|
Author |
Message |
|
Director
Joined: 27 May 2008
Posts: 554
Followers: 4
Kudos [?]:
107
[1] , given: 0
|
M16 Q35 PS from GMAT club tests [#permalink]
 14 Aug 2008, 09:25
1
This post received
KUDOS
Question Stats:
47% (02:35) correct
52% (02:05) wrong based on 71 sessions
X , A , and B are positive integers. When X is divided by A , the remainder is B . If when X is divided by B , the remainder is A - 2 , which of the following must be true? (A) A is even (B) X + B is divisible by A(C) X - 1 is divisible by A(D) B = A - 1(E) A + 2 = B + 1Source: GMAT Club Tests - hardest GMAT questions REVISED VERSION OF THIS QUESTION IS HERE: m16-q35-ps-from-gmat-club-tests-68861.html#p1220163
|
|
|
|
|
|
|
|
|
Manager
Joined: 04 Jun 2008
Posts: 162
Followers: 2
Kudos [?]:
7
[1] , given: 0
|
Re: PS from GMAT club test M16 Q35 [#permalink]
14 Aug 2008, 09:42
1
This post received
KUDOS
durgesh79 wrote: spent 10 minutes on this one .... and finally guessed it and it was right ...  X, A, and B are positive integers. When X is divided by A, the remainder is B. When X is divided by B, the remainder is A-2 . Which of the following must be true? A is even X+B is divisible by A X-1 is divisible by A B = A-1 A+2 = B+1 D guessing.. From X / A = p * A + B X/B = Q* B + (A-2) So.. B < A and (A-2) < B So B < A < B+2 Since A and b ARE INTEGERS A should be B+1 So I vote for D spent more than 3 Mins
|
|
|
|
|
|
SVP
Joined: 30 Apr 2008
Posts: 1900
Location: Oklahoma City
Schools: Hard Knocks
Followers: 25
Kudos [?]:
339
[0], given: 32
|
Re: PS from GMAT club test M16 Q35 [#permalink]
14 Aug 2008, 09:53
you never define p for this: Quote: X / A = p * A + B to be true, p must be negative. that doesn't make any sense. \frac{x}{A} = Ap + Bx = pA^2 + ABTake x = 9, a = 7 \frac{9}{7} = 7p + 99 = 49p + 63-54 = 49p-\frac{54}{49} = pDo you mean this: \frac{x}{a} = \frac{x-b}{a} + \frac{b}{a}
_________________
------------------------------------
J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
SVP
Joined: 07 Nov 2007
Posts: 1842
Location: New York
Followers: 20
Kudos [?]:
291
[9] , given: 5
|
Re: PS from GMAT club test M16 Q35 [#permalink]
14 Aug 2008, 09:58
9
This post received
KUDOS
durgesh79 wrote: spent 10 minutes on this one .... and finally guessed it and it was right ... X, A, and B are positive integers. When X is divided by A, the remainder is B. When X is divided by B, the remainder is A-2 . Which of the following must be true? A is even X+B is divisible by A X-1 is divisible by A B = A-1 A+2 = B+1 D firm: When X is divided by A, the remainder is B. -- means A>B (remainder always less A) e.g. 5/10 -- remainder -- 5 25/10 -- remainder - 5 ( B<A) When X is divided by B, the remainder is A-2 that means B>A-2 --> B+2>A Combine both equations. B+2>A>B (A, B are positive intergers.. there is only one values posible between B and B+2.. that is B+1 so A=B+1
_________________
Your attitude determines your altitude
Smiling wins more friends than frowning
Last edited by x2suresh on 14 Aug 2008, 10:01, edited 1 time in total.
|
|
|
|
|
|
SVP
Joined: 07 Nov 2007
Posts: 1842
Location: New York
Followers: 20
Kudos [?]:
291
[0], given: 5
|
Re: PS from GMAT club test M16 Q35 [#permalink]
14 Aug 2008, 10:01
chan4312 wrote: durgesh79 wrote: D guessing..
From
X / A = p * A + B
X/B = Q* B + (A-2)
spent more than 3 Mins Above equations are incorrect. X = p * A + B X = Q* B + (A-2)
_________________
Your attitude determines your altitude
Smiling wins more friends than frowning
|
|
|
|
|
|
Intern
Joined: 25 Apr 2010
Posts: 2
Followers: 0
Kudos [?]:
0
[0], given: 3
|
Re: M16 Q35 PS from GMAT club tests [#permalink]
27 Apr 2010, 23:07
Also from substitution method it we can see that by taking numbers for A and B , taking 3 and 2 the closer number would be 5, as the conditions get satisfied so we can assure that 3 and 2 are A,B. Thus satisfies the conditions.
Took 2 min
|
|
|
|
|
|
Manager
Status: On my way !!!
Joined: 11 Apr 2011
Posts: 115
Location: France
Concentration: Operations, Strategy
GMAT 1: 760 Q50 V44
GPA: 3.1
WE: Manufacturing and Production (Energy and Utilities)
Followers: 1
Kudos [?]:
14
[1] , given: 4
|
Re: M16 Q35 PS from GMAT club tests [#permalink]
28 Apr 2011, 10:20
1
This post received
KUDOS
spent more than 10 min trying to solve, finally substituted numbers (A=3, B=2) to arrive at (D) ... great approach by x2suresh ... divisor>remainder ... life can be so simple 
_________________
http://pyarapopat.wordpress.com
|
|
|
|
|
|
Intern
Joined: 28 Apr 2011
Posts: 1
Followers: 0
Kudos [?]:
0
[0], given: 0
|
Re: M16 Q35 PS from GMAT club tests [#permalink]
28 Apr 2011, 15:57
D.
Plugging in numbers and backsolving - Solving from the last option.
X=5;A=3;B=2 -> We can eliminate all the answer choices except D. <1 Min
|
|
|
|
|
|
Manager
Affiliations: The Earth organization, India
Joined: 25 Dec 2010
Posts: 196
WE 1: SAP consultant-IT 2 years
WE 2: Entrepreneur-family business 2 years
Followers: 4
Kudos [?]:
8
[0], given: 12
|
Re: M16 Q35 PS from GMAT club tests [#permalink]
30 Jun 2011, 01:33
I know this is a dumb question- but I cant solve these 2 inequalities mathematically :  b < a a-2 <b
_________________
Cheers !!
Quant 47-Striving for 50
Verbal 34-Striving for 40
|
|
|
|
|
|
Intern
Joined: 11 Jan 2010
Posts: 32
Followers: 1
Kudos [?]:
34
[0], given: 6
|
Re: M16 Q35 PS from GMAT club tests [#permalink]
02 May 2012, 11:29
Excellent Concept Problem: D is correct answer.
When X is divided by A, the remainder is B. => A > B
When X is divided by B, the remainder is (A-2). => B > A - 2
Combining the two inequalities: A > B > A - 2
i.e.: B is between A and (A-2), so B must be equal to A-1.
B = A - 1. (D) is the correct answer.
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11566
Followers: 1796
Kudos [?]:
9577
[1] , given: 826
|
Re: M16 Q35 PS from GMAT club tests [#permalink]
03 May 2013, 05:18
1
This post received
KUDOS
durgesh79 wrote: X , A , and B are positive integers. When X is divided by A , the remainder is B . If when X is divided by B , the remainder is A - 2 , which of the following must be true? (A) A is even (B) X + B is divisible by A(C) X - 1 is divisible by A(D) B = A - 1(E) A + 2 = B + 1Source: GMAT Club Tests - hardest GMAT questions spent 10 minutes on this one .... and finally guessed it and it was right ... BELOW IS REVISED VERSION OF THIS QUESTION:If x, a, and b are positive integers such that when x is divided by a, the remainder is b and when x is divided by b, the remainder is a-2, then which of the following must be true?A. a is even B. x+b is divisible by aC. x-1 is divisible by aD. b=a-1E. a+2=b+1When x is divided by a, the remainder is b --> x=aq+b --> remainder=b<a=divisor (remainder must be less than divisor); When x is divided by b, the remainder is a-2 --> x=bp+(a-2) --> remainder=(a-2)<b=divisor. So we have that: a-2<b<a, as a and b are integers, then it must be true that b=a-1 (there is only one integer between a-2 and a, which is a-1 and we are told that this integer is b, hence b=a-1). Answer: D.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
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. NEW!!!
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. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Intern
Joined: 12 Apr 2013
Posts: 9
Location: Germany
Concentration: Finance, Accounting
GMAT Date: 05-28-2013
GPA: 3.6
Followers: 0
Kudos [?]:
10
[0], given: 20
|
Re: PS from GMAT club test M16 Q35 [#permalink]
05 May 2013, 13:47
x2suresh wrote:
X / A = p * A + B
X/B = Q* B + (A-2)
Above equations are incorrect.
X = p * A + B
X = Q* B + (A-2)
took me almost 10 minutes to accept that the first 2 equations are really incorrect. But it helps to substitude numbers. 
_________________
........................................................................................
See it big and keep it simple.
|
|
|
|
|
|
Intern
Joined: 15 Sep 2011
Posts: 22
Location: United States
Concentration: Finance, International Business
WE: Corporate Finance (Manufacturing)
Followers: 0
Kudos [?]:
5
[0], given: 5
|
Re: PS from GMAT club test M16 Q35 [#permalink]
09 May 2013, 18:01
Ultimor wrote: x2suresh wrote:
X / A = p * A + B
X/B = Q* B + (A-2)
Above equations are incorrect.
X = p * A + B
X = Q* B + (A-2)
took me almost 10 minutes to accept that the first 2 equations are really incorrect. But it helps to substitude numbers. Agreed. It's a good trap, one that testmakers know people fall into, easily.  [old way of thinking & bad habits!!!] 
_________________
https://www.youtube.com/watch?v=D_Vg4uyYwEk
Study. Study in earnest. If you are to be salt and light, you need knowledge, ability. Or do you imagine that an idle and lazy life will entitle you to receive infused knowledge? - St. Jose Maria Escriva
Somos lo que hacemos día a día; de modo que la excelencia no es un acto, sino un hábito
I've missed more than 9000 shots in my career. I've lost almost 300 games. 26 times, I've been trusted to take the game winning shot and missed. I've failed over and over and over again in my life. And that is why I succeed... Michael Jordan
Me gusta Kudos! Mil gracias!!
|
|
|
|
|
|
Intern
Joined: 21 Sep 2012
Posts: 1
Followers: 0
Kudos [?]:
0
[0], given: 21
|
Re: M16 Q35 PS from GMAT club tests [#permalink]
11 May 2013, 07:27
Simple Plugin type Question :-
X = 11
A = 3
B = 2
...........................
Substitute in answer choices and you will find that only D satisfies the condition.
Solved in under 1:30 min.
|
|
|
|
|
|
|
Re: M16 Q35 PS from GMAT club tests
[#permalink]
11 May 2013, 07:27
|
|
|
|
|
|
|
|
|
|
|
close
