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

It is currently 23 Jun 2018, 07:01

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

M28-50

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46295
M28-50 [#permalink]

Show Tags

New post 16 Sep 2014, 01:44
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

48% (00:53) correct 52% (01:33) wrong based on 71 sessions

HideShow timer Statistics

If \(0 \lt x \lt y\) and \(x\) and \(y\) are consecutive perfect squares, what is the remainder when \(y\) is divided by \(x\)?


(1) Both \(x\) and \(y\) have 3 positive factors.

(2) Both \(\sqrt{x}\) and \(\sqrt{y}\) are prime numbers.

_________________

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

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46295
Re M28-50 [#permalink]

Show Tags

New post 16 Sep 2014, 01:44
1
2
Official Solution:


If \(0 \lt x \lt y\) and \(x\) and \(y\) are consecutive perfect squares, what is the remainder when \(y\) is divided by \(x\)?

Notice that since \(x\) and \(y\) are consecutive perfect squares, then \(\sqrt{x}\) and \(\sqrt{y}\) are consecutive integers.

(1) Both \(x\) and \(y\) have 3 positive factors. This statement implies that \(x=(prime_1)^2\) and \(y=(prime_2)^2\). From above we have that \(\sqrt{x}=prime_1\) and \(\sqrt{y}=prime_2\) are consecutive integers. The only two consecutive integers which are primes are 2 and 3. Thus, \(x=(prime_1)^2=4\) and \(y=(prime_2)^2=9\). The remainder when 9 is divided by 4 is 1. Sufficient.

(2) Both \(\sqrt{x}\) and \(\sqrt{y}\) are prime numbers. The same here: \(\sqrt{x}=2\) and \(\sqrt{y}=3\). Sufficient.


Answer: D
_________________

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

1 KUDOS received
Current Student
avatar
B
Joined: 08 Jan 2015
Posts: 82
GMAT ToolKit User
Re: M28-50 [#permalink]

Show Tags

New post 23 Jun 2016, 22:48
1
I think it's a low quality question, since there is no commonly used definition for consecutive perfect squares. The correct definition should be - perfect squares of consecutive integers. Otherwise the only pair of consecutive perfect squares is 0^2 and 1^2. https://proofwiki.org/wiki/Zero_and_One_are_the_only_Consecutive_Perfect_Squares.
Besides that, If the question implies that 36 are 49 are consecutive perfect squares (since it's 6^2 and 7^2), then I don't see a reason, why should one not consider 7 and 11 as consecutive primes. Which then makes the correct answer choice E, because 1 and 2 are tautological.
1 KUDOS received
Intern
Intern
avatar
Joined: 13 Jul 2016
Posts: 2
Re: M28-50 [#permalink]

Show Tags

New post 28 Oct 2016, 13:06
1
I think this is a poor-quality question and I don't agree with the explanation. This is a poor quality question and meaning of consecutive perfect squares is not clear while attempting...
Intern
Intern
avatar
B
Joined: 09 Jul 2016
Posts: 17
GMAT 1: 730 Q50 V39
Reviews Badge
Re: M28-50 [#permalink]

Show Tags

New post 29 May 2017, 10:35
I think this is a poor-quality question and I don't agree with the explanation. Question statement is not clear enough.
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46295
Re: M28-50 [#permalink]

Show Tags

New post 29 May 2017, 11:10
siddhanthsivaraman wrote:
I think this is a poor-quality question and I don't agree with the explanation. This is a poor quality question and meaning of consecutive perfect squares is not clear while attempting...


Consecutive perfect square are say 1^1 = 2 and 2^2 = 4 or 5^2 = 25 and 6^2 = 36.
_________________

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

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46295
Re: M28-50 [#permalink]

Show Tags

New post 29 May 2017, 11:12
Manager
Manager
avatar
S
Joined: 18 May 2016
Posts: 171
Location: India
GMAT 1: 710 Q48 V40
WE: Marketing (Other)
GMAT ToolKit User Reviews Badge CAT Tests
Re: M28-50 [#permalink]

Show Tags

New post 14 Jun 2017, 20:24
Vikram_Katti wrote:
I think this is a poor-quality question and I don't agree with the explanation. Question statement is not clear enough.


I think in a hurry to solve the problem, it was assumed that the numbers are consecutives primes, and not just consecutive numbers. When actually we need to find consecutives numbers that are prime.
Hence the mistake, which I also committed and was baffled at the explanation.

On second thoughts, its a clear cut question, absolutely GMAT style.

my 2c!
Intern
Intern
avatar
B
Joined: 22 May 2015
Posts: 14
Location: India
GMAT 1: 650 Q46 V34
GPA: 3.4
Re: M28-50 [#permalink]

Show Tags

New post 30 Jul 2017, 03:21
I think this is a high-quality question and I agree with explanation.
Manager
Manager
avatar
B
Joined: 16 Jul 2016
Posts: 140
Location: India
GPA: 4
WE: Brand Management (Retail)
Reviews Badge
Re: M28-50 [#permalink]

Show Tags

New post 23 Aug 2017, 07:49
poor quality question

From above we have that x√=prime1x=prime1 and y√=prime2y=prime2 are consecutive integers. How was this proved ?
Expect a better explanation.
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46295
Re: M28-50 [#permalink]

Show Tags

New post 23 Aug 2017, 11:32
Yashkumar wrote:
poor quality question

From above we have that x√=prime1x=prime1 and y√=prime2y=prime2 are consecutive integers. How was this proved ?
Expect a better explanation.


x and y are consecutive perfect squares, so x and y could be:
\(x = 1\) and \(y = 4\) --> \(\sqrt{x}=1\) and \(\sqrt{y}=2\), consecutive integers;
\(x = 4\) and \(y = 9\) --> \(\sqrt{x}=2\) and \(\sqrt{y}=3\), consecutive integers;
\(x = 9\) and \(y = 16\) --> \(\sqrt{x}=3\) and \(\sqrt{y}=4\), consecutive integers;
...
_________________

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

SVP
SVP
User avatar
P
Joined: 26 Mar 2013
Posts: 1677
Reviews Badge CAT Tests
Re: M28-50 [#permalink]

Show Tags

New post 24 Aug 2017, 08:40
Bunuel wrote:
Yashkumar wrote:
poor quality question

From above we have that x√=prime1x=prime1 and y√=prime2y=prime2 are consecutive integers. How was this proved ?
Expect a better explanation.


x and y are consecutive perfect squares, so x and y could be:
\(x = 1\) and \(y = 4\) --> \(\sqrt{x}=1\) and \(\sqrt{y}=2\), consecutive integers;
\(x = 4\) and \(y = 9\) --> \(\sqrt{x}=2\) and \(\sqrt{y}=3\), consecutive integers;
\(x = 9\) and \(y = 16\) --> \(\sqrt{x}=3\) and \(\sqrt{y}=4\), consecutive integers;
...



Dear Bunuel

As u stated above the consecutive perfect square 1, 4, 9, 16, 25.

From statement 1, it is invalid to consider 9 & 16 because both are consecutive but 16 does not consist of 3 factors. Am I right?
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46295
Re: M28-50 [#permalink]

Show Tags

New post 24 Aug 2017, 10:32
Mo2men wrote:
Bunuel wrote:
Yashkumar wrote:
poor quality question

From above we have that x√=prime1x=prime1 and y√=prime2y=prime2 are consecutive integers. How was this proved ?
Expect a better explanation.


x and y are consecutive perfect squares, so x and y could be:
\(x = 1\) and \(y = 4\) --> \(\sqrt{x}=1\) and \(\sqrt{y}=2\), consecutive integers;
\(x = 4\) and \(y = 9\) --> \(\sqrt{x}=2\) and \(\sqrt{y}=3\), consecutive integers;
\(x = 9\) and \(y = 16\) --> \(\sqrt{x}=3\) and \(\sqrt{y}=4\), consecutive integers;
...



Dear Bunuel

As u stated above the consecutive perfect square 1, 4, 9, 16, 25.

From statement 1, it is invalid to consider 9 & 16 because both are consecutive but 16 does not consist of 3 factors. Am I right?


We can consider the above values from the stem. From (1), the only values possible are \(x=(prime_1)^2=4\) and \(y=(prime_2)^2=9\).
_________________

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

Moderator
avatar
V
Joined: 29 Jan 2015
Posts: 805
Location: India
WE: General Management (Non-Profit and Government)
GMAT ToolKit User Reviews Badge CAT Tests
Re: M28-50 [#permalink]

Show Tags

New post 25 Jan 2018, 05:33
Bunuel wrote:
Official Solution:


If \(0 \lt x \lt y\) and \(x\) and \(y\) are consecutive perfect squares, what is the remainder when \(y\) is divided by \(x\)?

Notice that since \(x\) and \(y\) are consecutive perfect squares, then \(\sqrt{x}\) and \(\sqrt{y}\) are consecutive integers.

(1) Both \(x\) and \(y\) have 3 positive factors. This statement implies that \(x=(prime_1)^2\) and \(y=(prime_2)^2\). From above we have that \(\sqrt{x}=prime_1\) and \(\sqrt{y}=prime_2\) are consecutive integers. The only two consecutive integers which are primes are 2 and 3. Thus, \(x=(prime_1)^2=4\) and \(y=(prime_2)^2=9\). The remainder when 9 is divided by 4 is 1. Sufficient.

(2) Both \(\sqrt{x}\) and \(\sqrt{y}\) are prime numbers. The same here: \(\sqrt{x}=2\) and \(\sqrt{y}=3\). Sufficient.


Answer: D


Hi Bunuel,

In the above question Statement 1 says that both x and y have 3 positive factor and you have written that the statement implies that x=(prime1)2x=(prime1)2 and y=(prime2)2y=(prime2)2. How did you arrive at this? Can you please elaborate? Thanks.
_________________

If you liked my post, kindly give me a Kudos. Thanks.

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46295
Re: M28-50 [#permalink]

Show Tags

New post 25 Jan 2018, 05:46
rohan2345 wrote:
Bunuel wrote:
Official Solution:


If \(0 \lt x \lt y\) and \(x\) and \(y\) are consecutive perfect squares, what is the remainder when \(y\) is divided by \(x\)?

Notice that since \(x\) and \(y\) are consecutive perfect squares, then \(\sqrt{x}\) and \(\sqrt{y}\) are consecutive integers.

(1) Both \(x\) and \(y\) have 3 positive factors. This statement implies that \(x=(prime_1)^2\) and \(y=(prime_2)^2\). From above we have that \(\sqrt{x}=prime_1\) and \(\sqrt{y}=prime_2\) are consecutive integers. The only two consecutive integers which are primes are 2 and 3. Thus, \(x=(prime_1)^2=4\) and \(y=(prime_2)^2=9\). The remainder when 9 is divided by 4 is 1. Sufficient.

(2) Both \(\sqrt{x}\) and \(\sqrt{y}\) are prime numbers. The same here: \(\sqrt{x}=2\) and \(\sqrt{y}=3\). Sufficient.


Answer: D


Hi Bunuel,

In the above question Statement 1 says that both x and y have 3 positive factor and you have written that the statement implies that x=(prime1)2x=(prime1)2 and y=(prime2)2y=(prime2)2. How did you arrive at this? Can you please elaborate? Thanks.


Finding the Number of Factors of an Integer

First make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers.

The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: \(450=2^1*3^2*5^2\)

Total number of factors of 450 including 1 and 450 itself is \((1+1)*(2+1)*(2+1)=2*3*3=18\) factors.

So, according to the above, an integer to have 3 factor it must be \(x=(prime)^2\). In this case the number of factors = (2 + 1) = 3: 1, prime and prime^2. For example, 2^2 has three factors 1, 2, and 4; 3^2 has three factors 1, 3, and 9.
_________________

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: 72
WE: Sales (Internet and New Media)
CAT Tests
M28-50 [#permalink]

Show Tags

New post 19 Jun 2018, 02:05
Bunuel wrote:
If \(0 \lt x \lt y\) and \(x\) and \(y\) are consecutive perfect squares, what is the remainder when \(y\) is divided by \(x\)?


(1) Both \(x\) and \(y\) have 3 positive factors.

(2) Both \(\sqrt{x}\) and \(\sqrt{y}\) are prime numbers.


D was very prominent , but I overthought ,
1st statement : 3 positive factors , this means the number is prime . But in this case , 5 & 11 can also be a option ? even 5 & 7 ? If y is 7 , and x is 5 then the remainder is 2 , and if y is 3 and x is 2 , then the remainder is 1 . This is the only confusion I'm having .
other that both the statement clearly indicates that x and y are prime .

Statement 2 , clearly says , that x & y are prime , as both are perfect squares

I chose E , as I overlooked that X & Y are consecutive perfect square. I was determined that X & Y both are prime, Now when I'm reading it again , it bloody says consecutive perfect square , hence 2 & 3 are the only option. Makes perfect sense.

Nice question Bunuel .
_________________

" Can't stop learning and failing"

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46295
Re: M28-50 [#permalink]

Show Tags

New post 19 Jun 2018, 02:13
loserunderachiever wrote:
Bunuel wrote:
If \(0 \lt x \lt y\) and \(x\) and \(y\) are consecutive perfect squares, what is the remainder when \(y\) is divided by \(x\)?


(1) Both \(x\) and \(y\) have 3 positive factors.

(2) Both \(\sqrt{x}\) and \(\sqrt{y}\) are prime numbers.


D was very prominent , but I overthought ,
1st statement : 3 positive factors , this means the number is prime . But in this case , 5 & 11 can also be a option ? even 5 & 7 ? If y is 7 , and x is 5 then the remainder is 2 , and if y is 3 and x is 2 , then the remainder is 1 . This is the only confusion I'm having .
other that both the statement clearly indicates that x and y are prime . Can you please explain the remainder keeps on changing if we are considering other primes except 2 and 3 .

I chose E , I was determined that I should be D , but as the remainder was changing I chose E .

Bunuel


It seems that you are missing the crucial part the stem tells us: \(x\) and \(y\) are consecutive perfect squares. So, for example:
1^2 and 2^2;
2^2 and 3^2;
3^2 and 4^2;
...


So, if \(x\) and \(y\) are consecutive perfect squares, then \(\sqrt{x}\) and \(\sqrt{y}\) are consecutive integers:
1 and 2;
2 and 3;
3 and 4;
...

Both statements imply that \(\sqrt{x}\) and \(\sqrt{y}\) are primes. The only two consecutive integers which are primes are 2 and 3.
_________________

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: 72
WE: Sales (Internet and New Media)
CAT Tests
Re: M28-50 [#permalink]

Show Tags

New post 19 Jun 2018, 02:26
Bunuel wrote:
loserunderachiever wrote:
Bunuel wrote:
If \(0 \lt x \lt y\) and \(x\) and \(y\) are consecutive perfect squares, what is the remainder when \(y\) is divided by \(x\)?


(1) Both \(x\) and \(y\) have 3 positive factors.

(2) Both \(\sqrt{x}\) and \(\sqrt{y}\) are prime numbers.


D was very prominent , but I overthought ,
1st statement : 3 positive factors , this means the number is prime . But in this case , 5 & 11 can also be a option ? even 5 & 7 ? If y is 7 , and x is 5 then the remainder is 2 , and if y is 3 and x is 2 , then the remainder is 1 . This is the only confusion I'm having .
other that both the statement clearly indicates that x and y are prime . Can you please explain the remainder keeps on changing if we are considering other primes except 2 and 3 .

I chose E , I was determined that I should be D , but as the remainder was changing I chose E .

Bunuel


It seems that you are missing the crucial part the stem tells us: \(x\) and \(y\) are consecutive perfect squares. So, for example:
1^2 and 2^2;
2^2 and 3^2;
3^2 and 4^2;
...


So, if \(x\) and \(y\) are consecutive perfect squares, then \(\sqrt{x}\) and \(\sqrt{y}\) are consecutive integers:
1 and 2;
2 and 3;
3 and 4;
...

Both statements imply that \(\sqrt{x}\) and \(\sqrt{y}\) are primes. The only two consecutive integers which are primes are 2 and 3.


Makes sense ! bloodyhell , I missed the question stem as consecutive perfect squares. Thank you Bunuel . Nice question.
_________________

" Can't stop learning and failing"

Re: M28-50   [#permalink] 19 Jun 2018, 02:26
Display posts from previous: Sort by

M28-50

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

Moderators: chetan2u, Bunuel



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®.