Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 10 Mar 2014
Posts: 212

Re: The Discreet Charm of the DS
[#permalink]
Show Tags
01 Jun 2014, 21:18
Bunuel wrote: 8. If x=0.abcd, where a, b, c and d are digits from 0 to 9, inclusive, is x>7/9?First of all 7/9 is a recurring decimal =0.77(7). For more on converting Converting Decimals to Fractions see: mathnumbertheory88376.html(1) a+b>14 > the least value of a is 6 (6+9=15>14), so in this case x=0.69d<0.77(7) but a=7 and b=9 is also possible, and in this case x=0.79d>0.77(7). Not sufficient. (2) ac>6 > the least value of a is 7 (70=7>6), but we don't know the value of b. Not sufficient. (1)+(2) The least value of a is 7 and in this case from (1) least value of b is 8 (7+8=15>14), hence the least value of x=0.78d>0.77(7). Sufficient. Answer: C. Hi Bunnel, One question here. in st2 i can consider 80 also then why we are considering only least value. in st1 we are considering least value as well as other value. why this is different in st2? Thanks



Math Expert
Joined: 02 Sep 2009
Posts: 47948

Re: The Discreet Charm of the DS
[#permalink]
Show Tags
02 Jun 2014, 01:23
PathFinder007 wrote: Bunuel wrote: 8. If x=0.abcd, where a, b, c and d are digits from 0 to 9, inclusive, is x>7/9?First of all 7/9 is a recurring decimal =0.77(7). For more on converting Converting Decimals to Fractions see: mathnumbertheory88376.html(1) a+b>14 > the least value of a is 6 (6+9=15>14), so in this case x=0.69d<0.77(7) but a=7 and b=9 is also possible, and in this case x=0.79d>0.77(7). Not sufficient. (2) ac>6 > the least value of a is 7 (70=7>6), but we don't know the value of b. Not sufficient. (1)+(2) The least value of a is 7 and in this case from (1) least value of b is 8 (7+8=15>14), hence the least value of x=0.78d>0.77(7). Sufficient. Answer: C. Hi Bunnel, One question here. in st2 i can consider 80 also then why we are considering only least value. in st1 we are considering least value as well as other value. why this is different in st2? Thanks Because considering the least value of a (7), while knowing nothing about b is enough to say that the second statement is not sufficient. If b=8, then the answer is yes but if b is 0, then the answer is no.
_________________
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: 30 Apr 2014
Posts: 3

Re: The Discreet Charm of the DS
[#permalink]
Show Tags
03 Jun 2014, 00:39
Hi Bunuel, Referring to below: 4. How many numbers of 5 consecutive positive integers is divisible by 4? (1) The median of these numbers is odd (2) The average (arithmetic mean) of these numbers is a prime number
The average (arithmetic mean) of these numbers is a prime number > in any evenly spaced set the arithmetic mean (average) is equal to the median > mean=median=prime. Since it's not possible that median=2=even, (in this case not all 5 numbers will be positive), then median=odd prime, and we have the same case as above. Sufficient.
I didn't quite get the explanation on the second statement. Do you mind explaining with some numbers?
Thanks, Mitesh



Math Expert
Joined: 02 Sep 2009
Posts: 47948

Re: The Discreet Charm of the DS
[#permalink]
Show Tags
03 Jun 2014, 01:49
mrvora wrote: Hi Bunuel, Referring to below: 4. How many numbers of 5 consecutive positive integers is divisible by 4? (1) The median of these numbers is odd (2) The average (arithmetic mean) of these numbers is a prime number
The average (arithmetic mean) of these numbers is a prime number > in any evenly spaced set the arithmetic mean (average) is equal to the median > mean=median=prime. Since it's not possible that median=2=even, (in this case not all 5 numbers will be positive), then median=odd prime, and we have the same case as above. Sufficient.
I didn't quite get the explanation on the second statement. Do you mind explaining with some numbers?
Thanks, Mitesh If mean=median=prime=2, then the 5 consecutive integers would be { 0, 1, 2, 3, 4}. But this set is not possible since we are told that the set consists of 5 positive integers and 0 is neither positive nor negative integer. Hence, mean=median= odd prime > {Odd, Even, Odd prime, Even, Odd}. So, the set includes 2 consecutive even numbers. Out of 2 consecutive even integers only one is a multiple of 4. 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: 47948

Re: The Discreet Charm of the DS
[#permalink]
Show Tags
18 Sep 2014, 11:05
ajaym28 wrote: Bunuel wrote: 9. If x and y are negative numbers, is x<y?
(1) 3x + 4 < 2y + 3 > \(3x<2y1\). \(x\) can be some very small number for instance 100 and \(y\) some large enough number for instance 3 and the answer would be YES, \(x<y\) BUT if \(x=2\) and \(y=2.1\) then the answer would be NO, \(x>y\). Not sufficient.
(2) 2x  3 < 3y  4 > \(x<1.5y\frac{1}{2}\) > \(x<y+(0.5y\frac{1}{2})=y+negative\) > \(x<y\) (as y+negative is "more negative" than y). Sufficient.
Answer: B. Hi Bunnel, Please clear my doubt regarding second statement: assumtion 1 : x = 1 y = 2 it means x > y it will give me 2(1)  3 < 3(2)  4 5 < 10 [False] assumtion 2 : x = 2 y = 1 it means x < y it will give me 2(2)  3 < 3(1)  4 7 < 7 [False] How x < y is satisfying through numbers .. pls help When you pick numbers, they must satisfy the statement you are testing and the info given in the stem. So, when picking numbers for (2) numbers must satisfy 2x  3 < 3y  4 and x and y must be negative (stem). Then you should try to get an YES and NO answer to the question to prove insufficiency.
_________________
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: 14 Apr 2014
Posts: 65

Re: The Discreet Charm of the DS
[#permalink]
Show Tags
18 Sep 2014, 11:18
Bunuel wrote: ajaym28 wrote: Bunuel wrote: 9. If x and y are negative numbers, is x<y?
(1) 3x + 4 < 2y + 3 > \(3x<2y1\). \(x\) can be some very small number for instance 100 and \(y\) some large enough number for instance 3 and the answer would be YES, \(x<y\) BUT if \(x=2\) and \(y=2.1\) then the answer would be NO, \(x>y\). Not sufficient.
(2) 2x  3 < 3y  4 > \(x<1.5y\frac{1}{2}\) > \(x<y+(0.5y\frac{1}{2})=y+negative\) > \(x<y\) (as y+negative is "more negative" than y). Sufficient.
Answer: B. Hi Bunnel, Please clear my doubt regarding second statement: assumtion 1 : x = 1 y = 2 it means x > y it will give me 2(1)  3 < 3(2)  4 5 < 10 [False] assumtion 2 : x = 2 y = 1 it means x < y it will give me 2(2)  3 < 3(1)  4 7 < 7 [False] How x < y is satisfying through numbers .. pls help When you pick numbers, they must satisfy the statement you are testing and the info given in the stem. So, when picking numbers for (2) numbers must satisfy 2x  3 < 3y  4 and x and y must be negative (stem). Then you should try to get an YES and NO answer to the question to prove insufficiency. Thanks Bunnel, just one more ques putting number in that kind of equations will be good idea or solving it by algebra(like you did) is a good idea ? i mean how to figure what to use and when ?



Math Expert
Joined: 02 Sep 2009
Posts: 47948

Re: The Discreet Charm of the DS
[#permalink]
Show Tags
18 Sep 2014, 11:29
ajaym28 wrote: Bunuel wrote: ajaym28 wrote: Hi Bunnel,
Please clear my doubt regarding second statement:
assumtion 1 :
x = 1 y = 2 it means x > y
it will give me 2(1)  3 < 3(2)  4 5 < 10 [False]
assumtion 2 :
x = 2 y = 1 it means x < y
it will give me 2(2)  3 < 3(1)  4 7 < 7 [False]
How x < y is satisfying through numbers .. pls help
When you pick numbers, they must satisfy the statement you are testing and the info given in the stem. So, when picking numbers for (2) numbers must satisfy 2x  3 < 3y  4 and x and y must be negative (stem). Then you should try to get an YES and NO answer to the question to prove insufficiency. Thanks Bunnel, just one more ques putting number in that kind of equations will be good idea or solving it by algebra(like you did) is a good idea ? i mean how to figure what to use and when ? When you decide that a statement is sufficient based only on plugin method you should make sure that you tried several different numbers (and saw some pattern maybe), and even in this case you may not be 100% sure that the answer would be correct. Though if several numbers give the same answer and you are able to see some pattern, then you can make an educated guess that a statement is sufficient and moveon. Generally on DS questions when plugging numbers, your goal is to prove that the statement is NOT sufficient. So you should try to get an YES answer with one chosen number(s) and a NO with another. 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



Manager
Joined: 02 Jul 2012
Posts: 202
Location: India
GPA: 2.6
WE: Information Technology (Consulting)

Re: The Discreet Charm of the DS
[#permalink]
Show Tags
20 Oct 2014, 20:40
Dear Bunuel, If every one will have 4 then the difference will be 0 which is not even. Posted from my mobile device
_________________
Give KUDOS if the post helps you...



Math Expert
Joined: 02 Sep 2009
Posts: 47948

Re: The Discreet Charm of the DS
[#permalink]
Show Tags
21 Oct 2014, 00:56



Intern
Joined: 18 Jul 2013
Posts: 42

The Discreet Charm of the DS
[#permalink]
Show Tags
04 Nov 2014, 10:30
Hi Bunnel,
I am sorry to say i did read the link before and has query that taking (x+y)^2 or (xy)^2 ,both are correct or not. And if the first scenario is not right than why is it so? Your reply do not help me to clarify my doubt? Please bear with me if i am asking silly question but understand that i need to know it.



Math Expert
Joined: 02 Sep 2009
Posts: 47948

Re: The Discreet Charm of the DS
[#permalink]
Show Tags
04 Nov 2014, 10:42



Manager
Status: Kitchener
Joined: 03 Oct 2013
Posts: 91
Location: Canada
Concentration: Finance, Finance
GPA: 2.9
WE: Education (Education)

The Discreet Charm of the DS
[#permalink]
Show Tags
28 Jan 2015, 08:17
Bunuel wrote: 2. Is xy<=1/2?
(1) x^2+y^2=1. Recall that \((xy)^2\geq{0}\) (square of any number is more than or equal to zero) > \(x^22xy+y^2\geq{0}\) > since \(x^2+y^2=1\) then: \(12xy\geq{0}\) > \(xy\leq{\frac{1}{2}}\). Sufficient.
(2) x^2y^2=0 > \(x=y\). Clearly insufficient.
Answer: A. So, Bunuel could you please show me how we can get (xy)^2 from x^2+y^2=1? I faced difficulty in understand this point. Thank you
_________________
Click +1 Kudos if my post helped



Math Expert
Joined: 02 Sep 2009
Posts: 47948

Re: The Discreet Charm of the DS
[#permalink]
Show Tags
28 Jan 2015, 08:31



Intern
Joined: 27 Dec 2015
Posts: 5
Concentration: Statistics, Operations

Re: The Discreet Charm of the DS
[#permalink]
Show Tags
20 Jan 2016, 04:12
Bunuel wrote: 11. If x and y are integers, is x a positive integer?
(1) x*y is a prime number > since only positive numbers can be primes, then: x*y=positive > x=positive. Sufficient
(2) x*y is nonnegative integer. Notice that we are told that x*y is nonnegative, not that it's positive, so x can be positive as well as zero. Not sufficient.
Answer: A. My line of reasoning: We are told that x and y are integers, and are asked to ascertain if x is positive. Consider x*y. y = y, when y > 0; y = y, when y < 0 Case A: y > 0 => xy is a prime number, prime numbers are positive, hence x HAS TO BE positive Case B: y < 0 => xy is a prime number, prime numbers are positive, to make positive the quantity, the negative y has to be multiplied by a negative x, and so x is negative How could Statement 1 alone then, be sufficient? Kindly clarify



Math Expert
Joined: 02 Sep 2009
Posts: 47948

Re: The Discreet Charm of the DS
[#permalink]
Show Tags
20 Jan 2016, 06:18
BigFatBassist wrote: Bunuel wrote: 11. If x and y are integers, is x a positive integer?
(1) x*y is a prime number > since only positive numbers can be primes, then: x*y=positive > x=positive. Sufficient
(2) x*y is nonnegative integer. Notice that we are told that x*y is nonnegative, not that it's positive, so x can be positive as well as zero. Not sufficient.
Answer: A. My line of reasoning: We are told that x and y are integers, and are asked to ascertain if x is positive. Consider x*y. y = y, when y > 0; y = y, when y < 0 Case A: y > 0 => xy is a prime number, prime numbers are positive, hence x HAS TO BE positive Case B: y < 0 => xy is a prime number, prime numbers are positive, to make positive the quantity, the negative y has to be multiplied by a negative x, and so x is negative How could Statement 1 alone then, be sufficient? Kindly clarify In case B: if y is negative, then y is positive, thus xy = x*(y)= x*positive = prime = positive > x = positive.
_________________
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: 04 Sep 2016
Posts: 1

The Discreet Charm of the DS
[#permalink]
Show Tags
06 Nov 2016, 05:18
Bunuel wrote: 11. If x and y are integers, is x a positive integer?
(1) x*y is a prime number > since only positive numbers can be primes, then: x*y=positive > x=positive. Sufficient
(2) x*y is nonnegative integer. Notice that we are told that x*y is nonnegative, not that it's positive, so x can be positive as well as zero. Not sufficient.
Answer: A. I think the option should be E Option 1 x * y will result in positive, where x is negative. Can you explain further..??



Math Expert
Joined: 02 Sep 2009
Posts: 47948

Re: The Discreet Charm of the DS
[#permalink]
Show Tags
06 Nov 2016, 06:06
hardik0491 wrote: Bunuel wrote: 11. If x and y are integers, is x a positive integer?
(1) x*y is a prime number > since only positive numbers can be primes, then: x*y=positive > x=positive. Sufficient
(2) x*y is nonnegative integer. Notice that we are told that x*y is nonnegative, not that it's positive, so x can be positive as well as zero. Not sufficient.
Answer: A. I think the option should be E Option 1 x * y will result in positive, where x is negative. Can you explain further..?? If x is negative, then x*y = negative*nonnegative = nonpositive, which cannot be prime, since only positive numbers are primes.
_________________
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: 13 Sep 2015
Posts: 3

Re: The Discreet Charm of the DS
[#permalink]
Show Tags
15 Dec 2016, 11:16
Hello Bunuel,
For question 9, option B  What if we assign the 100 for x and 99 for y? x<y, but the equation (rearranged) 3y2x>1 does not hold true. Please help!



Math Expert
Joined: 02 Sep 2009
Posts: 47948

Re: The Discreet Charm of the DS
[#permalink]
Show Tags
15 Dec 2016, 11:23



Intern
Joined: 09 May 2016
Posts: 43

Re: The Discreet Charm of the DS
[#permalink]
Show Tags
10 Jun 2017, 11:50
Bunuel wrote: 5. What is the value of integer x?
(1) 2x^2+9<9x > factor qudratics: \((x\frac{3}{2})(x3)<0\) > roots are \(\frac{3}{2}\) and 3 > "<" sign indicates that the solution lies between the roots: \(1.5<x<3\) > since there only integer in this range is 2 then \(x=2\). Sufficient.
(2) x+10=2x+8 > LHS is an absolute value, which is always non negative, hence RHS must also be nonnegative: \(2x+8\geq{0}\) > \(x\geq{4}\), for this range \(x+10\) is positive hence \(x+10=x+10\) > \(x+10=2x+8\) > \(x=2\). Sufficient.
Answer: D.
Hi Bunuel, a small doubt instead of \(2x+8\geq{0}\) > \(x\geq{4}\) this logic if we take x+10 to be both positive and negative we get 2 vale by solving equation x=2 and x=6. however by putting values back in eqtn we can see that only for x=2 equation is satisfying. Is this correct approach?




Re: The Discreet Charm of the DS &nbs
[#permalink]
10 Jun 2017, 11:50



Go to page
Previous
1 2 3 4 5 6
Next
[ 108 posts ]



