Author 
Message 
Intern
Joined: 20 Feb 2008
Posts: 10

1
This post received KUDOS
2
This post was BOOKMARKED
Is \(X\) divisible by 15? 1. When \(X\) is divided by 10, the result is an integer 2. \(X^2\) is a multiple of 30 Source: GMAT Club Tests  hardest GMAT questions REVISED VERSION OF THIS QUESTION IS HERE: m057053120.html#p1255538



CIO
Joined: 02 Oct 2007
Posts: 1209

Re: m05 #22 [#permalink]
Show Tags
01 Apr 2009, 03:32
5
This post received KUDOS
I've changed the OE a bit. From S1 we know that \(X\) is an integer divisible by 10. Not sufficient by itself. From S2 we know that \(X\) might be divisible by 15 but not in all cases. Consider \(X=\sqrt{30}\) (not divisible by 15) vs. \(X=30\) (divisible by 15). From S1+S2 we know that \(X\) is an integer and that its square is divisible by 30. This is only possible if \(X\) is divisible by 30. Hope this helps. klb15 wrote: The explanation does not seem correct... My ANS is E.
Can anyone explain further?
_________________
Welcome to GMAT Club! Want to solve GMAT questions on the go? GMAT Club iPhone app will help. Please read this before posting in GMAT Club Tests forum Result correlation between real GMAT and GMAT Club Tests Are GMAT Club Test sets ordered in any way? Take 15 free tests with questions from GMAT Club, Knewton, Manhattan GMAT, and Veritas.
GMAT Club Premium Membership  big benefits and savings



Director
Joined: 01 Apr 2008
Posts: 837
Name: Ronak Amin
Schools: IIM Lucknow (IPMX)  Class of 2014

Re: m05 #22 [#permalink]
Show Tags
01 Apr 2009, 05:04
C. From 1 ) X is an integer =>NSF From 2) X has atleast one 2,5 and 3 as factors.
1 + 2. X is divisible by 15.



CIO
Joined: 02 Oct 2007
Posts: 1209

Re: m05 #22 [#permalink]
Show Tags
01 Apr 2009, 05:08
Not necessarily. \(X\) can equal \(\sqrt{30}\) or \(\sqrt{60}\). Economist wrote: C. From 1 ) X is an integer =>NSF From 2) X has atleast one 2,5 and 3 as factors.
1 + 2. X is divisible by 15.
_________________
Welcome to GMAT Club! Want to solve GMAT questions on the go? GMAT Club iPhone app will help. Please read this before posting in GMAT Club Tests forum Result correlation between real GMAT and GMAT Club Tests Are GMAT Club Test sets ordered in any way? Take 15 free tests with questions from GMAT Club, Knewton, Manhattan GMAT, and Veritas.
GMAT Club Premium Membership  big benefits and savings



CIO
Joined: 02 Oct 2007
Posts: 1209

Re: m05 #22 [#permalink]
Show Tags
27 Jul 2010, 07:53
3
This post received KUDOS
Hi, This is Data Sufficiency (DS) GMAT quant question. DS questions have 2 statements (1) and (2). Here are the options for DS questions: (A) Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient (B) Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient (D) EACH statement ALONE is sufficient (E) Statements (1) and (2) TOGETHER are NOT sufficient Welcome to the Forum! kalyanit wrote: I am new to the forum. Pls tell me What r the options your considering ? What is the meaning of Option C ?
_________________
Welcome to GMAT Club! Want to solve GMAT questions on the go? GMAT Club iPhone app will help. Please read this before posting in GMAT Club Tests forum Result correlation between real GMAT and GMAT Club Tests Are GMAT Club Test sets ordered in any way? Take 15 free tests with questions from GMAT Club, Knewton, Manhattan GMAT, and Veritas.
GMAT Club Premium Membership  big benefits and savings



Intern
Joined: 19 Dec 2009
Posts: 34

Re: m05 #22 [#permalink]
Show Tags
27 Jul 2010, 17:34
Came to same conclusion as many, C.
1. means x must be an integer. 2. + 1 means that Sqrt of n*30 must be an integer
2 + 1 mean that x must be divisible by 30. i.e. for Sqrt of n*30 to be an integer n must equals to at least (2*5*3).
Good question!



Manager
Status: Bouncing back from failure
Joined: 08 Mar 2010
Posts: 87
Schools: Wharton,MIT, Tepper, Kelly,
WE 1: 7 years Service Managament, poject Management, Business Consultant Retail

Re: m05 #22 [#permalink]
Show Tags
28 Jul 2010, 03:25
1
This post received KUDOS
Is X divisible by 15?
1. When X is divided by 10, the result is an integer  X=K*2*5 NOt sufficient 2. X^2 is a multiple of 30  X^2= K1*2*3*5 since X might not be integer..Not sufficeint
Combining both .. sufficient Ans C



Manager
Status: 700 (q47,v40); AWA 6.0
Joined: 16 Mar 2011
Posts: 80

Re: m05 #22 [#permalink]
Show Tags
05 Apr 2011, 20:55
4
This post received KUDOS
I'd take any division questions the following way: From 1, X=10k for some positive integer k. Since this value could be ANy integer and nt merely a multiple of 3, I'd consider this insufficient. From 2, X^2 = 30m for some positive integer m. Now this means that X = 30^1/2*m^1/2 which could result in an irrational number also apart from the regular integers. This appears insufficient too. Let both clauses be combined now: We have X^2 = 100(k^2) = 30m for some k and m. This means k^2/m is some 3/10. So K^2 is proportional to 3 and this is impossible for integer values of K unless K is a factor of some multiple of 3 and hence is itself divisible by 3. (Reductio ad absurdum in simpler terms). So X=10k now reduces to X=30n for some natural number n. Ergo, X is a multiple of 30 and hence 15. Regards Rahul
_________________
Regards Rahul



Intern
Joined: 24 Jun 2011
Posts: 42

Re: m05 #22 [#permalink]
Show Tags
29 Jul 2011, 07:07
With B you can have X = square root (30) also as a possibility, which is not divisible by 15.



Senior Manager
Joined: 18 Sep 2009
Posts: 333

Re: m05 #22 [#permalink]
Show Tags
29 Jul 2011, 08:02
HAi retro ,
I got your point up to k*k/m=3/10. After that we said k is proportional to 3 and so on. I did not understand that. Can you explain in detail. I got almost wrong these type of questions. Your explanation will help me a lot
tomB



Intern
Joined: 02 Aug 2010
Posts: 4

Re: m05 #22 [#permalink]
Show Tags
31 Jul 2011, 11:39
I thought the answer is 'B' second statement says 2. X^2 is a multiple of 30
I guessed this would mean any multiple of 30 which is a square number would satisfy the equation x^2=30n. for example 900 or 3600. Please suggest .



Intern
Joined: 28 Jul 2011
Posts: 3

Re: m05 #22 [#permalink]
Show Tags
31 Jul 2011, 12:12
I agree hemadri. That's the same doubt I've. Cause every multiple of 30 is surely divisible by 15.
Posted from my mobile device



Manager
Joined: 16 May 2011
Posts: 198
Concentration: Finance, Real Estate
GMAT Date: 12272011
WE: Law (Law)

Re: m05 #22 [#permalink]
Show Tags
31 Jul 2011, 23:59
1
This post received KUDOS
hey, S1: 10 i.e is not divisible but 30 is. 20 isn't and 60 is NS S2: you said that x^2=30n so: x^2 can be 30*30 which means that x=30 hence divisible by 15, but
x^2 cab be 30*2 which means that x=root 60 , hence not divisible by 15. NS
combining:
x^2=30A x=10B
X^2/X=30A/10B X= 3*(A/B) since x has 3 in it and from S1 we know that A/B must be 10(0r 2*5) or else it wont be an integer
x=3* 2something*5 something. which means 30;60;90 etc.. allways divisible by 15



Intern
Joined: 03 May 2011
Posts: 3

Re: m05 #22 [#permalink]
Show Tags
10 Aug 2011, 22:55
st 1 : X divisible by 10 Insuff
st 2 : X^2 divisible by 30 . As pointed out by dzyubam, x could be root 30 (30^1/2) Insuff
My doubt is combining both, we get X could be 10 root 30 . Which is not divisible by 15. Pls explain



Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1909

Re: m05 #22 [#permalink]
Show Tags
11 Aug 2011, 00:54
1
This post received KUDOS
GMATmay wrote: st 1 : X divisible by 10 Insuff
st 2 : X^2 divisible by 30 . As pointed out by dzyubam, x could be root 30 (30^1/2) Insuff
My doubt is combining both, we get X could be 10 root 30 . Which is not divisible by 15. Pls explain \(10\sqrt{30}\) doesn't satisfy statement 1. Per statement 1 X has to be ....20,10,0,10,20,30... A multiple of 10. \(10\sqrt{30}\) is NOT a multiple of 10.
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Manager
Joined: 16 May 2011
Posts: 198
Concentration: Finance, Real Estate
GMAT Date: 12272011
WE: Law (Law)

Re: m05 #22 [#permalink]
Show Tags
11 Aug 2011, 01:21
1
This post received KUDOS
s1 x can be 10 no or 30yes (divisible by 15). so x=10a S2 x^2=30b. b can be 2 so not divisible or b=30 then x divisible.
combining: x^2=30b and x=10a
x^2/x=30b/10a so x= 3(a/b). from S1 we know that x is an integer and a multiple of 10 so x^2 must conclude at least one 2 one 3 and one 5 to be an integer (30=2*5*3) so 3*(a/b)= 3*(2*5/2*5*3) and it must be an integer.



Director
Status: Final Countdown
Joined: 17 Mar 2010
Posts: 504
Location: India
GPA: 3.82
WE: Account Management (Retail Banking)

Re: m05 #22 [#permalink]
Show Tags
02 Aug 2012, 05:45
Bunuel, please throw some light here, (c) is right as per many of us but why not (E)?
_________________
" Make more efforts " Press Kudos if you liked my post



Intern
Joined: 23 Jul 2012
Posts: 14
Location: United States
Concentration: Entrepreneurship, Strategy
GMAT 1: 640 Q49 V27 GMAT 2: 690 Q50 V33 GMAT 3: 700 Q50 V34 GMAT 4: 740 Q50 V39
GRE 1: 1430 Q800 V630
GPA: 3.08
WE: Research (Pharmaceuticals and Biotech)

Re: m05 #22 [#permalink]
Show Tags
02 Aug 2012, 06:10
Statement 1 is clearly insufficient.
Now coming to Statement 2, we have x^2 = 30*k for some positive integer k. So now, x^2 = 30*k is a quadratic equation (degree 2) which will have 2 roots. Hence, x = +sqrt(30*k) and x = sqrt(30*k). Nowhere in the question it is given that x is positive. So we by ourselves cannot take x = +sqrt(30*k). Therefore, the answer has to be E.



Math Expert
Joined: 02 Sep 2009
Posts: 44668

Re: m05 #22 [#permalink]
Show Tags
02 Aug 2012, 06:39
3
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
thevenus wrote: Bunuel, please throw some light here, (c) is right as per many of us but why not (E)? Is \(x\) divisible by 15?(1) When \(x\) is divided by 10, the result is an integer > \(\frac{x}{10}=integer\) > \(x=10*integer\). Now, if \(x=0\) (in case \(integer=0\)), then the answer is YES but if \(x=10\) (in case \(integer=1\)), then the answer is NO. Not sufficient. From this statement though we can deduce that \(x\) is an integer (since \(x=10*integer=integer\)). (2) \(x^2\) is a multiple of 30 > if \(x=0\), then the answer is YES but if \(x=\sqrt{30}\), then the answer is NO. Not sufficient. (1)+(2) Since from (1) \(x=integer\) then \(x^2=integer\), and in order \(x^2\) to be divisible by 30=2*3*5, \(x\) must be divisible by 30 (\(x\) must be a multiple of 2, 3 and 5, else how can this primes appear in \(x^2\)?), hence \(x\) is divisible by 15 too. Sufficient. Notice that \(x\) can be positive, negative or even zero, but in any case it'll be divisible by 30.Answer: C. Next, every GMAT divisibility question will tell you in advance that any unknowns represent positive integers (ALL GMAT divisibility questions are limited to positive integers only). So, we edited this question and in the new GMAT Club tests this question reads: 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 > since \(x\) is an integer, then \(x^2\) is a perfect square. 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. Hope it's clear.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Director
Status: Final Countdown
Joined: 17 Mar 2010
Posts: 504
Location: India
GPA: 3.82
WE: Account Management (Retail Banking)

Re: m05 #22 [#permalink]
Show Tags
02 Aug 2012, 07:07
Bunuel wrote: thevenus wrote: Bunuel, please throw some light here, (c) is right as per many of us but why not (E)? Is \(x\) divisible by 15?(1) When \(x\) is divided by 10, the result is an integer > \(\frac{x}{10}=integer\) > \(x=10*integer\). Now, if \(x=0\) (in case \(integer=0\)), then the answer is YES but if \(x=10\) (in case \(integer=1\)), then the answer is NO. Not sufficient. From this statement though we can deduce that \(x\) is an integer (since \(x=10*integer=integer\)). (2) \(x^2\) is a multiple of 30 > if \(x=0\), then the answer is YES but if \(x=\sqrt{30}\), then the answer is NO. Not sufficient. (1)+(2) Since from (1) \(x=integer\) then \(x^2=integer\), and in order \(x^2\) to be divisible by 30=2*3*5, \(x\) must be divisible by 30 (\(x\) must be a multiple of 2, 3 and 5, else how can this primes appear in \(x^2\)?), hence \(x\) is divisible by 15 too. Sufficient. Notice that \(x\) can be positive, negative or even zero, but in any case it'll be divisible by 30.Answer: C. Next, every GMAT divisibility question will tell you in advance that any unknowns represent positive integers (ALL GMAT divisibility questions are limited to positive integers only). So, we edited this question and in the new GMAT Club tests this question reads: 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 > since \(x\) is an integer, then \(x^2\) is a perfect square. 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. Hope it's clear. Thanks a lot, Kudos for you +1 Wasn't the previous one was tougher? why did you changed / modified ? Now the GMAT can't put such an option (of choosing irrational no. at least if not negative numbers?)
_________________
" Make more efforts " Press Kudos if you liked my post







Go to page
1 2
Next
[ 29 posts ]



