Author 
Message 
TAGS:

Hide Tags

Current Student
Joined: 12 Aug 2015
Posts: 2518

Re: STONECOLD'S MATH CHALLENGE  PS AND DS QUESTION COLLECTION.
[#permalink]
Show Tags
02 Mar 2018, 23:56
loserunderachiever wrote: Stone ,
Can you give me a solution of these two ? Sure! Let me try > Question 1) Here, just for the ease of calculation > let us assume that \(25 = a\) and \(10√6= b\) such that \(T = √a+b + √ab\)
\(T = √a+b + √ab\) \(T^2 = a+b + a  b + 2√a+b * √ab = 2a + 2√a^2b^2\)
Now, put back the values of a and b \(T^2 = 50 + 2√625600\) \(T^2 = 50 + 2*√25\) \(T^2 = 50 + 10 = 60\) \(T = √60\) \(T = 2√15\)
SMASH that C!
Question 2) Now, This one is tricky. But notice that this is an infinite loop. So there must be a major trick to solve this. We can actually replace the value in the root symbol after the first 6 with x. \(x = √(6+x)\) \(x^2 = 6+x\) \(x^2x6 = 0\) \(x^23x+2x6=0\) \(x(x3)+2(x3)=0\) \((x3)(x+2)=0\) \(x=3\) or \(x=2\)
But x cannot be negative since its a root value and a root is always passive. So x≠2
Hence x = 3 SMASH that B!
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 65062

Re: STONECOLD'S MATH CHALLENGE  PS AND DS QUESTION COLLECTION.
[#permalink]
Show Tags
03 Mar 2018, 01:13
loserunderachiever wrote: Stone ,
Can you give me a solution of these two ? First question is discussed here: https://gmatclub.com/forum/newtoughan ... l#p1029216Second question is discussed here: https://gmatclub.com/forum/newtoughan ... l#p1029228 PLEASE FOLLOW THE RULES WHEN POSTING QUESTIONS: https://gmatclub.com/forum/rulesforpo ... 33935.html Questions should NOT be posted in this thread they should be posted in respective forums! Thank you.
_________________



Intern
Joined: 10 Feb 2017
Posts: 9

Re: STONECOLD'S MATH CHALLENGE  PS AND DS QUESTION COLLECTION.
[#permalink]
Show Tags
07 Mar 2018, 22:27
Hi stonecoldjust a quick ask... this question is from Mock 1 and I am just wondering if the answer is correct. Please let me know as I am getting 270 total factors. 2^8*3^4*5^2*7^1 so basically = (8+1)(4+1)(2+1)(1+1) 48)If n is the product of all the integers from 1 to 10 exclusive,how many factors does n have? [Obscure] Spoiler: 160.



Current Student
Joined: 12 Aug 2015
Posts: 2518

STONECOLD'S MATH CHALLENGE  PS AND DS QUESTION COLLECTION.
[#permalink]
Show Tags
07 Mar 2018, 22:39
Bobzi wrote: Hi stonecoldjust a quick ask... this question is from Mock 1 and I am just wondering if the answer is correct. Please let me know as I am getting 270 total factors. 2^8*3^4*5^2*7^1 so basically = (8+1)(4+1)(2+1)(1+1) 48)If n is the product of all the integers from 1 to 10 exclusive,how many factors does n have? [Obscure] Spoiler: 160.
Hi, Your solution is incorrect.
See >
\(2*3*4*5*6*7*8*9= 2^7*3^4*5*7\)
=> # of factors = \(8*5*2*2 = 160\)
Your mistake > You did not read the question properly. Notice the word EXCLUSIVE. You must EXCLUDE 1 and 10.
_________________



Intern
Joined: 09 Oct 2017
Posts: 2
Location: India
WE: Analyst (Consulting)

Re: STONECOLD'S MATH CHALLENGE  PS AND DS QUESTION COLLECTION.
[#permalink]
Show Tags
09 Mar 2018, 05:07
This is a gold mine of information!



Current Student
Joined: 12 Aug 2015
Posts: 2518

Re: STONECOLD'S MATH CHALLENGE  PS AND DS QUESTION COLLECTION.
[#permalink]
Show Tags
11 Apr 2018, 10:51
DebUSA wrote: This is a gold mine of information! I am glad you found it useful. I will be updating the tests soon.
All the best
_________________



Director
Joined: 06 Jan 2015
Posts: 784
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)

Re: STONECOLD'S MATH CHALLENGE  PS AND DS QUESTION COLLECTION.
[#permalink]
Show Tags
25 Apr 2018, 07:12
14)If p is a positive integer and 200 multiplies by p is square of an integer,what is the value of p? A)2 B)3 C)5 D)10 E)Cannot be determined. HI stonecold, \(x^2 = p*200\) In this question why can't p =2 ?
_________________
आत्मनॊ मोक्षार्थम् जगद्धिताय च Resource: GMATPrep RCs With Solution



Intern
Joined: 22 Mar 2018
Posts: 19
Location: United States (CA)
Concentration: Strategy, Technology
GPA: 3.9

Re: STONECOLD'S MATH CHALLENGE  PS AND DS QUESTION COLLECTION.
[#permalink]
Show Tags
26 May 2018, 21:57
Firstly, thanks for having these questions  they are a great help!
Wanted to ask, though, about the question below:
7)What is the units digit of 23^99∗14^352+9002^1003∗918^437986
I keep getting 7 * 1 + 8 * 4 = 9. I'm using cyclicity here. Thanks in advanced.



Board of Directors
Status: Emory Goizueta Alum
Joined: 18 Jul 2015
Posts: 3598

STONECOLD'S MATH CHALLENGE  PS AND DS QUESTION COLLECTION.
[#permalink]
Show Tags
26 May 2018, 23:59
wchin24 wrote: Firstly, thanks for having these questions  they are a great help!
Wanted to ask, though, about the question below:
7)What is the units digit of 23^99∗14^352+9002^1003∗918^437986
I keep getting 7 * 1 + 8 * 4 = 9. I'm using cyclicity here. Thanks in advanced. Hey wchin24 , The mistake you did is highlighted above. 14^352 The pattern of 4 is 4,6 This means cyclicity is 2. When you divide the power with 2, you will get 0 remainder. That means last digit is last place of the pattern, which is 6 here. Hence, the last digit of 14^352 is 6. Does that make sense?
_________________
My LinkedIn abhimahna.  My GMAT Story: From V21 to V40  My MBA Journey: My 10 years long MBA DreamMy Secret Hacks: Best way to use GMATClub  Importance of an Error Log!Verbal Resources: All SC Resources at one place  All CR Resources at one placeGMAT Club Inbuilt Error Log Functionality  View More  Best Reply Functionality on GMAT Club!New Visa Forum  Ask all your Visa Related Questions  here  Have OPT questions?  Post them here. Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for freeCheck our new About Us Page here.  Blog: Subscribe to Question of the Day BlogNew! Executive Assessment (EA) Exam  All you need to know!



Intern
Joined: 22 Mar 2018
Posts: 19
Location: United States (CA)
Concentration: Strategy, Technology
GPA: 3.9

Re: STONECOLD'S MATH CHALLENGE  PS AND DS QUESTION COLLECTION.
[#permalink]
Show Tags
27 May 2018, 00:16
abhimahna wrote: wchin24 wrote: Firstly, thanks for having these questions  they are a great help!
Wanted to ask, though, about the question below:
7)What is the units digit of 23^99∗14^352+9002^1003∗918^437986
I keep getting 7 * 1 + 8 * 4 = 9. I'm using cyclicity here. Thanks in advanced. Hey wchin24 , The mistake you did is highlighted above. 14^352 The pattern of 4 is 4,6 This means cyclicity is 2. When you divide the power with 2, you will get 0 remainder. That means last digit is last place of the pattern, which is 6 here. Hence, the last digit of 14^352 is 6. Does that make sense? OMG YES! Thank you! I was tripping up since I was seeing it as 4^0, but in reality this just means that it'll end up at the last place of the pattern here.



Current Student
Joined: 12 Aug 2015
Posts: 2518

STONECOLD'S MATH CHALLENGE  PS AND DS QUESTION COLLECTION.
[#permalink]
Show Tags
27 May 2018, 19:31
NandishSS wrote: 14)If p is a positive integer and 200 multiplies by p is square of an integer,what is the value of p? A)2 B)3 C)5 D)10 E)Cannot be determined. HI stonecold, \(x^2 = p*200\) In this question why can't p =2 ? Hi, You are right in saying that p CAN be 2. But you missing the big picture here. Ask yourself, is that the only possible value of p? What if p is \(2*5^2\) or \(2*11^2\) or \(2*101^2\) ?
You see, there are various value of the variable p that are possible in thus question. Hence the OA is E.
_________________



Manager
Joined: 08 Dec 2016
Posts: 58
GMAT 1: 610 Q49 V25 GMAT 2: 610 Q46 V28 GMAT 3: 750 Q50 V40
GPA: 3.4

STONECOLD'S MATH CHALLENGE  PS AND DS QUESTION COLLECTION.
[#permalink]
Show Tags
02 Aug 2018, 19:30
121)Data Sufficiency>How many divisors does the positive integer N have?
(1)27N^3 has 16 factors. (2)90<N^3<200
as explained, how can we say that N is prime from Statement 1. N could be 3^4 as well. If N= 3^4 then 27N^3 = 3^3*((3^4)^3)= 3^3*3^12= 3^15 Hence Factors will be 15+1=16. And Nos of Divisor of N = 3^4 is Five. Not 2 as in the case if N is prime.
Please explain if anything wrong in my understanding



Manager
Joined: 21 Jul 2018
Posts: 173

Re: STONECOLD'S MATH CHALLENGE  PS AND DS QUESTION COLLECTION.
[#permalink]
Show Tags
28 Jan 2019, 01:38
Hi stonecoldFor question 18 It looks like answer should be C and not E as only possible option after combining both the statement is P = 3, Could you please advise if I am missing something. chetan2u, Bunuel, VeritasKarishma, gmatbusters, amanvermagmatstonecold wrote: 18)Data Sufficiency>What is the value of positive integer p? A)300 multiplied by p is square of an integer. B)p is a factor of 75
Spoiler: :: E. Combing the two statements > p can be 3 or 3*5^2



Math Expert
Joined: 02 Aug 2009
Posts: 8753

Re: STONECOLD'S MATH CHALLENGE  PS AND DS QUESTION COLLECTION.
[#permalink]
Show Tags
28 Jan 2019, 01:42
Gmatprep550 wrote: Hi stonecoldFor question 18 It looks like answer should be C and not E as only possible option after combining both the statement is P = 3, Could you please advise if I am missing something. chetan2u, Bunuel, VeritasKarishma, gmatbusters, amanvermagmatstonecold wrote: 18)Data Sufficiency>What is the value of positive integer p? A)300 multiplied by p is square of an integer. B)p is a factor of 75
Spoiler: :: E. Combing the two statements > p can be 3 or 3*5^2 No, both 3 and 75 will fit in.. A)300 multiplied by p is square of an integer...300*3=900=30^2 and 300*75=22500=150^2 B)p is a factor of 75... Factors of 75 are 1,3,5,15,25,75, so both 3 and 75 fit in
_________________



Manager
Joined: 21 Jul 2018
Posts: 173

Re: STONECOLD'S MATH CHALLENGE  PS AND DS QUESTION COLLECTION.
[#permalink]
Show Tags
28 Jan 2019, 03:27
Hi chetan2u, Bunuel, VeritasKarishma, Gladiator59, generisFor question 23 statement 78 I am only able to find that "All the prime numbers greater than 3 can be written as either 6n+1 or 6n1." Not able to find anything for 6+1 and 4n+1 or 4n1. Could you please review and advise if I am missing something. stonecold wrote: 23)Which of the following statements must be true> 1)A prime number must be positive. 2)For any prime number p,there is no x such that 1<x<p and x is a divisor of p. 3)The product of first ten primes is even. 4)All prime numbers greater than 71 are odd. 5)2 and 3 are the only consecutive integers that are also prime numbers. 6)p is a prime number and x and y are positive integers.If p=x*y then one out of x or y must be one. 7)All the prime numbers greater than 3 can be written as either 4n+1 or 4n1. 8)All the prime numbers greater than 3 can be written as either 6+1 or 6n1.
Spoiler: :: All statements are true.



Math Expert
Joined: 02 Aug 2009
Posts: 8753

STONECOLD'S MATH CHALLENGE  PS AND DS QUESTION COLLECTION.
[#permalink]
Show Tags
28 Jan 2019, 04:09
Gmatprep550 wrote: Hi chetan2u, Bunuel, VeritasKarishma, Gladiator59, generisFor question 23 statement 78 I am only able to find that "All the prime numbers greater than 3 can be written as either 6n+1 or 6n1." Not able to find anything for 6+1 and 4n+1 or 4n1. Could you please review and advise if I am missing something. stonecold wrote: 23)Which of the following statements must be true> 1)A prime number must be positive. 2)For any prime number p,there is no x such that 1<x<p and x is a divisor of p. 3)The product of first ten primes is even. 4)All prime numbers greater than 71 are odd. 5)2 and 3 are the only consecutive integers that are also prime numbers. 6)p is a prime number and x and y are positive integers.If p=x*y then one out of x or y must be one. 7)All the prime numbers greater than 3 can be written as either 4n+1 or 4n1. 8)All the prime numbers greater than 3 can be written as either 6+1 or 6n1.
Spoiler: :: All statements are true. Hi.. All prime numbers have to be of type of 6n+1 or 6n1 Now 4n+1 and 4n1 is nothing but set of all odd numbers.. When n=1, 4n+1 and 4n1 becomes 3 and 5 and when n=2, 4n+1 and 4n1 becomes 7 and 9..so 3,5,7,9,11,... And all primes above 2 are odd numbers..so primes are also of type 4n+1 or 4n1, basically they will be odd
_________________



Manager
Joined: 21 Jul 2018
Posts: 173

Re: STONECOLD'S MATH CHALLENGE  PS AND DS QUESTION COLLECTION.
[#permalink]
Show Tags
28 Jan 2019, 04:43
Thanks chetan2u for valuable response. It helped me



Retired Moderator
Joined: 27 Oct 2017
Posts: 1843
WE: General Management (Education)

STONECOLD'S MATH CHALLENGE  PS AND DS QUESTION COLLECTION.
[#permalink]
Show Tags
28 Jan 2019, 08:24
As perfectly explained by chetan2u Sir, All prime numbers greater than 3 can be written as 6n+/1 or 4n+/1. But vice versa is not truefor example, for n =4, 6*4+1= 25 , but it is not prime Similarly, for n = 2, 4n+1 = 2*4+1= 9, which is not prime In fact, there is no direct formula, which can find whether a number is prime or not. All prime numbers greater than 3 can be written as 6n+/1 or 4n+/1, but all numbers in form of 6n+/1 or 4n+/1 are not prime. Gmatprep550 wrote: Hi chetan2u, Bunuel, VeritasKarishma, Gladiator59, generisFor question 23 statement 78 I am only able to find that "All the prime numbers greater than 3 can be written as either 6n+1 or 6n1." Not able to find anything for 6+1 and 4n+1 or 4n1. Could you please review and advise if I am missing something. stonecold wrote: 23)Which of the following statements must be true> 1)A prime number must be positive. 2)For any prime number p,there is no x such that 1<x<p and x is a divisor of p. 3)The product of first ten primes is even. 4)All prime numbers greater than 71 are odd. 5)2 and 3 are the only consecutive integers that are also prime numbers. 6)p is a prime number and x and y are positive integers.If p=x*y then one out of x or y must be one. 7)All the prime numbers greater than 3 can be written as either 4n+1 or 4n1. 8)All the prime numbers greater than 3 can be written as either 6+1 or 6n1.
Spoiler: :: All statements are true.
_________________



Manager
Joined: 23 Apr 2018
Posts: 160

Re: STONECOLD'S MATH CHALLENGE  PS AND DS QUESTION COLLECTION.
[#permalink]
Show Tags
18 Feb 2019, 13:18
@14)If p is a positive integer and 200 multiplies by p is square of an integer,what is the value of p? A)2 B)3 C)5 D)10 E)Cannot be determined.
Hi, can you explain, how have you written p=2*2^2 expression in the first set of questions, numbered 1517.. What does this expression mean? i am confused in this and the DS questions that contain 300 and 200 too



Intern
Joined: 18 Aug 2018
Posts: 1

Re: STONECOLD'S MATH CHALLENGE  PS AND DS QUESTION COLLECTION.
[#permalink]
Show Tags
01 Mar 2020, 14:54
where is the link of mock test 1 and 2?




Re: STONECOLD'S MATH CHALLENGE  PS AND DS QUESTION COLLECTION.
[#permalink]
01 Mar 2020, 14:54



Go to page
Previous
1 2 3 4
[ 80 posts ]

