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New Set of Mixed Questions!!!

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New Set of Mixed Questions!!! [#permalink] New post 01 Apr 2013, 06:48
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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: 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


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Re: New Set of Mixed Questions!!! [#permalink] New post 19 Apr 2013, 20:29
Bunuel wrote:
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%

64% of her salary on food;
16% of her salary on meat;

64%-16%=48% on food but not on meat --> 48/64=3/4=75% of the salary spent on food were not spent on meat.

Answer: E.


Here is another way to go after this one. Since Mary spent 16% of her salary on meat which means she spent 1/4 of the 64% of her salary on meat and the rest, 3/4 not on meat. So 75%.
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Re: New Set of Mixed Questions!!! [#permalink] New post 20 Apr 2013, 04:15
Expert's post
pikachu wrote:
Bunuel wrote:
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

Find the x and y intercepts.

When y=0, then x=30 or x=-30.
When x=0, then y=90 or x=-90.

So, we have 4 points: (30, 0), (-30, 0) (0, 90), (0, -90). When joining these points we get the rhombus:
Attachment:
2.png
The area of a rhombus is \frac{d_1*d_2}{2} (where d_1 and d_2 are the lengths of the diagonals), thus the area of the enclosed figure is 60*180/2=5,400.

Answer: D.


Bunuel what about the following points that also meets the given conditions of |x/3| + | y/9| = 10 but come with a different area.

(x,y) = (-3,81)
(x,y) = (-3,-81)
(x,y) = (3,-81)
(x,y) = (3,81)

In this case Area of the rectangle will be = 972

or you can have

(x,y) = (6,72)
(x,y) = (6,-72)
(x,y) = (-6,-72)
(x,y) = (-6,72)

In this case the area of the rectangle will be = 1728.

Can you please clarify


Below is the graph of |x/3|+|y/9|=10:
Image
The points you mention are on it and not making some other figure.
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Re: New Set of Mixed Questions!!! [#permalink] New post 28 Apr 2013, 21:13
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

The problem can be translated to "If 5 red marbles and 3 blue marbles are arranged in a row, what is the probability that the last marble is red?"

Total number of arrangements = 8!/[(5!)*(3!)] = 8*7*6/3! = 8*7
Number of arrangements such that last marble is red = Number of arrangements for 4 red marbles and 3 blue marbles = 7!/[(4!)*(3!)] = 786*5/3! = 7*5

Hence, required probability = 7*5/(887) = 5/8
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Re: New Set of Mixed Questions!!! [#permalink] New post 23 May 2013, 12:26
Expert's post
SaraLotfy wrote:
Bunuel wrote:
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
Wouldn't -x^2 = +1/4 since the power is even? or should I treat this as -|X|^2?
Since 1/2 is in the set, the so must be:
-x^2 = -1/4;
-x^3 = -1/8.

Since -1/4 is in the set, the so must be:
-x^3 = 1/64;

Since -1/8 is in the set, the so must be:
-x^2 = -1/64.

The only number we cannot get is 1/2^(1/3).

Answer: D.


-x^2=-(\frac{1}{2})^2=-\frac{1}{4} (its -x^2 not (-x)^2).

Hope it's clear.
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Re: New Set of Mixed Questions!!! [#permalink] New post 22 Jun 2013, 22:46
g106 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

A, B, and C, can complete a certain task in 10, 5 and x hours respectively
A completes 1/10 of the total work in 1 hr
B Completes 1/5 of the total work in 1 hr
C completes 1/x of the total work in 1 hr
A starts working alone and 2 hours later B joins. After another 2 hours joins C.
A completes 2/10 of the total work in 2 hrs later B joins A
A&B together can complete 1/10 + 1/5 of the total work in 1 hr
= 3/10
A&B work together for 2 hour and they complete 2 * 3/10 = 6/10 of the total work

By the time C joins A&B 8/10 of the total work is complete

To complete 2/10 of the work A, B & C together take 15 minutes (1/4 hr)
2/10 = ¼( 1/10 + 1/5+ 1/x)
8/10 = 3/10 + 1/X
5/10 = 1/X
X = 2
Answer = C

Hi,

plz help me to find out.
i dont understand this point " To complete 2/10 of the work A, B & C together take 15 minutes (1/4 hr) "

How come u got 2/10? A and b joins to complete 6/10 of work then c joins. But C'r work rate is 1/X.
Then how u got 2/10?

Please help me

Thanks in adavnce,
RRSNATHAN
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Re: New Set of Mixed Questions!!! [#permalink] New post 23 Jun 2013, 00:39
Expert's post
rrsnathan wrote:
g106 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

A, B, and C, can complete a certain task in 10, 5 and x hours respectively
A completes 1/10 of the total work in 1 hr
B Completes 1/5 of the total work in 1 hr
C completes 1/x of the total work in 1 hr
A starts working alone and 2 hours later B joins. After another 2 hours joins C.
A completes 2/10 of the total work in 2 hrs later B joins A
A&B together can complete 1/10 + 1/5 of the total work in 1 hr
= 3/10
A&B work together for 2 hour and they complete 2 * 3/10 = 6/10 of the total work

By the time C joins A&B 8/10 of the total work is complete

To complete 2/10 of the work A, B & C together take 15 minutes (1/4 hr)
2/10 = ¼( 1/10 + 1/5+ 1/x)
8/10 = 3/10 + 1/X
5/10 = 1/X
X = 2
Answer = C

Hi,

plz help me to find out.
i dont understand this point " To complete 2/10 of the work A, B & C together take 15 minutes (1/4 hr) "

How come u got 2/10? A and b joins to complete 6/10 of work then c joins. But C'r work rate is 1/X.
Then how u got 2/10?

Please help me

Thanks in adavnce,
RRSNATHAN


Check here: new-set-of-mixed-questions-150204-100.html#p1208445

Hope it helps.

Links to OE's are given in the original post.
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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

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Re: New Set of Mixed Questions!!! [#permalink] New post 08 Jul 2013, 23:40
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Re: New Set of Mixed Questions!!! [#permalink] New post 17 Jul 2013, 03:29
Bunuel wrote:
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

Basically we need to find the probability that the seventh marble drawn is red (so not blue).

Now, the initial probability of drawing red marble is 5/8. Without knowing the other results, the probability of drawing red marble will not change for ANY successive draw: second, third, fourth, ..., seventh. Thus the probability that the seventh marble is red is 5/8.

The same for blue marble: the probability of drawing blue marble is 3/8, the probability that for instance the 8th marble drawn is blue is still 3/8. There is simply no reason to believe WHY is any draw different from another (provided we don't know the other results).

Answer: D.



Hi Bunuel,
Can you please elaborate your thinking on this qn ? I am having a hard time wrapping my head arnd this. My line of thinking was to calculate the probability that you are left with 1 or two red marbles when you are about to draw the seventh one. Not only was this approach very drawn out, i didnt get this answer.

Thanks.
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Re: New Set of Mixed Questions!!! [#permalink] New post 17 Jul 2013, 05:12
Expert's post
vs129 wrote:
Bunuel wrote:
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

Basically we need to find the probability that the seventh marble drawn is red (so not blue).

Now, the initial probability of drawing red marble is 5/8. Without knowing the other results, the probability of drawing red marble will not change for ANY successive draw: second, third, fourth, ..., seventh. Thus the probability that the seventh marble is red is 5/8.

The same for blue marble: the probability of drawing blue marble is 3/8, the probability that for instance the 8th marble drawn is blue is still 3/8. There is simply no reason to believe WHY is any draw different from another (provided we don't know the other results).

Answer: D.



Hi Bunuel,
Can you please elaborate your thinking on this qn ? I am having a hard time wrapping my head arnd this. My line of thinking was to calculate the probability that you are left with 1 or two red marbles when you are about to draw the seventh one. Not only was this approach very drawn out, i didnt get this answer.

Thanks.


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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.


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Re: New Set of Mixed Questions!!! [#permalink] New post 06 Aug 2013, 16:27
the function f is defined for positive three digit integer n by f(n) = 2^x3^y5^z, where x,y,z are the hundreds, tens, and units digits of n, respectively. if m and v are three digit positive integers such that f(m) = 9 f(v), then m - v = note: 2^x denote x is power of 2
anyone please give me solution of this problem
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Re: New Set of Mixed Questions!!! [#permalink] New post 11 Aug 2013, 09:30
Expert's post
Riyad47 wrote:
the function f is defined for positive three digit integer n by f(n) = 2^x3^y5^z, where x,y,z are the hundreds, tens, and units digits of n, respectively. if m and v are three digit positive integers such that f(m) = 9 f(v), then m - v = note: 2^x denote x is power of 2
anyone please give me solution of this problem


Discussed here: the-function-f-is-defined-for-each-positive-three-digit-100847.html
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Re: New Set of Mixed Questions!!! [#permalink] New post 11 Aug 2013, 11:14
Bunuel wrote:
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!!!


really a good set of practice...thanks
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Re: New Set of Mixed Questions!!! [#permalink] New post 02 Sep 2013, 11:44
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

Ans is D, probability of not drawing a blue is not dependent on the position, considering that there is no restriction or criterion defined on sequence of draws any ball can be drawn before 7th not blue ball condition. Therefore it should be Redballs/totalballs i.e 5/8.
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Re: New Set of Mixed Questions!!! [#permalink] New post 25 Sep 2013, 05:02
4.
Volume of pool = V
Water added in pool BY rain in 6 hours = 3x6=18liters
Standard pump output rate (V/4) for 6 hours V6/4

Thus
V + 18 - V6/4 =0

V=36
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Re: New Set of Mixed Questions!!! [#permalink] New post 01 Jan 2014, 03:06
Bunuel wrote:
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

Basically we need to find the probability that the seventh marble drawn is red (so not blue).

Now, the initial probability of drawing red marble is 5/8. Without knowing the other results, the probability of drawing red marble will not change for ANY successive draw: second, third, fourth, ..., seventh. Thus the probability that the seventh marble is red is 5/8.

The same for blue marble: the probability of drawing blue marble is 3/8, the probability that for instance the 8th marble drawn is blue is still 3/8. There is simply no reason to believe WHY is any draw different from another (provided we don't know the other results).

Answer: D.


Hi Bunuel,
Why is the probability not changing? If we keep withdrawing marbles withoout replacing then following things are changing:-
1. total no. of marble (hence the denominator in probability)
2. No. of Red marbles left.
3. No. of blue marbles left.
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Re: New Set of Mixed Questions!!! [#permalink] New post 01 Jan 2014, 04:44
Expert's post
Nilabh_s wrote:
Bunuel wrote:
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

Basically we need to find the probability that the seventh marble drawn is red (so not blue).

Now, the initial probability of drawing red marble is 5/8. Without knowing the other results, the probability of drawing red marble will not change for ANY successive draw: second, third, fourth, ..., seventh. Thus the probability that the seventh marble is red is 5/8.

The same for blue marble: the probability of drawing blue marble is 3/8, the probability that for instance the 8th marble drawn is blue is still 3/8. There is simply no reason to believe WHY is any draw different from another (provided we don't know the other results).

Answer: D.


Hi Bunuel,
Why is the probability not changing? If we keep withdrawing marbles withoout replacing then following things are changing:-
1. total no. of marble (hence the denominator in probability)
2. No. of Red marbles left.
3. No. of blue marbles left.


Consider this: there are 8 cards, 5 spades, 3 hearts. What is the probability that the first card you pick will be spade? Clearly 5/8.

Now next question, suppose I throw away three cards at random, not telling you which cards I thrown away. What is the probability NOW that you pick a spade out of 5 remaining cards? I've just reduced the sample from which you pick, but does the probability changed? WHY should it change?

Another question, the same cards 5 spades and 3 hearts: I say that you can pick one card but only out of randomly selected 5 cards. What is the probability that the card you pick will be spade?

There is no difference in ALL above cases and the probability will remain 5/8. If it changed, increased (or decreased), it would mean that the probability of picking heart on the other hand decreased (or increased). Why would it?

Similar questions to practice:
a-box-contains-3-yellow-balls-and-5-black-balls-one-by-one-90272.html
a-bag-contains-3-white-balls-3-black-balls-2-red-balls-100023.html
each-of-four-different-locks-has-a-matching-key-the-keys-101553.html
if-40-people-get-the-chance-to-pick-a-card-from-a-canister-97015.html
a-bag-contains-3-white-balls-3-black-balls-2-red-balls-100023.html

Hope this helps.
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

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Re: New Set of Mixed Questions!!! [#permalink] New post 01 Jan 2014, 10:40
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

answer:

We fix the seventh ball to be red. Since all balls are same it doesnt matter which of the red balls.

So the rest 7 balls can be arranged in 7!/(4!*3!)= 35 ways becoz there are 4 identical red balls and 3 identical blue balls.

Without any restriction 8 balls can be arranged in 8!/(5!*3!) = 56 ways.

Therefore probability is 35/56 = 5/8.
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Re: New Set of Mixed Questions!!! [#permalink] New post 01 Jan 2014, 10:52
when i say arranging i mean different possibilities or orders in which the balls can be taken out from the box.
I hope Thats understood...
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Re: New Set of Mixed Questions!!! [#permalink] New post 01 Jan 2014, 18:21
Bunuel wrote:
Nilabh_s wrote:
Bunuel wrote:
.Consider this: there are 8 cards, 5 spades, 3 hearts. What is the probability that the first card you pick will be spade? Clearly 5/8.

Now next question, suppose I throw away three cards at random, not telling you which cards I thrown away. What is the probability NOW that you pick a spade out of 5 remaining cards? I've just reduced the sample from which you pick, but does the probability changed? WHY should it change?

Another question, the same cards 5 spades and 3 hearts: I say that you can pick one card but only out of randomly selected 5 cards. What is the probability that the card you pick will be spade?

There is no difference in ALL above cases and the probability will remain 5/8. If it changed, increased (or decreased), it would mean that the probability of picking heart on the other hand decreased (or increased). Why would it?


Hope this helps.


For the statement
" NOW that you pick a spade out of 5 remaining cards"

If you throw 3 cards then how are we sure than 5 spades are still remaining. Following three cards may have been thrown:-
1. All 3 spades.
2. All three hearts.
3. 2 spade & 1 heart & vice-versa.

Hence how can we be sure that 5 spades are till remaining?
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Re: New Set of Mixed Questions!!! [#permalink] New post 02 Jan 2014, 04:51
Expert's post
Nilabh_s wrote:
Bunuel wrote:
Bunuel wrote:
.Consider this: there are 8 cards, 5 spades, 3 hearts. What is the probability that the first card you pick will be spade? Clearly 5/8.

Now next question, suppose I throw away three cards at random, not telling you which cards I thrown away. What is the probability NOW that you pick a spade out of 5 remaining cards? I've just reduced the sample from which you pick, but does the probability changed? WHY should it change?

Another question, the same cards 5 spades and 3 hearts: I say that you can pick one card but only out of randomly selected 5 cards. What is the probability that the card you pick will be spade?

There is no difference in ALL above cases and the probability will remain 5/8. If it changed, increased (or decreased), it would mean that the probability of picking heart on the other hand decreased (or increased). Why would it?


Hope this helps.


For the statement
" NOW that you pick a spade out of 5 remaining cards"

If you throw 3 cards then how are we sure than 5 spades are still remaining. Following three cards may have been thrown:-
1. All 3 spades.
2. All three hearts.
3. 2 spade & 1 heart & vice-versa.

Hence how can we be sure that 5 spades are till remaining?


Yes, but we don't know which cards are thrown and this won't affect the probability. Please follow the links in my previous post for better understanding of such problems.
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
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Re: New Set of Mixed Questions!!!   [#permalink] 02 Jan 2014, 04:51
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