mathewhe/aqua_rat huggingface dataset:
Question: At an elementary school, 60% of the faculty members are women and 60% of the faculty members are married. If 3/4 of the men are single, what fraction of the men are married?
(A) 3/4
(B) 2/5
(C) 4/5
(D) 2/3
(E) 1/4
Rationale: --------------------M------W--------Total
Marrried---------10-----50---------60
Not married-----30-----10---------40
Total-------------40-----60--------100
need married man/total man, so 10/40=1/4
E
Answer: (E) 1/4
Question: If the Average of 10 consecutive integers is 24.5 then the 10th integer is :-
(A) 15
(B) 20
(C) 23
(D) 29
(E) 25
Rationale: The average falls between the 5th and 6th integers,
integer 5 = 24, integer 6 = 25.
Counting up to the tenth integer
we get 29.
ANSWER:D
Answer: (D) 29
Question: In a certain company, the ratio of the number of managers to the number of non-managers in any department must always be greater than 7 : 37. In the company, what is the maximum number of non-managers in a department that has 9 managers?
(A) 44
(B) 45
(C) 46
(D) 47
(E) 48
Rationale: 9/7 * 37 = 47.6
The answer is D.
Answer: (D) 47
Question: A certain list of 300 test scores has an arithmetic mean of 74 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 302 test scores with a standard deviation less than d?
(A)  75 and 80
(B)  80 and 85
(C)  74 and 74
(D)  75 and 75
(E)  70 and 80
Rationale: Ans: C
Deviation means spreading of the numbers from one median point value..
as the set is already established and we need to add only two numbers, this means we can only add numbers which are closer to the median to reduce the deviation.
so 74 and 74 are the most close numbers and they will increase the number of elements in the set without changing the median value.
C
Answer: (C)  74 and 74
Question: A cube has a volume of 125 cubic feet. If a similar cube is twice as long, twice as wide, and twice as high, then the volume, in cubic feet of such cube is?
(A) 24
(B) 48
(C) 64
(D) 80
(E) 1000
Rationale: Volume = 125 = side^3
i.e. Side of Cube = 5
New Cube has dimensions 10, 10, and 10 as all sides are twice of teh side of first cube
Volume = 10*10*10 = 1000 square feet
Answer: option E
Answer: (E) 1000
Question: If m is a positive integer greater than 1, what is the sum of the multiples of m from m to m^2, inclusive?
(A)  m(m + 1)(m-1)
(B)  m^2(m + 1)/2
(C)  m^2(m-1)
(D)  (x^3 + 2x)/2
(E)  x(x-1)^2
Rationale: Ans :- B=m^2(m + 1)/2
I substituted 3 in all answer choices.
Option B and C were both satisfying the condition.
So i substituted 4 instead of 3 in all answer choices,
Only B option satisfied.
Answer: (B)  m^2(m + 1)/2
Question: A can do a piece of work in 15 days. A does the work for 5 days only and leaves the job. B does the remaining work in 6 days.In how many days B alone can do the work?
(A) 5days
(B) 7 days
(C) 12 days
(D) 9 days
(E) 10 days
Rationale: Explanation:
A’s 5 day work = 5*1/15=1/3
Remaining work = 1-1/3=2/3
B completes 2/3 work in 6 days
B alone can do in x days
2/3*x=6
X=9 days
Answer: Option D
Answer: (D) 9 days
Question: If f(b)=b^2 and b is a positive integer, which of the following CANNOT be the value of f(f(b))?
(A) 1
(B) 81
(C) 200
(D) 256
(E) 625
Rationale: f(b)=b^2
f(f(b)) = (b^2)^2 = b^4
Therefore f(f(b)) will be numbers that are 4th power of other numbers.
Checking the options:
1 = 1^$
81 = 3^4
200. This cannot be written as the 4th power of any number
256 = 4^4
625 = 5^4
Answer: C
Answer: (C) 200
Question: I walk a certain distance and ride back taking a total time of 37 minutes. I could walk both ways in 55 minutes. How long would it take me to ride both ways?
(A) 12 mins
(B) 10 mins
(C) 19 mins
(D) 15 mins
(E) 20 mins
Rationale: Let the distance be x km. Then,
( Time taken to walk x km) + (time taken to ride x km) =37 min.
( Time taken to walk 2x km ) + ( time taken to ride 2x km )= 74 min.
But, the time taken to walk 2x km = 55 min.
Time taken to ride 2x km = (74-55)min =19 min.
Ans: C
Answer: (C) 19 mins
Question: An investor receives a total combined return of 10% on his two different investments. On his $10,000 investment he receives a return of 6%. What is the return on his $20,000 investment?
(A) 7.25%
(B) 12%
(C) 8%
(D) 8.5%
(E) 9%
Rationale: 0.06 * 10000 + 20000x = 0.10(30000)
solving for x give x = 12%
option B
Answer: (B) 12%
Question: Drum X is 1/2 full of oil and drum Y, which has twice the capacity of drum X, is 1/2 full of oil. If all of the oil in drum X is poured into drum Y, then drum Y will be filled to what capacity?
(A) 2/3
(B) 3/4
(C) 4/5
(D) 5/6
(E) 7/8
Rationale: (1/2)X = (1/4)Y
(1/4)Y + (1/2)Y = (3/4)Y
The answer is B.
Answer: (B) 3/4
Question: Thomas's age and Matt's age are in the ratio 2:3. Two years ago the ratio of their ages was 1:2. Find the ratio of their ages four years hence?
(A) 1:2
(B) 2:3
(C) 3:4
(D) 4:5
(E) 5:6
Rationale: Let ages of Thomas and Matt be x and y respectively.
x/y = 2/3 => x = 2/3 y
(x- 2)/(y - 2) = 1/2
=> 2x - 4 = y - 2 => 2x = y + 2
But x = 2/3 y
2 * 2/3 y = y + 2
4y = 3y + 6 => y = 6years
=> x = 4 years
Ratio of their ages five years hence, (4 +4)/(6 + 4) = 8/10. => 4:5
Answer:D
Answer: (D) 4:5
Question: The function f is defined for all positive integers u by the following rule. f(u) is the number of positive integers each of which is less than u and has no positive factor in common with u other than 1. If s is any prime, number then f(s)=
(A) 2
(B) s-2
(C) (s+1)/2
(D) (s-1)/2
(E) S-1
Rationale: If not the wording the question wouldn't be as tough as it is now. The GMAT often hides some simple concept in complicated way of delivering it.
This question for instance basically asks: how many positive integers are less than given prime number s which have no common factor with s except 1.
Well as s is a prime, all positive numbers less than s have no common factors with s (except common factor 1). So there would be s-1 such numbers (as we are looking number of integers less than s).
For example: if s=4 how many numbers are less than 4 having no common factors with 4: 1, 2, 3, 4,--> 4-1=3.
Answer: E.
Answer: (E) S-1
Question: The charge for a single room at Hotel P is 30 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ?
(A) 28%
(B) 20%
(C) 40%
(D) 50%
(E) 150%
Rationale: Let rate in R = 100x
then P = 70x
G = 100y
P = 90y
Thus
70 x=90y
or x = 1.28 y
Ans R = 128y
so increase = 28%
Answer: A
Answer: (A) 28%
Question: Two stations P and Q are 290 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?
(A) 10 am
(B) 12 am
(C) 10.30 am
(D) 12.30 pm
(E) 2 pm
Rationale: Assume both trains meet after x hours after 7 am
Distance covered by train starting from P in x hours = 20x km
Distance covered by train starting from Q in (x-1) hours = 25(x-1)
Total distance = 290
=> 20x + 25(x-1) = 290
=> 45x = 315
=> x= 7
Means, they meet after 7 hours after 7 am, ie, they meet at 2 pm
Answer is E.
Answer: (E) 2 pm
Question: In an exam, A scored 75 percent, B scored 25 percent and C scored 32 percent. The maximum score awarded in the exam is 500. Find the average mark scored by all the three candidates?
(A) 190
(B) 200
(C) 210
(D) 220
(E) 230
Rationale: Average mark scored by all the three boys
= [75/100 (500) + 25/100 (500) + 32/100 (500)] / 3
= 220
Answer: D
Answer: (D) 220
Question: It is well known that a triangle’s area is √(p(p-a)(p-b)(p-c)),
when p=(a+b+c)/2, such that a, b, c are the lengths of sides of the triangle. If the triangle has 300, 300, and 300 as the side’s lengths, what is the triangle’s area?
(A) 34,200
(B) 36,200
(C) 38,200
(D) 42,200
(E) 38,971
Rationale: It is well known that a triangle’s area is √(p(p-a)(p-b)(p-c)),
when p=(a+b+c)/2,
-> P=(300+300+300)/2=450, area=√(450(450-300)(450-300)(450-300))=38,971. Therefore, the answer is E.
Answer: (E) 38,971
Question: In a kilometer race, A beats B by 40 meters or 10 seconds. What time does A take to complete the race?
(A) 290 sec
(B) 190 sec
(C) 199 sec
(D) 192 sec
(E) 240 sec
Rationale: Time taken by B run 1000 meters
= (1000 * 10)/40 = 250 sec.
Time taken by A = 250 - 10 = 240 sec.
Answer: E
Answer: (E) 240 sec
Question: A candidate appearing for an examination has to secure 52% marks to pass paper I. But he secured only 45 marks and failed by 35 marks. What is the maximum mark for paper I?
(A) 110
(B) 154
(C) 130
(D) 140
(E) 150
Rationale: he secured 45 marks nd fail by 35 marks so
total marks for pass the examinatn=80
let toal marks x
x*52/100=80
x=154
ANSWER:B
Answer: (B) 154
Question: A certain kind of necklace is made from 9 green, 6 white, and 3 orange beads. What is the maximum number of these necklaces that can be made from 45 beads of each color ?
(A) 7
(B) 8
(C) 5
(D) 6
(E) 2
Rationale: Atleast 9 green breads are needed to make a necklace, so irrespective of the combinations of white and orange beads, the number of necklaces that can be formed will be
45/9 =5
Answer:- C
Answer: (C) 5
Question: A factory that employs 1000 assembly line workers pays each of these workers $5 per hour for the first 40 hours worked during a week and 1½ times that rate for hours worked in excess of 40. What was the total payroll for the assembly-line workers for a week in which 30 percent of them worked 10 hours, 50 percent worked 40 hours, and the rest worked 50 hours?
(A)  $180,000
(B)  $185,000
(C)  $170,000
(D)  $200,000
(E)  $205,000
Rationale: 30% of 1000 = 300 worked for 20 hours
Payment @ 5/hr
Total Payment = 300*10*5 = 15000
50 % of 1000 = 500 worked for 40 hours
Payment @ 5/hr
Total payment = 500*40*5 = 100000
Remaining 200 worked for 50 Hours
Payment for first 40 Hours @ 5 /hr
Payment = 200*40*5 = 40000
Payment for next 10 hr @ 7.5/hr
Payment = 200 * 10 * 7.5 = 15000
Total Payment = 15000+100000 + 40000 +15000 = 170000
Hence , answer is C
Answer: (C)  $170,000
Question: COMPLETE THE SERIES..
1, 3, 7, 11, 13,... ?
(A) 16
(B) 17
(C) 18
(D) 19
(E) 20
Rationale: i think in this series we need to divide series in two parts i.e in terms of even place term and odd place term.i.e
1,7,13 so in odd term you see a difference of 6.
and in even terms there is difference of 8
3,11 so next term will be 11+8=19.
so series is like this
1,3,7,11,13,19.
ANSWER:D
Answer: (D) 19
Question: Pipes A and B can fill a tank in 2 and 3 hours. Pipe C can empty it in 15 hours. If all pipes are opened together, then the tank will be filled in?
(A) 60/17 hr
(B) 13/12 hr
(C) 42/11 hr
(D) 6 hr
(E) 30/23 hr
Rationale: Net part filled in 1 hour = 1/2 + 1/3 - 1/15 = 23/30
The tank will be full in 30/23 hr
Answer is E
Answer: (E) 30/23 hr
Question: The average of ten numbers is 7 .If each number is multiplied by 12 , then the average of new set of numbers is
(A) 28
(B) 236
(C) 288
(D) 84
(E) 26
Rationale: Explanation:
If each number is multiplied by K, then the new average increases by K times. So new average = 84
Answer:D
Answer: (D) 84
Question: The closest approximation of (69.28 × 0.004)/0.03 is
(A) 0.092
(B) 0.92
(C) 9.2
(D) 92
(E) 920
Rationale: (69.28 × 0.004)/0.03
1. 0.004 = 4 × 10^(-3)
2. 0.03 = 3 × 10^(-2)
3. (a × b)/c = a × (b/c)
4. 0.004/0.03 = 4 × 10^(-3)/ (3 × 10^(-2)) = 4 × 10^( -3 - (-2))/3 = 4 × 10^(-1) / 3 = (4/3) × 10^(-1) = 1.333 × 10^(-1)
Therefore,
(69.28 × 0.004)/0.03 = 69.28 × (0.004/0.03) = 69.28 × 1.33 × 10^(-1) = 69.28 × 1.33/10 = 6.928*1.33
Now,
7 × 2 = 14
7 × 1 = 7
or better:
6.9 × 1 = 6.9
6.9 × 2 = 13.8
hence,
6.9 <6.928 × 1.33 < 13.8
9.2 is the only answer that satisfies this condition.
ANSWER:C
Answer: (C) 9.2
Question: A sum of Rs. 2665 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
(A) 1888
(B) 1640
(C) 2768
(D) 2976
(E) 2691
Rationale: (x*8*3)/100 = ((2665 - x)*3*5)/100
24x/100 = 39975/100 - 15x/100
39x = 39975 => x = 1025
Second sum = 2665 – 1025
= 1640
Answer: B
Answer: (B) 1640
Question: Two trains starting at the same time from two stations 200 km apart and going in opposite directions cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds?
(A) 21 : 9
(B) 11 : 9
(C) 71 : 9
(D) 91 : 9
(E) 21 : 2
Rationale: Explanation:
In the same time, they cover 110 km and 90 km respectively.
{\color{Blue} \therefore } Ratio of their speeds = 110 : 90 = 11 : 9
Answer: B
Answer: (B) 11 : 9
Question: If 0 < x ≤ 3, then which one of the following is the maximum value of (x – 1)^2 + x ?
(A) –2
(B) –1
(C) 7
(D) 1
(E) 2
Rationale: the maximum value of (x – 1)^2 + x for 0 < x ≤ 3 is when x=3 --> (x – 1)^2 + x =7
Answer C
Answer: (C) 7
Question: If 42/330 = 0.1272, what is the 32nd digit to the right of the decimal point of the fraction?
(A) 1
(B) 4
(C) 5
(D) 7
(E) 2
Rationale: we are not concerned what 42/330 means..
we have to look at the decimal..
0..1272 means 0.1272727...
so leaving first digit to the right of decimal, all ODD numbered are 7 and all EVEn numbered are 2.
here 32 is EVEN, so ans is 2
Answer is E
Answer: (E) 2
Question: In Township K, 1/5 of the housing units are equiped with cable Tv. If 1/10 of the housing units, including 1/6 of those that are equiped with cable tv, are equipped with videocassette recorders, what fraction of the housing units have neither cable tv nor videocassette recorders?
(A) 23/30
(B) 11/15
(C) 7/10
(D) 1/6
(E) 2/15
Rationale: 1/5 -- cable TV (This includes some data from video cassette recorder)
1/10 -- video cassette recorder including 1/6(equiped with cable tv) i.e. 1/6(1/5) = 1/30
therefore only video cassette recorder = 1/10 - 1/30 = 1/15
Total = 1/5+1/15+neither cable tv nor videocassette recorders
1 = 4/15 + neither cable tv nor videocassette recorders
therefore neither cable tv nor videocassette recorders = 1-4/15 = 11/15
Hence B.
Answer: (B) 11/15
Question: A sock drawer contains seven socks, each one a different solid color. The colors of the socks are orange, yellow, green, blue, indigo, and violet. A person reaches into the drawer, pulls out two socks, and puts a single sock on each foot. If each sock can fit either the left or the right foot, and if it matters whether a particular sock is on the left or the right foot, how many different sock fashion combinations could the person make from the six socks?
(A) 12
(B) 15
(C) 21
(D) 36
(E) 30
Rationale: It's a question of permutation since order matters here ....
It can be deduced to-
6P2 = 6!/4! = 6*5 = 30 .........Answer is - E
Answer: (E) 30
Question: In how many ways can a Chief Minister and a Vice Minister be elected from a team of 14 members?
(A) 132
(B) 144
(C) 158
(D) 170
(E) 182
Rationale: There are 14 choices for the Chief Minister.
Then there are 13 choices for the Vice Minister.
The total number of ways is 14*13 = 182.
The answer is E.
Answer: (E) 182
Question: A room has both an entrance and an exit door. The room can fill up with people in 5 hours. The room can be empty of people in 15 hours. If it is desired that the room should be filled, from empty, exactly 6 hours after people begin entering the room at 9:30am, then at what time should people begin exiting the room?
(A) 10:00am
(B) 10:45am
(C) 12:00pm
(D) 12:30pm
(E) 1:30pm
Rationale: In 6 hours the entrance door is opened to fill the room equal to 6*1/5 = 6/5 of the room. So, 1/5 more than necessary, which should be compensated by people using the exit door. To empty out 1/5 of the people, the exit door needs 15/5 = 3 hours.
Therefore, the exit door should be used at 9:30am + 6 hours - 3 hours = 12:30pm.
Answer: D.
Answer: (D) 12:30pm
Question: The dimensions of each book in an encyclopedia set measures 8 in x 4 in x 12 in. (l x w x h). Each shelf (i.e. each divider) has a surface area of 848 sq in., where the thickness is 1 in and the width is 16 in. Assuming there is enough space in between shelves, how many shelves are needed to fit all of the books?
(A) 7
(B) 12
(C) 13
(D) 5
(E) 26
Rationale: Surface area of each shelf= 2ab + 2ac + 2bc
848 = 2 x 1 x 16 + 2 x 1 x c + 2 x 16 x c
848 = 32 + 2c + 32c
816 = 34c
c = 24 in. (i.e. the length of each shelf)
Each book is 4 in thick
24/4 = 6 books per shelf
26/6 = 4.333=5 shelves
Answer is D
Answer: (D) 5
Question: From a Group of 8 People, Including Timo and Gary, 3 people are to be selected at random to work on a certain project. What is the probability that 3 people selected will include Timo but not Gary
(A) 5/56
(B) 9/56
(C) 15/56
(D) 21/56
(E) 25/56
Rationale: Number of ways of selecting 3 people out of 8 people = 8C3
In the three members Timo will always be there in the team. At this step we have vacancy for 2 more members and 7 members are available. Gary cannot be there in the team. So 2 members have to be selected and the number of available members = 7 -Gary = 6
Number of ways to form a 3 member team that includes Timo and excludes Gary = 6C2
Probability = 6C2/8C3 = 15/56
Answer: C
Answer: (C) 15/56
Question: The price of a car and AC are in the ratio 3:2. If the scooter costs $500 more than the AC. then the price of the AC?
(A) 1500
(B) 200
(C) 1700
(D) 2000
(E) 2500
Rationale: Let the price of the Car and AC is 3x and 2x
3x-2x = 500
x = 500
Price of AC = 3*500 = $1500
Answer is A
Answer: (A) 1500
Question: The difference between the ages of two persons is 10 years.Fifteen years ago ,the elder one was twice as old as the younger one.The present age of the elder person is :
(A) 25 years
(B) 35 years
(C) 45 years
(D) 55 years
(E) 75 years
Rationale: Solution
Let their ages be x year and (x + 10) years respectively.
Then,(x + 10) - 15 = 2 (x - 15) ⇔ x-5 = 2x-30 ⇔ x =25.
∴ Present age of the elder person =(x + 10) =35 years. Answer B
Answer: (B) 35 years
Question: A dog takes 4 leaps for every 5 leaps of a hare but 3 leaps of a dog are equal to 4 leaps of the hare. Compare their speeds?
(A) 4:5
(B) 16:15
(C) 9:13
(D) 5:15
(E) 9:17
Rationale: Let the distance covered in 1 leap of the dog be x and that covered in 1 leap of the hare be y
Then 3x = 4y
x = 4/3 y
4x = 16/3 y
Ratio of speeds of dog and hare = Ratio of distances covered by them in the same time
= 4x:5y = 16/3 y : 5 = 16:15
Answer is B
Answer: (B) 16:15
Question: The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 47. The corrected new mean is?
(A) 36.7
(B) 36.1
(C) 36.5
(D) 36.02
(E) 36.3
Rationale: Correct sum
= (36 * 50 + 48 - 47)
= 1801.
Correct mean = 1801/50
= 36.02
Answer:D
Answer: (D) 36.02
Question: If a equals the sum of the even integers from 2 to 20, inclusive, and b equals the sum of the odd integers from 1 to 19, inclusive, what is the value of a - b ?
(A) 1
(B) 10
(C) 19
(D) 20
(E) 21
Rationale: Sum of consecutive odd or even integers = (no. of odd or even ints) * (first int + last int) / 2
Here A = sum of even ints from 2 to 20, inclusive
number of even ints = 10,
first int + last int = 2+20 = 22
A = 10*22 / 2 = 110
B = sum of odd ints from 1 to 19, inclusive
number of odd ints = 10,
first int + last int = 1+19 = 20
A = 10*20 / 2 = 100
A-B = 110 - 100 = 10
ANSWER:C
Answer: (C) 19
Question: The length of the longest tape in cm which can be used to measure exactly, the length 6m; 5m ; and 12m is:
(A) 200
(B) 100
(C) 50
(D) 1200
(E) 500
Rationale: The three lengths in cm are 600,500 & 1200.
HCF of 600, 500 & 1200 is 100
Hence, the answer is 100 cm.
ANSWER:B
Answer: (B) 100
Question: Find the numbers which are in the ratio 3:2:4 such that the sum of the first and the second added to the difference of the third and the second is 21.
(A) 9, 6, 16
(B) 9, 6, 19
(C) 9, 6, 16
(D) 9, 6, 12
(E) 9, 6, 11
Rationale: Let the numbers be a, b and c.
a:b:c = 3:2:4
Given, (a + b) + (c - b) = 21
=> a + c = 21
=> 3x + 4x = 21 => x = 3
a, b, c are 3x, 2x, 4x
a, b, c are 9, 6, 12.
Answer: D
Answer: (D) 9, 6, 12
Question: A rectangular cube has sides measuring 15 inches long by 12 inches wide by 2 inches high. If the surface area of the rectangle is the same as a cube, what do the sides/walls of the cube measure? Round to the nearest whole number.
(A) 7
(B) 5
(C) 9
(D) 6
(E) 4
Rationale: First calculate the surface area of the rectangle by multiplying the length and width of the rectangle together, then multiply by 2 to get both sides of the rectangle. This calculates to 360 inches. Find the surface area of the sides of the rectangular cube. Multiply the height by the length of the rectangle. Multiply the answer by 2 (for the 2 sides on the rectangular cube). This calculates to 60 inches. Then multiply the width of the rectangle by the height. Multiply the answer by 2 (for the 2 sides on the rectangular cube). This calculates to 48 inches. Add the totals together to get the rectangular cube surface area of 468 inches. Since a square cube has 6 sides - divide the surface area by 6. This calculates to 78 inches as the surface area of each side of the cube. The square root of 78 is 8.831. Rounding to the nearest whole number that makes each side of the cube measuring 9 inches. The correct answer is (C).
Answer: (C) 9
Question: Each of three investments has a 20% of becoming worthless within a year of purchase, independently of what happens to the other two investments. If Simone invests an equal sum V in each of these three investments on January 1, the approximate chance that by the end of the year, she loses no more than 1/3 of her original investment is
(A) 90%
(B) 80%
(C) 70%
(D) 60%
(E) 40%
Rationale: The problem asks for the approximate chance that no more than 1/3 of the original investment is lost. We can apply the “1 – x” technique: what’s the chance that more than 1/3 of the original investment is lost? There are two outcomes we have to separately measure:
(a) All 3 investments become worthless.
(b) 2 of the 3 investments become worthless, while 1 doesn’t.
Outcome (a): The probability is (0.2)(0.2)(0.2) = 0.008, or a little less than 1%.
Outcome (b): Call the investments X, Y, and Z. The probability that X retains value, while Y and Z become worthless, is (0.8)(0.2)(0.2) = 0.032. Now, we have to do the same thing for the specific scenarios in which Y retains value (while X and Z don’t) and in which Z retains value (while X and Y don’t). Each of those scenarios results in the same math: 0.032. Thus, we can simply multiply 0.032 by 3 to get 0.096, or a little less than 10%.
The sum of these two probabilities is 0.008 + 0.096 = 0.104, or a little more than 10%. Finally, subtracting from 100% and rounding, we find that the probability we were looking for is approximately 90%.
The correct answer is A.
This problem illustrates the power of diversification in financial investments. All else being equal, it’s less risky to hold a third of your money in three uncorrelated (independent) but otherwise equivalent investments than to put all your eggs in one of the baskets. That said, be wary of historical correlations! Housing price changes in different US cities were not so correlated—and then they became highly correlated during the recent housing crisis (they all fell together), fatally undermining spreadsheet models that assumed that these price changes were independent.
Answer: (A) 90%
Question: A cistern is filled by a tap in 3 1/2 hours. Due to leak in the bottom of the cistern, it takes half an hour longer to fill the cistern. If the cistern is full how long will it take the leak to empty it?
(A) 29
(B) 28
(C) 99
(D) 72
(E) 61
Rationale: 2/7 - 1/x = 1/4
x = 28
Answer: B
Answer: (B) 28
Question: A cyclist covers a distance of 90km in 6 hours. Find the speed of the cyclist.
(A) 30 km/hr.
(B) 25 km/hr.
(C) 20 km/hr.
(D) 15 km/hr.
(E) 35 km/hr.
Rationale: Speed of the cyclist =D/T =90/6 =15km/hr. Answer : D
Answer: (D) 15 km/hr.