Author 
Message 
TAGS:

Hide Tags

Director
Joined: 22 Mar 2011
Posts: 604
WE: Science (Education)

Re: The sum of n consecutive positive integers is 45
[#permalink]
Show Tags
29 Jul 2012, 06:27
Q4. Is y – x positive? (1) y > 0 (2) x = 1 – y The question we are asked is in fact is y>x? (1) Not sufficient, as we don't know anything about x. (2) We have x+y=1, again not sufficient. We can have x=y=0.5, or x=0.25 < y=0.75, or x=0.75 > y=0.25 (1) and (2) not sufficient, we can use the examples from the analysis for (2) above. Answer E
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Director
Joined: 22 Mar 2011
Posts: 604
WE: Science (Education)

Re: The sum of n consecutive positive integers is 45
[#permalink]
Show Tags
29 Jul 2012, 06:46
Q5. If a and b are integers, and a not= b, is ab > 0? (1) a^b > 0 (2) a^b is a nonzero integer The question can be rephrased as are a and b distinct nonzero integers and is b positive? (1) We can deduce that \(a\neq0\), but b can be 0. Take a=1, b=0, then \(a^0=1>0\) and ab=0. But if we take a=2 and b=1, then \(a^b=2>0\) and ab=2>0. Not sufficient. (2) Again \(a\neq0\). But a can be 1, in which case b can be negative or 0. Not sufficient. (1) and (2) Since we cannot guarantee that \(b\neq0\), again not sufficient. Answer E
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Director
Joined: 22 Mar 2011
Posts: 604
WE: Science (Education)

Re: The sum of n consecutive positive integers is 45
[#permalink]
Show Tags
29 Jul 2012, 06:56
Q6. If M and N are integers, is (10^M + N)/3 an integer? 1. N = 5 2. MN is even (1) M can be negative, in which case \((10^M + N)/3\) is not an integer. But for example, if M=0, N=5, \((10^M + N)/3=6/3=2\) is an integer. Not sufficicent. (2) MN even means at least one of the two numbers must be even. We can take M=0 and N=3, then \((10^M + N)/3=4/3\) it's not an integer. But for M=1 and N=2, \((10^M + N)/3=12/3=4\) it is an integer. Not sufficient. (1) and (2): N=5, but since MN is even, it means that M must be even. Still, we cannot exclude the case M negative, for which the given expression is not an integer. Therefore, not sufficient. Answer E
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Director
Joined: 22 Mar 2011
Posts: 604
WE: Science (Education)

Re: The sum of n consecutive positive integers is 45
[#permalink]
Show Tags
29 Jul 2012, 07:04
Q8. If x and y are nonzero integers and x + y = 32, what is xy? (1) 4x  12y = 0 (2) x  y = 16 (1) From the given equality we get 4x=12y, or x=3y, which gives x=3y. We can deduce that y=8, x=24, and xy=xy=192. Not sufficient, because xy=192 or 192. (2) Since x=y+16, we find again that y=8, x=24, and xy=xy=192. Same situation as in (1), not sufficient. (1) and (2) together cannot help, as seen above. Answer E
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Math Expert
Joined: 02 Sep 2009
Posts: 47112

Re: The sum of n consecutive positive integers is 45
[#permalink]
Show Tags
29 Jul 2012, 07:10
EvaJager wrote: Q8. If x and y are nonzero integers and x + y = 32, what is xy? (1) 4x  12y = 0 (2) x  y = 16
(1) From the given equality we get 4x=12y, or x=3y, which gives x=3y. We can deduce that y=8, x=24, and xy=xy=192. Not sufficient, because xy=192 or 192.
(2) Since x=y+16, we find again that y=8, x=24, and xy=xy=192. Same situation as in (1), not sufficient.
(1) and (2) together cannot help, as seen above.
Answer E Answer to this question is A, not E. If x and y are nonzero integers and x + y = 32, what is xy? (1) \(4x  12y = 0\) > \(x+3y=0\) > \(x=3y\) > \(x\) and \(y\) have opposite signs > so either \(x=x\) and \(y=y\) OR \(x=x\) and \(y=y\) > either \(x+y=x+y=3y+y=4y=32\): \(y=8\), \(x=24\), \(xy=24*8\) OR \(x+y=xy=3yy=4y=32\): \(y=8\), \(x=24\), \(xy=24*8\), same answer. Sufficient. (2) \(x  y = 16\). Sum this one with th equations given in the stem > \(2x=48\) > \(x=24\), \(y=8\). \(xy=24*8\) (x and y have opposite sign) or \(xy=24*8\) (x and y have the same sign). Multiple choices. Not sufficient. Answer: A. 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



Math Expert
Joined: 02 Sep 2009
Posts: 47112

Re: The sum of n consecutive positive integers is 45
[#permalink]
Show Tags
29 Jul 2012, 07:14
EvaJager wrote: Q7
Since the given equality must hold for any value of x, if we substitute x = 0, we obtain \(c=d^2\).
Then, we can immediately see that (1) alone is sufficient, but (2) is not.
Answer A The answer to this question is D, not A. If b, c, and d are constants and x^2 + bx + c = (x + d)^2 for all values of x, what is the value of c? \(x^2 + bx + c = (x + d)^2\) > \(x^2+bx+c=x^2+2dx+d^2\) > \(bx+c=2dx+d^2\). Now, as above expression is true "for ALL values of \(x\)" then it must hold true for \(x=0\) too > \(c=d^2\). Next, substitute \(c=d^2\) > \(bx+d^2=2dx+d^2\) > \(bx=2dx\) > again it must be true for \(x=1\) too > \(b=2d\). So we have: \(c=d^2\) and \(b=2d\). Question: \(c=?\) (1) \(d=3\) > as \(c=d^2\), then \(c=9\). Sufficient (2) \(b=6\) > as \(b=2d\) then \(d=3\) > as \(c=d^2\), then \(c=9\). Sufficient. Answer: D. 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
Joined: 22 Mar 2011
Posts: 604
WE: Science (Education)

Re: The sum of n consecutive positive integers is 45
[#permalink]
Show Tags
29 Jul 2012, 07:17
Q9. Is the integer n odd (1) n is divisible by 3 (2) 2n is divisible by twice as many positive integers as n (1) There are odd as well as even numbers, which are divisible by 3 (3 and 6, for example). Not sufficient. (2) The statement is true for any nonzero integer. But still, n can be even or odd. Try n=3 and n=4, for example. Remark: n cannot be 0, as zero has infinitely many divisor (any nonzero integer is a factor of 0). Not sufficient. (1) and (2): From the above, it is clear that not sufficient. Answer E
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Math Expert
Joined: 02 Sep 2009
Posts: 47112

Re: The sum of n consecutive positive integers is 45
[#permalink]
Show Tags
29 Jul 2012, 07:25
EvaJager wrote: Q9. Is the integer n odd (1) n is divisible by 3 (2) 2n is divisible by twice as many positive integers as n
(1) There are odd as well as even numbers, which are divisible by 3 (3 and 6, for example). Not sufficient.
(2) The statement is true for any nonzero integer. But still, n can be even or odd. Try n=3 and n=4, for example. Remark: n cannot be 0, as zero has infinitely many divisor (any nonzero integer is a factor of 0). Not sufficient.
(1) and (2): From the above, it is clear that not sufficient.
Answer E Answer to this question is B, not E. Is the integer n odd ?(1) n is divisible by 3. Clearly insufficient, consider n=3 and n=6. (2) 2n is divisible by twice as many positive integers as n TIP: When odd number n is doubled, 2n has twice as many factors as n. Thats because odd number has only odd factors and when we multiply n by two, we remain all these odd factors as divisors and adding exactly the same number of even divisors, which are odd*2. Sufficient. Answer: B. For more on this topic check Number Theory chapter of Math Book: mathnumbertheory88376.htmlHope 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? Extrahard Quant Tests with Brilliant Analytics



Director
Joined: 22 Mar 2011
Posts: 604
WE: Science (Education)

Re: The sum of n consecutive positive integers is 45
[#permalink]
Show Tags
29 Jul 2012, 07:31
Q10. The sum of n consecutive positive integers is 45. What is the value of n? (1) n is odd (2) n >= 9 (1) When n is odd, the sum of the consecutive numbers is a multiple of the middle term. For example, we can have 9 terms, with the middle term 5, so the numbers are 1,2,3,4,5,6,7,8,9 or we can have 5 terms, with the middle term 9  7,8,9,10,11. Not sufficient. (2) If n=9, the numbers are as above from 1 to 9. If n is greater than 9, than the average of the numbers is less than 45/9 = 5, and necessarily the sequence must contain nonpositive numbers, which is impossible. So, n must be 9, sufficient. Answer B
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Director
Joined: 22 Mar 2011
Posts: 604
WE: Science (Education)

Re: The sum of n consecutive positive integers is 45
[#permalink]
Show Tags
29 Jul 2012, 07:38
Bunuel wrote: EvaJager wrote: Q8. If x and y are nonzero integers and x + y = 32, what is xy? (1) 4x  12y = 0 (2) x  y = 16
(1) From the given equality we get 4x=12y, or x=3y, which gives x=3y. We can deduce that y=8, x=24, and xy=xy=192. Not sufficient, because xy=192 or 192.
(2) Since x=y+16, we find again that y=8, x=24, and xy=xy=192. Same situation as in (1), not sufficient.
(1) and (2) together cannot help, as seen above.
Answer E Answer to this question is A, not E. If x and y are nonzero integers and x + y = 32, what is xy? (1) \(4x  12y = 0\) > \(x+3y=0\) > \(x=3y\) > \(x\) and \(y\) have opposite signs > so either \(x=x\) and \(y=y\) OR \(x=x\) and \(y=y\) > either \(x+y=x+y=3y+y=4y=32\): \(y=8\), \(x=24\), \(xy=24*8\) OR \(x+y=xy=3yy=4y=32\): \(y=8\), \(x=24\), \(xy=24*8\), same answer. Sufficient. (2) \(x  y = 16\). Sum this one with th equations given in the stem > \(2x=48\) > \(x=24\), \(y=8\). \(xy=24*8\) (x and y have opposite sign) or \(xy=24*8\) (x and y have the same sign). Multiple choices. Not sufficient. Answer: A. Hope it's clear. Yes, you're right. completely forgot about x and y having opposite signs in (1).
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Director
Joined: 22 Mar 2011
Posts: 604
WE: Science (Education)

Re: The sum of n consecutive positive integers is 45
[#permalink]
Show Tags
29 Jul 2012, 07:39
Bunuel wrote: EvaJager wrote: Q7
Since the given equality must hold for any value of x, if we substitute x = 0, we obtain \(c=d^2\).
Then, we can immediately see that (1) alone is sufficient, but (2) is not.
Answer A The answer to this question is D, not A. If b, c, and d are constants and x^2 + bx + c = (x + d)^2 for all values of x, what is the value of c? \(x^2 + bx + c = (x + d)^2\) > \(x^2+bx+c=x^2+2dx+d^2\) > \(bx+c=2dx+d^2\). Now, as above expression is true "for ALL values of \(x\)" then it must hold true for \(x=0\) too > \(c=d^2\). Next, substitute \(c=d^2\) > \(bx+d^2=2dx+d^2\) > \(bx=2dx\) > again it must be true for \(x=1\) too > \(b=2d\). So we have: \(c=d^2\) and \(b=2d\). Question: \(c=?\) (1) \(d=3\) > as \(c=d^2\), then \(c=9\). Sufficient (2) \(b=6\) > as \(b=2d\) then \(d=3\) > as \(c=d^2\), then \(c=9\). Sufficient. Answer: D. Hope it's clear. Again, you are right. Did not check further that given b, one can find d, so c...Not worth speeding!
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Director
Joined: 22 Mar 2011
Posts: 604
WE: Science (Education)

Re: The sum of n consecutive positive integers is 45
[#permalink]
Show Tags
29 Jul 2012, 07:41
Bunuel wrote: EvaJager wrote: Q9. Is the integer n odd (1) n is divisible by 3 (2) 2n is divisible by twice as many positive integers as n
(1) There are odd as well as even numbers, which are divisible by 3 (3 and 6, for example). Not sufficient.
(2) The statement is true for any nonzero integer. But still, n can be even or odd. Try n=3 and n=4, for example. Remark: n cannot be 0, as zero has infinitely many divisor (any nonzero integer is a factor of 0). Not sufficient.
(1) and (2): From the above, it is clear that not sufficient.
Answer E Answer to this question is B, not E. Is the integer n odd ?(1) n is divisible by 3. Clearly insufficient, consider n=3 and n=6. (2) 2n is divisible by twice as many positive integers as n TIP: When odd number n is doubled, 2n has twice as many factors as n. Thats because odd number has only odd factors and when we multiply n by two, we remain all these odd factors as divisors and adding exactly the same number of even divisors, which are odd*2. Sufficient. Answer: B. For more on this topic check Number Theory chapter of Math Book: mathnumbertheory88376.htmlHope it helps. Oooops! Terrible miss, as the factor 2 for an even number is not counted twice.
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Manager
Joined: 05 Nov 2012
Posts: 153

Re: The sum of n consecutive positive integers is 45
[#permalink]
Show Tags
25 Nov 2012, 11:49
Bunuel wrote: ANSWERS: 2. Is a product of three integers XYZ a prime? (1) X=Y (2) Z=1
(1) x=y > for xyz to be a prime z must be p AND x=y shouldn't be zero. Not sufficient. (2) z=1 > Not sufficient. (1)+(2) x=y and z=1 > x and y can be zero, xyz=0 not prime OR xyz is negative, so not prime. In either case we know xyz not prime.
Answer: C
i did not understand the explanation you gave..... a prime is a number which is divisible by 1 and itself right? if x,y,z are three integers..... and for it to be prime.... two for those three integers should be 1 or 1 or 1,1.... so the third one be prime number or negative prime number.... (1) says two of them are equal in magnitude... so z can be p to be prime or negative composite number or positive non prime in either case not sufficient... (2) z=1 nothing said about x,y..... not sufficient (1) + (2) product will be a positive or negative composite number or 1..... so not a prime which is sufficient.... am i thinking correctly?



Math Expert
Joined: 02 Sep 2009
Posts: 47112

Re: The sum of n consecutive positive integers is 45
[#permalink]
Show Tags
26 Nov 2012, 02:40
Amateur wrote: Bunuel wrote: ANSWERS: 2. Is a product of three integers XYZ a prime? (1) X=Y (2) Z=1
(1) x=y > for xyz to be a prime z must be p AND x=y shouldn't be zero. Not sufficient. (2) z=1 > Not sufficient. (1)+(2) x=y and z=1 > x and y can be zero, xyz=0 not prime OR xyz is negative, so not prime. In either case we know xyz not prime.
Answer: C
i did not understand the explanation you gave..... a prime is a number which is divisible by 1 and itself right? if x,y,z are three integers..... and for it to be prime.... two for those three integers should be 1 or 1 or 1,1.... so the third one be prime number or negative prime number.... (1) says two of them are equal in magnitude... so z can be p to be prime or negative composite number or positive non prime in either case not sufficient... (2) z=1 nothing said about x,y..... not sufficient (1) + (2) product will be a positive or negative composite number or 1..... so not a prime which is sufficient.... am i thinking correctly? We have that \(x=y\) and \(z=1\), thus \(xyz=x^2\). Now, \(x^2\leq{0}\), thus it cannot be a prime number (only positive numbers are primes). 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



Intern
Joined: 22 May 2012
Posts: 9
Concentration: Leadership, Other
WE: Engineering (Computer Software)

Re: The sum of n consecutive positive integers is 45
[#permalink]
Show Tags
06 Jan 2013, 04:24
Q Is a product of three integers XYZ a prime? (1) X=Y (2) Z=1
I'm unable to understand why (1) X=Y is not sufficient to answer the question?
In all cases if (1) X=Y, XYZ can not be a prime number, whether X, Y being 0 or Z being negative. I may be missing out something very basic, please help.



Math Expert
Joined: 02 Sep 2009
Posts: 47112

Re: The sum of n consecutive positive integers is 45
[#permalink]
Show Tags
07 Jan 2013, 04:20
pashraddha wrote: Q Is a product of three integers XYZ a prime? (1) X=Y (2) Z=1
I'm unable to understand why (1) X=Y is not sufficient to answer the question?
In all cases if (1) X=Y, XYZ can not be a prime number, whether X, Y being 0 or Z being negative. I may be missing out something very basic, please help. If \(x=1\), \(y=1\), \(z=7\), then \(xyz=(1)*1*(7)=7=prime\). Check here: thesumofnconsecutivepositiveintegersis8541320.html#p667155 and here: thesumofnconsecutivepositiveintegersis85413.html#p640133Hope 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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 02 Jul 2013
Posts: 20
Concentration: Technology, Other
GMAT Date: 01172014
GPA: 3.84

Re: The sum of n consecutive positive integers is 45
[#permalink]
Show Tags
22 Nov 2013, 10:20
I had a problem with number 8 and 9 8 Why is statement 2 not sufficient? I mean x means positive x so cant we then arrange it as xy=16 Same as xy=16 then use substitution method with the equation x+y=32 above? 9 You mentioned that “when odd number n is doubleb, 2n has twice as many factors as n” Is this always the case? Let’s say our odd number is 15 ,it has four factors 5 ,1,15and 3.when doubled it becomes 30.30 has 30,1,2,3,5 factors. Just one more factor than 15. My understanding for YES/NO DS question is that a statement is sufficient only if it satisfies the question always.



Math Expert
Joined: 02 Sep 2009
Posts: 47112

Re: The sum of n consecutive positive integers is 45
[#permalink]
Show Tags
26 Nov 2013, 08:35
mumbijoh wrote: I had a problem with number 8 and 9 8 Why is statement 2 not sufficient? I mean x means positive x so cant we then arrange it as xy=16 Same as xy=16 then use substitution method with the equation x+y=32 above? 9 You mentioned that “when odd number n is doubleb, 2n has twice as many factors as n” Is this always the case? Let’s say our odd number is 15 ,it has four factors 5 ,1,15and 3.when doubled it becomes 30.30 has 30,1,2,3,5 factors. Just one more factor than 15. My understanding for YES/NO DS question is that a statement is sufficient only if it satisfies the question always. Question 8 is discussed here: ifxandyarenonzerointegersandxy32whatis128845.htmlQuestion 9 is discussed here: istheintegernodd1nisdivisibleby322nis91399.htmlAs for your question: 15 has 4 factors: 1, 3, 5, and 15. 30 has 8 factors: 1, 2, 3, 5, 6, 10, 15, and 30. Hope this 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? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 17 Mar 2014
Posts: 68

Re: The sum of n consecutive positive integers is 45
[#permalink]
Show Tags
18 Apr 2014, 07:16
Bunuel wrote: Multiplication of the two digit numbers wx and cx, where w,x and c are unique nonzero digits, the product is a three digit number. What is w+cx? (1) The three digits of the product are all the same and different from w c and x. (2) x and w+c are odd numbers.
(1) wx+cx=aaa (111, 222, ... 999=37*k) > As x is the units digit in both numbers, a can be 1,4,6 or 9 (2,3,7 out because x^2 can not end with 2,3, or 7. 5 is out because in that case x also should be 5 and we know that x and a are distinct numbers). 1 is also out because 111=37*3 and we need 2 two digit numbers. 444=37*12 no good we need units digit to be the same. 666=37*18 no good we need units digit to be the same. 999=37*27 is the only possibility all digits are distinct except the unit digits of multiples. Sufficient (2) x and w+c are odd numbers. Number of choices: 13 and 23 or 19 and 29 and w+cx is the different even number.
Answer: A.
am I missing anything? it does not say that w x and c are positive, does it? w= 3, c= 2 and x= 7 37*27 = 999, here w+c 7 = 2 but we also can have w= 3 and c= 2 and x= 7 37*27 = 999, here w+c  7 = 12 Both of these sets satisfy both the conditions , hence I am getting E,



Math Expert
Joined: 02 Sep 2009
Posts: 47112

Re: The sum of n consecutive positive integers is 45
[#permalink]
Show Tags
18 Apr 2014, 11:12
qlx wrote: Bunuel wrote: Multiplication of the two digit numbers wx and cx, where w,x and c are unique nonzero digits, the product is a three digit number. What is w+cx? (1) The three digits of the product are all the same and different from w c and x. (2) x and w+c are odd numbers.
(1) wx+cx=aaa (111, 222, ... 999=37*k) > As x is the units digit in both numbers, a can be 1,4,6 or 9 (2,3,7 out because x^2 can not end with 2,3, or 7. 5 is out because in that case x also should be 5 and we know that x and a are distinct numbers). 1 is also out because 111=37*3 and we need 2 two digit numbers. 444=37*12 no good we need units digit to be the same. 666=37*18 no good we need units digit to be the same. 999=37*27 is the only possibility all digits are distinct except the unit digits of multiples. Sufficient (2) x and w+c are odd numbers. Number of choices: 13 and 23 or 19 and 29 and w+cx is the different even number.
Answer: A.
am I missing anything? it does not say that w x and c are positive, does it? w= 3, c= 2 and x= 7 37*27 = 999, here w+c 7 = 2 but we also can have w= 3 and c= 2 and x= 7 37*27 = 999, here w+c  7 = 12 Both of these sets satisfy both the conditions , hence I am getting E, w, x and c are unique nonzero digits of the two digit numbers wx and cx means that w, x, and c are 1, 2, 3, 4, 5, 6, 7, 8, or 9. 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




Re: The sum of n consecutive positive integers is 45 &nbs
[#permalink]
18 Apr 2014, 11:12



Go to page
Previous
1 2 3 4
Next
[ 71 posts ]



