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# New Set of Mixed Questions!!!

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Math Expert
Joined: 02 Sep 2009
Posts: 59720
New Set of Mixed Questions!!!  [#permalink]

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01 Apr 2013, 07:48
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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 Y-axis to point K is 1/3 of the distance from the X-axis to point K. If the coordinates of K are (-3, y), what is the distance between point K and X-axis?

A. 1/2
B. 1
C. 3
D. 4.5
E. 9.

Solution: https://gmatclub.com/forum/new-set-of-m ... l#p1208436

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

Solution: https://gmatclub.com/forum/new-set-of-m ... l#p1208441

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

Solution: http://gmatclub.com/forum/new-set-of-mi ... l#p1208445

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

Solution: http://gmatclub.com/forum/new-set-of-mi ... l#p1208449

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. III only,
D. I and II only
E. I, II and III

Solution: http://gmatclub.com/forum/new-set-of-mi ... l#p1208454

To maximize the number of members we have to minimize the number of dollars donated by each one. So we use 10$donations as long as we can, given the conditions in the question. Number of members who donated 10 dollars = 37. Tot = 370. The remaining 29 dollars are splitted between 2 members ( 15 and 14 for example) Tot members = 37+2=39 IMO C VP Status: Far, far away! Joined: 02 Sep 2012 Posts: 1010 Location: Italy Concentration: Finance, Entrepreneurship GPA: 3.8 Re: New Set of Mixed Questions!!! [#permalink] ### Show Tags 01 Apr 2013, 08:37 1 7. Mary spent 64 percent of her salary on food (including meat) and 16% of her salary on meat. What percent of the salary spent on food were not spent on meat? Salary 100$. 64 dollars on food, 16 dollars on meat and 64-16=48 dollars on "non-meat"
$on non-meat/$on food = 48/64= 0.75

IMO E
VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1010
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: New Set of Mixed Questions!!!  [#permalink]

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01 Apr 2013, 08:45
1
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 : 1-13=-12
B. xy > 0 False: 1*(-13)<0
C. If y < 0, then x > 0 False: -6-6=-12
D. If y > 0, then x < 0 True
E. x - y > 0 False: -13+1=-12 and -13-1<0
Manager
Joined: 26 Feb 2013
Posts: 51
Concentration: Strategy, General Management
GMAT 1: 660 Q50 V30
WE: Consulting (Telecommunications)
Re: New Set of Mixed Questions!!!  [#permalink]

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01 Apr 2013, 09:10
3
1. The distance from the Y-axis to point K is 1/3 of the distance from the X-axis to point K. If the coordinates of K are (-3, y), what is the distance between point K and X-axis?

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: 51
Concentration: Strategy, General Management
GMAT 1: 660 Q50 V30
WE: Consulting (Telecommunications)
Re: New Set of Mixed Questions!!!  [#permalink]

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01 Apr 2013, 09:13
2
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 x-axis at (30,0) and y-axis 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: 1010
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: New Set of Mixed Questions!!!  [#permalink]

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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 : $$(t-20+15)*\frac{6}{5}v=t*v$$ divide by v
$$(t-5)6/5=t$$
$$t=30$$

IMO D
Manager
Joined: 26 Feb 2013
Posts: 51
Concentration: Strategy, General Management
GMAT 1: 660 Q50 V30
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Re: New Set of Mixed Questions!!!  [#permalink]

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01 Apr 2013, 09:21
1
1
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: 51
Concentration: Strategy, General Management
GMAT 1: 660 Q50 V30
WE: Consulting (Telecommunications)
Re: New Set of Mixed Questions!!!  [#permalink]

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01 Apr 2013, 09:24
2
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 9-3= 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: 51
Concentration: Strategy, General Management
GMAT 1: 660 Q50 V30
WE: Consulting (Telecommunications)
Re: New Set of Mixed Questions!!!  [#permalink]

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01 Apr 2013, 09:27
2
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

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: 51
Concentration: Strategy, General Management
GMAT 1: 660 Q50 V30
WE: Consulting (Telecommunications)
Re: New Set of Mixed Questions!!!  [#permalink]

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01 Apr 2013, 09:30
1
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: 51
Concentration: Strategy, General Management
GMAT 1: 660 Q50 V30
WE: Consulting (Telecommunications)
Re: New Set of Mixed Questions!!!  [#permalink]

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01 Apr 2013, 09:32
1
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 = 64-16=48.--(2)
2 as a % of 1 is 48/64 = 75%
Manager
Joined: 26 Feb 2013
Posts: 51
Concentration: Strategy, General Management
GMAT 1: 660 Q50 V30
WE: Consulting (Telecommunications)
Re: New Set of Mixed Questions!!!  [#permalink]

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01 Apr 2013, 09:40
1
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
Re: New Set of Mixed Questions!!!   [#permalink] 01 Apr 2013, 09:40

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