Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49540

New Set of Mixed Questions!!!
[#permalink]
Show Tags
01 Apr 2013, 07:48
The next set of medium/hard PS questions. I'll post OA's with detailed explanations on Friday. Please, post your solutions along with the answers.1. The distance from the Yaxis to point K is 1/3 of the distance from the Xaxis to point K. If the coordinates of K are (3, y), what is the distance between point K and Xaxis?A. 1/2 B. 1 C. 3 D. 4.5 E. 9. Solution: https://gmatclub.com/forum/newsetofm ... l#p12084362. What is the area of a region enclosed by x/3+y/9=10?A. 675 B. 1350 C. 2700 D. 5400 E. 10800 Solution: https://gmatclub.com/forum/newsetofm ... l#p12084413. Three workers, A, B, and C, can complete a certain task in 10, 5 and x hours respectively. A starts working alone and 2 hours later B joins. After another 2 hours joins C. After that A, B, and C together complete the task in 15 minutes. What is the value of x?A. 1 B. 1.25 C. 2 D. 2.5 E. 4 Solution: http://gmatclub.com/forum/newsetofmi ... l#p12084454. A draining pipe can empty a pool in 4 hours. On a rainy day, when the pool is full, the draining pipe is opened and the pool is emptied in 6 hours. If rain inflow into the pool is 3 liters per hour, what is the capacity of the pool?A. 9 liters B. 18 liters C. 27 liters D. 36 liters E. 45 iters Solution: http://gmatclub.com/forum/newsetofmi ... l#p12084495. For a certain set of numbers, if x is in the set, then both x^2 and x^3 are also in the set. If the number 1/2 is in the set , which of the following must also be in the set ? I. 1/64 II. 1/64 III. 1/2^(1/3) A. I only, B. II only, C. III only, D. I and II only E. I, II and III Solution: http://gmatclub.com/forum/newsetofmi ... l#p12084546. A team contributes total of $399 from its members. If each member contributed at least $10, and no one contributed $19, what is the greatest number of members the club could have?A. 37 B. 38 C. 39 D. 40 E. 41 Solution: http://gmatclub.com/forum/newsetofmi ... l#p12084577. Mary spent 64 percent of her salary on food (including meat) and 16% of her salary on meat. What percent of the salary spent on food were not spent on meat? A. 16% B. 25% C. 32% D. 48% E. 75% Solution: http://gmatclub.com/forum/newsetofmi ... l#p12084598. Usually Holly leaves home to school at 9:00, however today she left home 20 minutes later. In order to be at school on time she increased her usual speed by 20% and still was at school 15 minutes later than usual. What is her usual time from home to school?A. 15 minutes B. 20 minutes C. 25 minutes D. 30 minutes E. 210 minutes Solution: http://gmatclub.com/forum/newsetofmi ... l#p12084629. If x and y are integers and x + y = 12, which of the following must be true?A. Both x and y are negative B. xy > 0 C. If y < 0, then x > 0 D. If y > 0, then x < 0 E. x  y > 0 Solution: http://gmatclub.com/forum/newsetofmi ... l#p120846610. If n is a nonnegative integer and the remainder when 3^n is divided by 4 is a multiple of 3, then which of the following must be true?I. n^2 divided by 4 yields the reminder of 1 II. (2)^n is less than 0 III. n is a prime number A. I only B. II only C. III only D. I and II only E. II and III only Solution: http://gmatclub.com/forum/newsetofmi ... l#p1208471BONUS QUESTION: 11. Certain bowl contains 5 red marbles and 3 blue marbles only. One by one, every marble is drawn at random and without replacement. What is the probability that the seventh marble drawn is NOT blue?A. 7/8 B. 3/4 C. 2/3 D. 5/8 E. 3/8 Solution: http://gmatclub.com/forum/newsetofmi ... l#p1208473Kudos points for each correct solution!!!
_________________
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: 49540

Re: New Set of Mixed Questions!!!
[#permalink]
Show Tags
05 Apr 2013, 05:06
3. Three workers, A, B, and C, can complete a certain task in 10, 5 and x hours respectively. A starts working alone and 2 hours later B joins. After another 2 hours joins C. After that A, B, and C together complete the task in 15 minutes. What is the value of x?A. 1 B. 1.25 C. 2 D. 2.5 E. 4 After 2 hours \(2*\frac{1}{10}=\frac{1}{5}\) of the taks will be done (as only A works); After 4 hours \(\frac{1}{5}+2*(\frac{1}{10}+\frac{1}{5})=\frac{4}{5}\) of the task will be done and \(\frac{1}{5}\) will be left to be done; We are told that \(\frac{1}{5}\)th of the task is done in 15 minutes (1/4th of an hour) by all three workers: \(\frac{1}{4}*(\frac{1}{10}+\frac{1}{5}+\frac{1}{x})=\frac{1}{5}\). From which we can find that \(x=2\) hours. Answer: C
_________________
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




VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1085
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: New Set of Mixed Questions!!!
[#permalink]
Show Tags
01 Apr 2013, 08:02
1. The distance from the Yaxis to point K is 1/3 of the distance from the Xaxis to point K. If the coordinates of K are (3, y), what is the distance between point K and Xaxis? Point k is on the line x=3, so its distance form the yaxis (x=0) is 3. Given that "The distance from the Yaxis to point K is 1/3 of the distance from the Xaxis", its distance to the yaxis is 3*3=9 IMO E
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture  Review: MGMAT workshop Strategy: SmartGMAT v1.0  Questions: Verbal challenge SC III CR New SC set out !! , My QuantRules for Posting in the Verbal Forum  Rules for Posting in the Quant Forum[/size][/color][/b]



VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1085
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: New Set of Mixed Questions!!!
[#permalink]
Show Tags
01 Apr 2013, 08:08
2. What is the area of a region enclosed by x/3+y/9=10? We can analize the function x/3 + y/9 = 10 first. y=903x This intersect the Yaxis is 90 and the Xaxis in 30. The original function ( with the absolute values) has the same graph as y=903x, only symmetric for value of x<0 and values of y <0. So the answer is: it defines a triangle of Area=\(\frac{90*30}{2}=1350\) IMO B
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture  Review: MGMAT workshop Strategy: SmartGMAT v1.0  Questions: Verbal challenge SC III CR New SC set out !! , My QuantRules for Posting in the Verbal Forum  Rules for Posting in the Quant Forum[/size][/color][/b]



VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1085
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: New Set of Mixed Questions!!!
[#permalink]
Show Tags
01 Apr 2013, 08:14
3. Three workers, A, B, and C, can complete a certain task in 10, 5 and x hours respectively. A starts working alone and 2 hours later B joins. After another 2 hours joins C. After that A, B, and C together complete the task in 15 minutes. What is the value of x? rates : A=1/10 B=1/5 c=1/x A*2h+(A+B)*2h+(A+B+C)*15min = 1 work. (1/10)*2 +(1/10+1/5)*2+(1/10+1/5+1/x)*1/4=1 x=2 IMO C
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture  Review: MGMAT workshop Strategy: SmartGMAT v1.0  Questions: Verbal challenge SC III CR New SC set out !! , My QuantRules for Posting in the Verbal Forum  Rules for Posting in the Quant Forum[/size][/color][/b]



VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1085
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: New Set of Mixed Questions!!!
[#permalink]
Show Tags
01 Apr 2013, 08:20
4. A draining pipe can empty a pool in 4 hours. On a rainy day, when the pool is full, the draining pipe is opened and the pool is emptied in 6 hours. If rain inflow into the pool is 3 liters per hour, what is the capacity of the pool?To empty X liters ==> 4 h. To empty X + 3*6 liters ==> 6 h. \(\frac{x}{4}=\frac{x+18}{6}\) \(x=36\) IMO D
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture  Review: MGMAT workshop Strategy: SmartGMAT v1.0  Questions: Verbal challenge SC III CR New SC set out !! , My QuantRules for Posting in the Verbal Forum  Rules for Posting in the Quant Forum[/size][/color][/b]



VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1085
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: New Set of Mixed Questions!!!
[#permalink]
Show Tags
01 Apr 2013, 08:28
5. For a certain set of numbers, if x is in the set, then both x^2 and x^3 are also in the set. If the number 1/2 is in the set , which of the following must also be in the set ?I. 1/64 II. 1/64 III. 1/2^(1/3) If 1/2 is in the set, then 1/2^2 and 1/3^3 are in the set. (1/4 and 1/8 are in the set) If 1/4 is in the set, then (1/4)^2 and (1/4)^3 are in the set. (1/4)^3 = 1/64 so II is in the set, IMO B
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture  Review: MGMAT workshop Strategy: SmartGMAT v1.0  Questions: Verbal challenge SC III CR New SC set out !! , My QuantRules for Posting in the Verbal Forum  Rules for Posting in the Quant Forum[/size][/color][/b]



VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1085
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: New Set of Mixed Questions!!!
[#permalink]
Show Tags
01 Apr 2013, 08:34
6. A team contributes total of $399 from its members. If each member contributed at least $10, and no one contributed $19, what is the greatest number of members the club could have?To maximize the number of members we have to minimize the number of dollars donated by each one. So we use 10$ donations as long as we can, given the conditions in the question. Number of members who donated 10 dollars = 37. Tot = 370. The remaining 29 dollars are splitted between 2 members ( 15 and 14 for example) Tot members = 37+2=39 IMO C
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture  Review: MGMAT workshop Strategy: SmartGMAT v1.0  Questions: Verbal challenge SC III CR New SC set out !! , My QuantRules for Posting in the Verbal Forum  Rules for Posting in the Quant Forum[/size][/color][/b]



VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1085
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: New Set of Mixed Questions!!!
[#permalink]
Show Tags
01 Apr 2013, 08:37
7. Mary spent 64 percent of her salary on food (including meat) and 16% of her salary on meat. What percent of the salary spent on food were not spent on meat?Salary 100$. 64 dollars on food, 16 dollars on meat and 6416=48 dollars on "nonmeat" $on nonmeat/$on food = 48/64= 0.75 IMO E
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture  Review: MGMAT workshop Strategy: SmartGMAT v1.0  Questions: Verbal challenge SC III CR New SC set out !! , My QuantRules for Posting in the Verbal Forum  Rules for Posting in the Quant Forum[/size][/color][/b]



VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1085
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: New Set of Mixed Questions!!!
[#permalink]
Show Tags
01 Apr 2013, 08:45
9. If x and y are integers and x + y = 12, which of the following must be true?A. Both x and y are negative False : 113=12 B. xy > 0 False: 1*(13)<0 C. If y < 0, then x > 0 False: 66=12 D. If y > 0, then x < 0 True E. x  y > 0 False: 13+1=12 and 131<0
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture  Review: MGMAT workshop Strategy: SmartGMAT v1.0  Questions: Verbal challenge SC III CR New SC set out !! , My QuantRules for Posting in the Verbal Forum  Rules for Posting in the Quant Forum[/size][/color][/b]



Manager
Joined: 26 Feb 2013
Posts: 52
Concentration: Strategy, General Management
WE: Consulting (Telecommunications)

Re: New Set of Mixed Questions!!!
[#permalink]
Show Tags
01 Apr 2013, 09:10
1. The distance from the Yaxis to point K is 1/3 of the distance from the Xaxis to point K. If the coordinates of K are (3, y), what is the distance between point K and Xaxis?
A. 1/2 B. 1 C. 3 D. 4.5 E. 9.
The distance between Y axis and (3,y) will be the distance between (0,y) and (3,y)
which is (3)^2=9



Manager
Joined: 26 Feb 2013
Posts: 52
Concentration: Strategy, General Management
WE: Consulting (Telecommunications)

Re: New Set of Mixed Questions!!!
[#permalink]
Show Tags
01 Apr 2013, 09:13
2. What is the area of a region enclosed by x/3+y/9=10?
A. 675 B. 1350 C. 2700 D. 5400 E. 10800
x/3+y/9=10 will touch the xaxis at (30,0) and yaxis at (0,90) in Q1. Area of this region will be .5*30*90=1350. Hence the total area of the figure formed on all the 4 quadrants is 4*1350=5400



VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1085
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: New Set of Mixed Questions!!!
[#permalink]
Show Tags
01 Apr 2013, 09:13
8. Usually Holly leaves home to school at 9:00, however today she left home 20 minutes later. In order to be at school on time she increased her usual speed by 20% and still was at school 15 minutes later than usual. What is her usual time from home to school?s=t*v She left 20 minuters later ==>you subtract 20 minutes for her time; but arrived 15 min later ==>you add 15 to her time She increase the speed by 20% ==> you multiply her speed by 6/5 = 1.2 And finally since she walked the same distance you equal her "normal" equation : space=time*speed, to her new equation so : \((t20+15)*\frac{6}{5}v=t*v\) divide by v \((t5)6/5=t\) \(t=30\) IMO D
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture  Review: MGMAT workshop Strategy: SmartGMAT v1.0  Questions: Verbal challenge SC III CR New SC set out !! , My QuantRules for Posting in the Verbal Forum  Rules for Posting in the Quant Forum[/size][/color][/b]



Manager
Joined: 26 Feb 2013
Posts: 52
Concentration: Strategy, General Management
WE: Consulting (Telecommunications)

Re: New Set of Mixed Questions!!!
[#permalink]
Show Tags
01 Apr 2013, 09:21
3. Three workers, A, B, and C, can complete a certain task in 10, 5 and x hours respectively. A starts working alone and 2 hours later B joins. After another 2 hours joins C. After that A, B, and C together complete the task in 15 minutes. What is the value of x?
A. 1 B. 1.25 C. 2 D. 2.5 E. 4
Work done by : A in 2 hrs = 2/10.(1) A and B in 2 hrs = 2(1/10 + 1/5)(2) A,B and C in 15 mins = 1/4(1/10 + 1/5 + 1/x)(3) (1)+(2)+(3) =1
on simplification 4/5 + 1/4(3/10 + 1/x) = 1
or 1/x= 4/5 3/10 = 5/10 = 1/2
X= 2 hrs



Manager
Joined: 26 Feb 2013
Posts: 52
Concentration: Strategy, General Management
WE: Consulting (Telecommunications)

Re: New Set of Mixed Questions!!!
[#permalink]
Show Tags
01 Apr 2013, 09:24
4. A draining pipe can empty a pool in 4 hours. On a rainy day, when the pool is full, the draining pipe is opened and the pool is emptied in 6 hours. If rain inflow into the pool is 3 liters per hour, what is the capacity of the pool?
A. 9 liters B. 18 liters C. 27 liters D. 36 liters E. 45 iters
I have actually back solved this question. Took 36 liters as capacity of the tank. Hence draining pipe rate is 36/4 = 9 l/hr.
now total out flow during rain is 93= 6 l/hr. multiply with 6 hrs  time taken to empty the tank we arrive back at the original capapcity of the tank = 36 L



Manager
Joined: 26 Feb 2013
Posts: 52
Concentration: Strategy, General Management
WE: Consulting (Telecommunications)

Re: New Set of Mixed Questions!!!
[#permalink]
Show Tags
01 Apr 2013, 09:27
5. For a certain set of numbers, if x is in the set, then both x^2 and x^3 are also in the set. If the number 1/2 is in the set , which of the following must also be in the set ?
I. 1/64 II. 1/64 III. 1/2^(1/3)
A. I only, B. II only, C. II only, D. I and II only E. I, II and III
My answer is D.
Since 1/2 is there we have 1/4 and 1/8 in the set. Since 1/4 is there we will have (1/4)^3= 1/64. 1/8 is there hence (1/8)^2 = 1/64 will be in the set.



Manager
Joined: 26 Feb 2013
Posts: 52
Concentration: Strategy, General Management
WE: Consulting (Telecommunications)

Re: New Set of Mixed Questions!!!
[#permalink]
Show Tags
01 Apr 2013, 09:30
6. A team contributes total of $399 from its members. If each member contributed at least $10, and no one contributed $19, what is the greatest number of members the club could have?
A. 37 B. 38 C. 39 D. 40 E. 41
37 ppl each contributing 10$ = total 370 $. remaining 29$ can be split between 2 people ( 14 + 15 or any other combination meeting the criteria.
Hence total 39 members



Manager
Joined: 26 Feb 2013
Posts: 52
Concentration: Strategy, General Management
WE: Consulting (Telecommunications)

Re: New Set of Mixed Questions!!!
[#permalink]
Show Tags
01 Apr 2013, 09:32
7. Mary spent 64 percent of her salary on food (including meat) and 16% of her salary on meat. What percent of the salary spent on food were not spent on meat?
A. 16% B. 25% C. 32% D. 48% E. 75%
let Mary's total salary = 100. Sal spent on food = 64(1), sal spent on meat = 16. food exp not spent on meat = 6416=48.(2) 2 as a % of 1 is 48/64 = 75%



Manager
Joined: 26 Feb 2013
Posts: 52
Concentration: Strategy, General Management
WE: Consulting (Telecommunications)

Re: New Set of Mixed Questions!!!
[#permalink]
Show Tags
01 Apr 2013, 09:40
8. Usually Holly leaves home to school at 9:00, however today she left home 20 minutes later. In order to be at school on time she increased her usual speed by 20% and still was at school 15 minutes later than usual. What is her usual time from home to school?
A. 15 minutes B. 20 minutes C. 25 minutes D. 30 minutes E. 210 minutes
D= dist of school. V= actual speed.
D/v= T time taken to reach school.
when she was 20 mins, time taken would be T+20
when she increased her speed to 6/5 ofher original. time taken is T+15.
now the difference of 5 mins in the time is due to 20% increase in speed.
d/v  (d/1.2v) = 5
1/6*(d/v) = 5
D/V= T= 30 mins



Manager
Joined: 26 Feb 2013
Posts: 52
Concentration: Strategy, General Management
WE: Consulting (Telecommunications)

Re: New Set of Mixed Questions!!!
[#permalink]
Show Tags
01 Apr 2013, 09:41
9. If x and y are integers and x + y = 12, which of the following must be true?
A. Both x and y are negative B. xy > 0 C. If y < 0, then x > 0 D. If y > 0, then x < 0 E. x  y > 0
By putting values for X and Y, only D must be true




Re: New Set of Mixed Questions!!! &nbs
[#permalink]
01 Apr 2013, 09:41



Go to page
1 2 3 4 5 6 7
Next
[ 135 posts ]



