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# New Set of Mixed Questions!!!

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Math Expert
Joined: 02 Sep 2009
Posts: 43891
New Set of Mixed Questions!!! [#permalink]

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01 Apr 2013, 06:48
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KUDOS
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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: new-set-of-mixed-questions-150204-100.html#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: new-set-of-mixed-questions-150204-100.html#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: new-set-of-mixed-questions-150204-100.html#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: new-set-of-mixed-questions-150204-100.html#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: new-set-of-mixed-questions-150204-100.html#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: new-set-of-mixed-questions-150204-100.html#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: new-set-of-mixed-questions-150204-100.html#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: new-set-of-mixed-questions-150204-100.html#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: new-set-of-mixed-questions-150204-100.html#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: new-set-of-mixed-questions-150204-100.html#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: new-set-of-mixed-questions-150204-100.html#p1208473

Kudos points for each correct solution!!!
_________________
Status: It`s Just a pirates life !
Joined: 21 Mar 2014
Posts: 235
Location: India
Concentration: Strategy, Operations
GMAT 1: 690 Q48 V36
GPA: 4
WE: Consulting (Manufacturing)
Re: New Set of Mixed Questions!!! [#permalink]

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29 Feb 2016, 08:51
"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"

Bunuel. Can you help me in this? I tried the below way. What is wrong in that?

As per the question, the Seventh marble is Red.

That means any of the below combo is possible

RRRRBBRB - Here - (5/8)*(4/7)*(3/6)*(2/5)*(3/4)*(2/3)*(1/2)*1 ---- What is wrong in this approach. Kindly help?
_________________

Aiming for a 3 digit number with 7 as hundredths Digit

Intern
Joined: 21 May 2016
Posts: 17
Location: United Kingdom
GMAT 1: 730 Q49 V41
GPA: 3.5
Re: New Set of Mixed Questions!!! [#permalink]

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28 May 2016, 08:53
Bunuel wrote:
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.

How do you calculate the fact that $$\frac{4}{5}$$ of the job has been completed after 4hrs? I understand why it was $$\frac{1}{5}$$ after A worked in isolation for 2hrs, and I also understand how to calculate the algebra, but my issue is knowing how to set it up.

I also don't quite understand how the final equation was set up (though perhaps that will become clearer once I understand how A&B were set up)
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Joined: 14 Nov 2016
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Location: Malaysia
New Set of Mixed Questions!!! [#permalink]

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01 Feb 2017, 19:16
Bunuel wrote:
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

Look at option D: if y is positive, then x must be negative in order the sum of x and y to be negative.

Dear Bunuel, What if C. If $$y < 0$$, then $$x > 0$$, $$x = 12$$, $$y = -24$$, $$x + y = 12 - 24 = -12$$?
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Math Expert
Joined: 02 Sep 2009
Posts: 43891
Re: New Set of Mixed Questions!!! [#permalink]

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02 Feb 2017, 05:14
ziyuenlau wrote:
Bunuel wrote:
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

Look at option D: if y is positive, then x must be negative in order the sum of x and y to be negative.

Dear Bunuel, What if C. If $$y < 0$$, then $$x > 0$$, $$x = 12$$, $$y = -24$$, $$x + y = 12 - 24 = -12$$?

C is not always true. y < 0 does not necessarily mean that x > 0. For example, consider y = -1 and x = -11.
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Re: New Set of Mixed Questions!!! [#permalink]

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08 Feb 2018, 08:23
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Re: New Set of Mixed Questions!!!   [#permalink] 08 Feb 2018, 08:23

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