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New Set of Mixed Questions!!!

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New Set of Mixed Questions!!! [#permalink]

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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


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

Solution: http://gmatclub.com/forum/new-set-of-mi ... l#p1208457


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%

Solution: http://gmatclub.com/forum/new-set-of-mi ... l#p1208459


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

Solution: http://gmatclub.com/forum/new-set-of-mi ... l#p1208462


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

Solution: http://gmatclub.com/forum/new-set-of-mi ... l#p1208466


10. If n is a non-negative 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/new-set-of-mi ... l#p1208471


BONUS 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/new-set-of-mi ... l#p1208473


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Re: New Set of Mixed Questions!!! [#permalink]

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New post 01 Apr 2013, 18:54
Q11) P(No Blue at 7) = 1 - P(Blue at 7)
using slot method _ _ _ _ _ _ _ = 5/8*4/7*3/6*2/5*3/3*2/2*1/1 = 1/56 and there are 14 such combinations.

P(Blue at 7) = 14/56 = 1/4. Answer: B
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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

Since (-3, y) are the coordinates of K, -3 is the distance from K to the Y-axis and y is the distance from the X-axis to K.

Given that the distance from the Y-axis to point K is 1/3 of the distance from the X-axis to point K, Thus : 3 = 1/3 * y --> y = 9

Answer : E
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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

In quadrant 1, this is just the line 3x+y=90. Which is a line with X-int=30 and Y-int=90. So area enclosed with axes in Q1, is just 0.5*30*90 = 1350 (a right angled triangle)

Now notice, if you replace x by -x the equation does not change
Hence, the figure must be symmetric about the Y-axis and Q2, must also have a right angled triangle, of area 1350 with the axis

Finally, if you replace y by -y, the equation is still the sameand hence, the figure must be symmetric about the X-axis
So Q3 and Q4 have a mirror image of the above two triangles

So total area = 1350*4 = 5400

Answer : D
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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?

Let the usual time, speed and the distance between her house and school be t,v, and s. We know that s = vt. Again, s = 1.2v*(t-20/60+15/60)

or s = 1.2v*(t-1/12)

On comparison, t = 1.2(t-1/12)

or t = 30 mins

D.
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3. Three workers, A, B, and C, can complete a certain task in 10, 5 and x hours re ,spectively. 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

A alone can do the work in 10 hours
B alone can do the work in 5 hours
C alone can do the work in x hours

Hence, in 1hour A alone will do W/10 and B alone W/5 and C alone W/x

From the figure below, W = W/5 + 3W/5 + W/40 + W/20 + W/4x -----> x = 2

Answer : C
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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 liters

To empty X liters, 4 hours are needed

To empty X + (3*6) liters, 6 hours are needed

Hence, \(X/4 = (X+18)/6\) --> \(X=36\)
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10. If n is a non-negative 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


Sol: From Q stem, we have n can be 0 or positive integer
Possible values of n = 0,1,2......
When 3^n/4 =3I where I is any Integer
Consider n= 1 so we have 3/4 and remainder is 3 which is of the form 3I
Consider n= 2 so we have 9/4 and remainder is 1 which is not of the form 3I
Consider n =3 , so we have 27/4 and remainder is 3 which is of the form 3I

Therefore n= 1,3,5...for Odd nos we have that when 3^n/4 will give remainder of the form 3I

Now St 1: n^2/4 yields remainder 1

for n= 1, remainder is 1
for n= 2, reminder is zero
n=3, remainder is 1

We can conclude that for all odd values of n i.e.1,3, 5 and so on remainder will be 1 and hence st 1 will be true

St 2: (-2)^n is less than 0

for any odd value of n the expression will always be less than 0 .
Ex for n = 1, we have (-2)^1 ----> -2<0
For n= 3, we have (-2)^3------> -8<0

Hence st2 is also true

St 3: n is a prime number
Now if n =3,5,7 then yes n is a prime no
But if n=15, n is not a prime no

Hence Ans should be Option D
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BONUS 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?


We have 8 positions to fill: R,R,R,R,R,B,B,B
My method is: the probability that a given position has a red marble is 5/8, the probability that a given position has a blue marble is 3/8.
So the probability that the 7th position has a NOT blue marlble ( a red one ) is 5/8.

IMO D.
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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.

Distance of a point(x, y) from the x-axis is given by the y-coordinate of the point i.e. |y| and the distance from the y-axis is given by the x-coordinate of the point i.e. |x|
So, distance of the point k(-3 , y) from x-axis = y, from y-axis = 3
As per question \(3 = 1/3(y)\) => \(y = 3*3 = 9\)
So distance of point k from x-axis = y = 9 (option E)
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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
Putting x= o we get y = +90, -90
Putting y= 0 we get x = +30, -30

Required area will be set of four Pythagorean triangles with the two perpendicular sides as 30 and 90
So required area = \(4 * (1/2 * 30 * 90) = 2 * 30 * 90 = 5400\)(option D)
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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

A alone can complete the task in 10 hours, in 1 hour he can do 1/10 of the task
B alone can complete the task in 5 hours, in 1 hour he can do 1/5 of the task
C alone can complete the task in x hours, in 1 hour he can do 1/x of the task
A and B combined can do (1/10 + 1/5) = 3/10 of the task in 1 hour hour
A, B and C combined can do (1/10 + 1/5 + 1/x) = (3/10 + 1/x) of the task in one hour

As per question, A starts the work and works for 2 hours so he completes 1/10 * 2 of the task i.e. 1/5 of the task
Then A and B work for next two hours i.e they complete 3/10 *2 = 3/5 of the task
Remaining task = 1 - (1/5 + 3/5) = 1/5
This remaining task is done by A, B and C combined in 15 mins.
So 1/5 = (1/10 + 1/5 + 1/x)* 15/60, that gives x =2 (option c)
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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

Let the draining rate of the pipe be x liters per hour
So the volume of the pool = 4x litres
As per question, 4x + 3*6 = 6x => x = 9

So the capacity of the tank = 4*9 = 36 liters (option D)
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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
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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 in the set, so -1/4 and -1/8 are also in the set
Since -1/4 is in the set, so \(- (-1/4)^3\) i.e. 1/64 is also in the set
Since -1/8 is in the set, so \(-(-1/8)^2\) i.es -1/64 is also in the set

So option D. I and II only
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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

Since we need to maximize the number of members we need to minimize each member's contribution which is gives as 10
So if we take no. of members as 39, their contribution = 39 * 10 = 390, remaining 9 can be shared among other members.
So maximum number of members = 39 (option C)
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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 Marry has 100 rupees with her
So amount spent on food = 64
amount spent on meat = 16
amount spent on food other then meat = 64 - 16 = 48
48 out of 64 is spent on food other than meat, % = 48/60 * 100 = 75% (option E)
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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

Holly increases her speed by 20% i.e by 1/5th of the original speed
Since, speed * time = distance (constant in this case)
Since speed increased by 1/5, for distance to be constant time must decrease by 1/6
Net decrease in time = 20 - 25 mins = 5 mins
So 1/6th of usual time = 5 mins
Usuall Time = 6 * 5 = 30 mins (option D)
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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

x + y = -12

A. Both x and y are negative; not necessary as x = 1 and y = -13 satisfies the equation
B. xy > 0; not necessary as x = 1 and y = -13 satisfies the equation
C. If y < 0, then x > 0; not necessary as y = -2 and x = -10 satisfies the equation
D. If y > 0, then x < 0; must be true
E. x - y > 0; not necessary as y = -2 and x = -10 satisfies the equation

Correct answer D. If y > 0, then x < 0
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10. If n is a non-negative 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

n being a non-negative integer and when 3^n is divided by 4, it leaves a remainder of 3
So n must be 1, 3, 5, 7, ...........odd integers
I. n^2 divided by 4 yields the reminder of 1; True
take any possible value of n say n = 3 so n^2 ie. 3^2 =9 when divided by 4 leaves a remainder of 1
II.(-2)^n is less than 0; True as n is odd
III. n is a prime number; False as n = 9 also satisfies the condition

So correct option is D. I and II only
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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?
ributed
A. 37
B. 38
C. 39
D. 40
E. 41

Sol: Since we need to find the greatest number of members, we should minimise the contribution of each member.
Min Contribution : $ 10
We can start by assuming no of members from any of the given options
starting with C we have, 39*10+ y= 399--> y = $9. This $9 can be shared by any contributed by any of the members

Lets take no. of members to be D then we have 400*10 > 399 and hence the case is not possible as Total contribution will exceed $ 399.

Assuming B as no of members we have 38*10+ y= 399----> y =$ 19 which can be given by eny of the remaining members (shared by 3 or more)

Hence max no possible be 39.

Ans should be C
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Re: New Set of Mixed Questions!!!   [#permalink] 02 Apr 2013, 06:03

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