divisible by 15, x has to contain at least the prime factors of \(15\) -> \((3*5)\).

From (1): We only know that x is similar to \(x*2*5\) ->\(x\) could be three. Not sufficient.

From (2): We only know that \(x^2\) is similar to \(x*x*2*2*3\) -> One of the \(x\) could be \(5\). Not sufficient.

From (1) + (2): We know that \(x\) contains at least one 3 and one 5 what makes it divisible by \(15\) -> \((3*5)\). Sufficient

______________
Yes, that's correct.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
B
Joined: 01 Nov 2016
Posts: 69
Concentration: Technology, Operations
M05-22  [#permalink]

Show Tags

New post 06 May 2017, 21:46
Bunuel wrote:
Important thing to know when solving this problem is that exponentiation does not "produce" primes. For example, for integer x if x^(positive integer) is divisible by 3, then x must be divisible by 3. How else would 3 appear in x^(positive integer)?

We are given that \(x^2\), where x is an integer, is a multiple of 12 = 2^2*3.This means that x must be a multiple of both 2 and 3. If they weren't how can x^2 have these primes?


I don't think I understand this. Are you saying that if \(x^2\) is divisible by 12 then x is divisible by 12?

So does that mean that if \(x^z\) is divisible by y then x is divisible by y (as long as z is positive)?
Intern
Intern
avatar
B
Joined: 11 Jan 2015
Posts: 34
GMAT ToolKit User
Re: M05-22  [#permalink]

Show Tags

New post 07 May 2017, 01:16
joondez wrote:
Bunuel wrote:
Important thing to know when solving this problem is that exponentiation does not "produce" primes. For example, for integer x if x^(positive integer) is divisible by 3, then x must be divisible by 3. How else would 3 appear in x^(positive integer)?

We are given that \(x^2\), where x is an integer, is a multiple of 12 = 2^2*3.This means that x must be a multiple of both 2 and 3. If they weren't how can x^2 have these primes?



So does that mean that if \(x^z\) is divisible by y then x is divisible by y (as long as z is positive)?


...as long as y is prime your statement should be correct.
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47168
Re: M05-22  [#permalink]

Show Tags

New post 07 May 2017, 02:03
paddy41 wrote:
joondez wrote:
Bunuel wrote:
Important thing to know when solving this problem is that exponentiation does not "produce" primes. For example, for integer x if x^(positive integer) is divisible by 3, then x must be divisible by 3. How else would 3 appear in x^(positive integer)?

We are given that \(x^2\), where x is an integer, is a multiple of 12 = 2^2*3.This means that x must be a multiple of both 2 and 3. If they weren't how can x^2 have these primes?



So does that mean that if \(x^z\) is divisible by y then x is divisible by y (as long as z is positive)?


...as long as y is prime your statement should be correct.


You should read more carefully. As correctly noted by paddy41, the property above is talking about primes.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
B
Joined: 24 Jun 2017
Posts: 6
Re: M05-22  [#permalink]

Show Tags

New post 13 Oct 2017, 04:57
how sqrt(180) gives a integer??? we cant take 180 has a sol..
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47168
Re: M05-22  [#permalink]

Show Tags

New post 13 Oct 2017, 06:37
Manager
Manager
User avatar
B
Joined: 26 Feb 2018
Posts: 71
WE: Sales (Internet and New Media)
CAT Tests
Re: M05-22  [#permalink]

Show Tags

New post 02 Jun 2018, 11:45
Bunuel wrote:
If \(x\) is a positive integer, is \(x\) divisible by 15?


(1) \(x\) is a multiple of 10

(2) \(x^2\) is a multiple of 12


Hi Bunuel ,

I got a wrong answer , chose B ,as this a Yes / No question , to find whether X is divisible by 15 or not (y/n)

statement 2 : says , X^2 is a multiple of 12 , so in this case the only possibility is 6^2 = 36 which is a multiple of 12 , hence it is NO , this means X should also has to a perfect square , then only number left out is 12 itself , (12*12) i.e 144, in this case also 15 is not divisible .

Why are we considering x = 12 *15 as a possibility , where it is mentioned X^2 is a multiple of 12 .

Can you please guide me ?
_________________

" Can't stop learning and failing"

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47168
Re: M05-22  [#permalink]

Show Tags

New post 02 Jun 2018, 12:13
1
loserunderachiever wrote:
Bunuel wrote:
If \(x\) is a positive integer, is \(x\) divisible by 15?


(1) \(x\) is a multiple of 10

(2) \(x^2\) is a multiple of 12


Hi Bunuel ,

I got a wrong answer , chose B ,as this a Yes / No question , to find whether X is divisible by 15 or not (y/n)

statement 2 : says , X^2 is a multiple of 12 , so in this case the only possibility is 6^2 = 36 which is a multiple of 12 , hence it is NO , this means X should also has to a perfect square , then only number left out is 12 itself , (12*12) i.e 144, in this case also 15 is not divisible .

Why are we considering x = 12 *15 as a possibility , where it is mentioned X^2 is a multiple of 12 .

Can you please guide me ?


Positive multiples of 12 are 12, 2*12 = 24, 3*12 = 36, 4*12 = 48, ....

(2) says that \(x^2\) is a multiple of 12. Since x^2 is a perfect square, then we are looking for multiples of 12 which are also perfect squares. So, x^2 could be:

36 (for x = 6);
144 (for x = 12);
324 (for x = 18);
576 (for x = 24);
900 (for x = 30);
1296 (for x = 36);
1764 (for x = 42);
2304 (for x = 48);
2916 (for x = 54);
3600 (for x = 60);
...

As you can see for some values, x is NOT a multiple of 15 but for some values x IS a multiple of 15 (for example, for x = 30 or x = 60)
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
User avatar
B
Joined: 26 Feb 2018
Posts: 71
WE: Sales (Internet and New Media)
CAT Tests
Re: M05-22  [#permalink]

Show Tags

New post 02 Jun 2018, 12:20
Bunuel wrote:
loserunderachiever wrote:
Bunuel wrote:
If \(x\) is a positive integer, is \(x\) divisible by 15?


(1) \(x\) is a multiple of 10

(2) \(x^2\) is a multiple of 12


Hi Bunuel ,

I got a wrong answer , chose B ,as this a Yes / No question , to find whether X is divisible by 15 or not (y/n)

statement 2 : says , X^2 is a multiple of 12 , so in this case the only possibility is 6^2 = 36 which is a multiple of 12 , hence it is NO , this means X should also has to a perfect square , then only number left out is 12 itself , (12*12) i.e 144, in this case also 15 is not divisible .

Why are we considering x = 12 *15 as a possibility , where it is mentioned X^2 is a multiple of 12 .

Can you please guide me ?


Positive multiples of 12 are 12, 2*12 = 24, 3*12 = 36, 4*12 = 48, ....

(2) says that \(x^2\) is a multiple of 12. Since x^2 is a perfect square, then we are looking for multiples of 12 which are also perfect squares. So, x^2 could be:

36 (for x = 6);
144 (for x = 12);
324 (for x = 18);
576 (for x = 24);
900 (for x = 30);
1296 (for x = 36);
1764 (for x = 42);
2304 (for x = 48);
2916 (for x = 54);
3600 (for x = 60);
...

As you can see for some values, x is NOT a multiple of 15 but for some values x IS a multiple of 15 (for example, for x = 30 or x = 60)


Oh , this clears up . I stopped my multiple list till 12*12 = 144 . Your explanation absolutely makes sense , I realised my mistake now . 30 & 60 , makes sense.

Faced this one in my GMAT club quant test. Now it's clear to me.

Thanks a lot Bunuel.
_________________

" Can't stop learning and failing"

Re: M05-22 &nbs [#permalink] 02 Jun 2018, 12:20
Display posts from previous: Sort by

M05-22

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

Moderators: chetan2u, Bunuel

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.