mathewhe/aqua_rat huggingface dataset:
Question: How many ways can the letters in the word COMMON be arranged?
(A) 6
(B) 30
(C) 90
(D) 120
(E) 180
Rationale: According to the above the # of permutations of 6 letters COMMON out of which 2 O's and 2 M's are identical is 6!2!∗2!=180
Answer: E.
Answer: (E) 180
Question: The angle between the minute hand and the hour hand of a clock when the time is 4.20° is
(A) 0°
(B) 5°
(C) 10°
(D) 20°
(E) None
Rationale: Sol.
Angle traced by hour hand in 13/3 hrs = (360/12 x 13/3)° = 130°
Angle traced by min. hand in 20 min. = (360/60 x 20)° = 120°
∴ Required angle = (130 - 120)° = 10°
Answer C
Answer: (C) 10°
Question: Two spherical balls lie on the ground touching. If one of the balls has a radius of 4 cm, and the point of contact is 6 cm above the ground, what is the radius of the other ball?
(A) 10 cm
(B) 12 cm
(C) 14 cm
(D) 16 cm
(E) 18 cm
Rationale: similar triangle properties..
2/r+4 = 4/r-4
giving r = 14.
Answer: C
Answer: (C) 14 cm
Question: 4 weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 14 weavers in 14 days?
(A) 40
(B) 45
(C) 49
(D) 53
(E) 58
Rationale: 1 weaver can weave 1 mat in 4 days.
14 weavers can weave 14 mats in 4 days.
14 weavers can weave 49 mats in 14 days.
The answer is C.
Answer: (C) 49
Question: The chance of rain on any given day in Tel-Aviv is 50%. What is the probability A that it rained in Tel-Aviv on exactly 4 out of 6 randomly chosen days?
(A) 15/64
(B) 30/64
(C) 1/2
(D) 1/4
(E) 52/64
Rationale: chances of rain on exactly 4 days and not rain on 2 days = (1/2)^4* (1/2)^2 = 1/64
Chosing 4 days out of 6 = 6!/(4!*2!) = 15
chances of rain on exactly 4 days out of 6 days A= 15/64
Ans A it is.
Answer: (A) 15/64
Question: If X is invested in a bank at a rate of simple interest of y% p.a. for two years, then the interest earned is 400. if X is invested at y% p.a., for two years when the interest is compounded annually, the interest is 410. What is the value of X?
(A) 8000
(B) 6000
(C) 5000
(D) 4000
(E) 3000
Rationale: Simple way to solve this question is to use options.
From SI, we know that X*y=20,000.
Now, put the value of X = 4000, we will have y = 5%
To calculate CI,
Now, we know 1st year Amount= 4000+5% of 4000= 4200.
2nd year, Amount = 4200 + 5% of 4200 = 4410.
We can see after 2 years Interest = 4410-4000= 410. hence, it satisfies the question. Hence D is the correct answer
Answer: (D) 4000
Question: Excluding stoppages, the average speed of a bus is 60 km/hr and including stoppages, the average speed of the bus is 40 km/hr. For how many minutes does the bus stop per hour?
(A) 60 min
(B) 18 min
(C) 37 min
(D) 20 min
(E) 21 min
Rationale: In 1hr, the bus covers 60 km without stoppages and 40 km with stoppages.
Stoppage time = time take to travel (60 - 40) km i.e 20 km at 60 km/hr.
stoppage time = 20/60 hrs = 20 min.
Answer:D
Answer: (D) 20 min
Question: What is the product of all the numbers in the dial of a telephone ?
(A) 0
(B) 53231
(C) 12312445
(D) 451231
(E) 461231
Rationale: Answer : A
Since one of the numbers on the dial of a telephone is zero, so the product of all the numbers on it is 0.
Answer: (A) 0
Question: Sabrina is contemplating a job switch. She is thinking of leaving her job paying $90,000 per year to accept a sales job paying $45,000 per year plus 15 percent commission for each sale made. If each of her sales is for $1,500, what is the least number of sales she must make per year if she is not to lose money because of the job change?
(A) 57
(B) 177
(C) 178
(D) 377
(E) 200
Rationale: Lets say she sales x items so her commission will be : x * 1500*15/100 = 225x
Salary difference is: 90000 - 45000 = 45000
So commission must at least be equal to salary difference i.e. x = 45000/225 = 200 (Approx).
Hence answer is E
Answer: (E) 200
Question: A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 4 years ago?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: Let's say
Age of Richard is "R"
Age of David is "D"
Age of Scott is "S"
Now
Richard is 6 years older than David,
i.e. R = D +6
David is 8 years older than Scott
i.e. D = S +8
If in 8 years, Richard will be twice as old as Scott
i.e. R+8 = 2x(S+8)
i.e. R+8 = 2S + 16
i.e. R = 2S+8
But R = D+6 = (S+8)+6 = S+14
therefore, 2S + 8 = S +14
i.e. S = 6
i.e. R = 20
i.e. D = 14
Now,
how old was David 4 years ago?
i.e. D-4 = 14-4 = 10 years
ANSWER:B
Answer: (B) 10
Question: A man walks at a speed of 2 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?
(A) 4 5/2 hours.
(B) 2 5/2 hours.
(C) 3 5/2 hours.
(D) 5 5/2 hours.
(E) 8 5/2 hours.
Rationale: Required time = (5 1/4)/2 + (5 1/4)/7 = 3 5/2 hours.
ANSWER:C
Answer: (C) 3 5/2 hours.
Question: A train is 560 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
(A) 56 seconds
(B) 18 seconds
(C) 40 seconds
(D) 19 seconds
(E) 45 seconds
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 560+140 = 700 meter
Time = Distance/speed
= 700 * (2/25)
= 56 seconds
Answer: A
Answer: (A) 56 seconds
Question: Simplfy
4b - [b -(a+b) - {b - (b - a+b)} + 2a]
(A) a
(B) 2a
(C) 4a
(D) 0
(E) 3b
Rationale: Explanation:
4b-[b-(a+b)-{b-(b-a+b)}+2a]
=4b-[b-a-b-{b-(2b-a)}+2a]
=4b-[-a-{b-2b+a}+2a]
=4b-[-a-{-b+a}+2a]
=4b-[-a+b-a+2a]
=4b-[-2a+b+2a]
=4b-b
=3b
Option E
Answer: (E) 3b
Question: Let's say in a lottery Samuel have a 4% chance of winning the jackpot.
All lined up and 1st four people on the line lose. Samuel is 5th in the row.
What's the chance of Samuel winning now?
(A) 1%
(B) 8%
(C) 9%
(D) 3%
(E) 4%
Rationale: E
4%
Explanation:
The winning chance probability is still 4% as the outcome of Samuel winning the lottery is a separate event from the 1st four losing it.
Answer: (E) 4%
Question: If the sum of 9 consecutive integers is x, which of the must be true?
I. x is even
II. x is odd
III. x is a multiple of 2
(A) I only
(B) II only
(C) III only
(D) I and III
(E) II and III
Rationale: sum of 3 consecutive integers
= (n) + (n+1) + (n+2) ++ (n+3) + (n+4) + (n+5)+(n+6)+(n+7)+(n+8)
=9n+36
= odd + even =odd
= 2(5n+18) = divisible by 2
Hence, x is odd and divisible by 2.
Answer: E
Answer: (E) II and III
Question: I. j; k; m; n; p
II. j - 10; m; m; m; p + 15
III. j + 2; k + 1; m; n - 1; p - 2
If j, k, m, n, and p are consecutive positive integers such that j < k < m < n < p, the data sets I, II, and III above are ordered from greatest standard deviation C to least standard deviation in which of the following?
(A)  I, III, II
(B)  II, I, III
(C)  II, III, I
(D)  III, I, II
(E)  III, II, I
Rationale: Range of 1st Set = (p-j)
Range of 2nd Set = P+15 - j +10 = (p-j) +25
Range of 3rd Set = P -2 - j - 2 = (p-j) - 4
R2 > R1 > R3 ==> SD2 > SD1 > SD3
Since, C=Higher the Range -> More Dispersion in the Set -> More Standard Deviation.B
Answer: (B)  II, I, III
Question: Find the middle one when The sum of three consecutive even numbers is 36?
(A) 10
(B) 12
(C) 15
(D) 16
(E) 20
Rationale: 3 consecutive numbers can be a - 1, a, a + 1
So sum of numbers = 3a = 36.
Hence a = 12.
B
Answer: (B) 12
Question: 9886 + x = 13200, then x is ?
(A) 3327
(B) 3237
(C) 3337
(D) 2337
(E) None of these
Rationale: Answer
x = 13200 - 9886 = 3314
Option: E
Answer: (E) None of these
Question: Evaluate: 22 + sqrt(- 4 + 6*4*3)=?
(A) 4
(B) 14
(C) 24
(D) 34
(E) 44
Rationale: According to order of operations, inner brackets first where 6?4?3 is first calculated since it has a multiplication and a division.
6*4*3 = 24*3 = 8
Hence
22 + sqrt(- 4 + 6*4*3) = 22 + sqrt(- 4 + 8)
= 22+ sqrt(4) = 22 + 2 = 24
correct answer C
Answer: (C) 24
Question: Carolyn bought 17 gumballs, Lew bought 12 gumballs, and Carey bought X gumballs. The average (arithmetic mean) number of gumballs the three bought is between 19 and 25, inclusive. What is the difference between the greatest number and the smallest number of gumballs Carey could have bought?
(A) 18
(B) 20
(C) 22
(D) 24
(E) 26
Rationale: Smallest gumballs = (19-17) + (19-12) +19= 28
Largest gumballs = (25-17) + (25-12) +25= 46
Difference = 46 - 28 = 18
A
Answer: (A) 18
Question: 10,12,15,20,27,?
(A) 34
(B) 35
(C) 36
(D) 37
(E) 38
Rationale: each number wil be obtained by adding the prime no. to the previous..
10+2=12
12+3=15
15+5=20
20+7=27
27+11=38
ANSWER:E
Answer: (E) 38
Question: The mean of 50 observations was 36. It was found later that an observation 46 was wrongly taken as 23. The corrected new mean is
(A) 35.24
(B) 36.16
(C) 36.24
(D) 36.46
(E) None
Rationale: Solution
Correct sum = (36x50+46-23)
= 1823.
âˆ´ Correct mean = 1823 / 50
= 36.46.
Answer D
Answer: (D) 36.46
Question: Danny can divide his herd into 5 equal parts and also to 6 equal parts, but not to 9 equal parts. What could be the number of cows Danny has in his herd?
(A) 120
(B) 155
(C) 180
(D) 336
(E) 456
Rationale: Danny can divide his herd into 5 equal parts and also to 6 equal parts =>
No of cows = Multiple of 5 and 6 = Multiple of 30.
Only option A and C qualify.
Now 2nd condition : but not to 9 equal parts :
So it should not be a multiple of 9.
ANSWER:A
Answer: (A) 120
Question: There are two concentric circles with radii 10 and 6. If the radius of the outer circle is increased by 20% and the radius of the inner circle decreased by 50%, by what percent does the area between the circles increase?
(A) 11
(B) 111
(C) 211
(D) 311
(E) 411
Rationale: The area of a circle is piR^2, where R is the radius.
The area of the big circle is 100pi.
The area of the small circle is 36pi.
The area A1 between the circles is 64pi.
When the big circle's radius increases, the new area is 144pi.
When the small circle's radius decreases, the new area is 9pi.
The area A2 between the circles is 135pi.
The ratio of A2/A1 is 135/64 = 2.11 which is an increase of 111%.
The answer is B.
Answer: (B) 111
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 199
(B) 87
(C) 120
(D) 150
(E) 388
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9) m = 150 m.Answer:D
Answer: (D) 150
Question: A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?
(A) 7 liters
(B) 15 liters
(C) 10 liters
(D) 9 liters
(E) None of these
Rationale: Explanation:
Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150 = 30 liters.
P liters of water added to the mixture to make water 25% of the new mixture.
Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).
(30 + P) = 25/100 * (150 + P)
120 + 4P = 150 + P => P = 10 liters.
ANSWER IS C
Answer: (C) 10 liters
Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/3 hours to fill the tank. The leak can drain all the water of the tank in?
(A) 17 hr
(B) 19 hr
(C) 10 hr
(D) 14 hr
(E) 16 hr
Rationale: Work done by the tank in 1 hour
= (1/2 - 1/3)
= 1/14 Leak will empty the tank in 14 hrs.
Answer:D
Answer: (D) 14 hr
Question: Different breeds of dogs get older at different rates in “dog years.” Livonian wolfhounds age 7 times as fast as humans, whereas Khazarian terriers age 5 times as fast and Akkadian retrievers age 4 times as fast. If Dan bought a newborn Akkadian on January 1, 2002, a newborn Khazarian 1 year later, and a newborn Livonian 1 year after that, in what year will the sum of the dog-year ages of the Akkadian and the Khazarian first be exceeded by twice the age of the Livonian in dog years, rounding all ages down to the nearest integer?
(A) 2013
(B) 2014
(C) 2015
(D) 2007
(E) 2017
Rationale: I'm going with C:
I made a chart starting at 2004:
A+K=13
L=0.
Then I added 9 to a+k for each year and 14 to L for each year.
2005:AK=22 L=14
2006:AK=31 L=28
2007:AK=40 L=42
thus, 2007 is the correct answer. => D
Answer: (D) 2007
Question: Anil spends 40% of his income on rent, 30% of the remaining on medicines and 20% of the remaining on education. If he saves Rs. 840 every month, then find his monthly salary?
(A) Rs. 2000
(B) Rs. 2500
(C) Rs. 2700
(D) Rs. 3000
(E) Rs. 2500
Rationale: Let's Anil's salary be Rs. 100.
Money spent on Rent = 40% of 100 = Rs. 40.
Money spent on medical grounds = 30% of (100 - 40) = 3/10 * 60 = Rs. 18.
Money spent on education = 20% of (60 - 18) = 1/5 * 42 = Rs. 8.40
Anil saves 100 - (40 + 18 + 8.40) i.e., Rs. 33.60
for 33.6 ---> 100 ; 840 ---> ?
Required salary = 840/33.6 * 100 = Rs. 2500
B)
Answer: (B) Rs. 2500
Question: Two trains of equal lengths take 15 sec and 20 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
(A) 16 sec
(B) 12 sec
(C) 17 sec
(D) 21 sec
(E) 23 sec
Rationale: Speed of the first train = 120/15 = 8 m/sec.
Speed of the second train = 120/20 = 6 m/sec.
Relative speed = 8 + 6 = 14 m/sec.
Required time = (120 + 120)/14 = 17 sec.
Answer: C
Answer: (C) 17 sec
Question: If YWVSQ is 25 - 23 - 21 - 19 - 11, Then MKIGF
(A) 13 - 11 - 9 - 7 - 9
(B) 13 - 11 - 9 - 7 - 6
(C) 13 - 11 - 9 - 7 - 7
(D) 13 - 11 - 9 - 7 - 3
(E) 11 - 11 - 9 - 7 - 1
Rationale: MKIGF = 11 - 11 - 9 - 7 - 1
Note: this is a dummy question. Dont answer these questions
Answer:E
Answer: (E) 11 - 11 - 9 - 7 - 1
Question: A shopkeeper sells 400 metres of cloth for Rs. 18000 at a loss of Rs.5 per metre. Find his cost price for one metre of cloth?
(A) Rs.59
(B) Rs.58
(C) Rs.09
(D) Rs.50
(E) Rs.13
Rationale: SP per metre = 18000/400
= Rs. 45 Loss per metre
= Rs. 5 CP per metre = 45 + 5
= Rs.50
Answer: D
Answer: (D) Rs.50
Question: 20 men can do a work in 40 days. When should 20 men leave the work so that the entire work is completed in 40 days after they leave the work?
(A) 0 days
(B) 10 days
(C) 20 days
(D) 30 days
(E) 40 days
Rationale: Total work to be done = 20 * 40 = 800
Let 20 men leave the work after 'P' days, so that the remaining work is completed in 40 days after they leave the work.
40P + (20 * 40) = 800
40P = 0 => P = 0 days
ANSWER:A
Answer: (A) 0 days
Question: A train is 288 meter long is running at a speed of 29 km/hour. In what time will it pass a bridge of 101 meter length?
(A) 48.29
(B) 50
(C) 26.8
(D) 45.29
(E) 30
Rationale: Speed = 29 Km/hr = 29*(5/18) m/sec = 145/18 m/sec
Total distance = 288+101 = 389 meter
Time = Distance/speed
= 389 * (18/145) = 48.29 seconds.
Answer: A
Answer: (A) 48.29
Question: If it is 6:27 in the evening on a certain day, what time in the morning was it exactly 2,880,715 minutes earlier? (Assume standard time in one location.)
(A) 6:22
(B) 6:24
(C) 6:27
(D) 6:30
(E) 6:33
Rationale: 6:27minus 2,880,715in any way must end with 2, the only answer choice which ends with 2 is A.
Answer: A.
Answer: (A) 6:22
Question: If 3 cats can kill 3 rats in 3 minutes, how long will it take 100 cats to kill 100 rats?
(A) 1 minutes
(B) 2 minutes
(C) 3 minutes
(D) 4 minutes
(E) 5 minutes
Rationale: It will take 3 minutes for 100 cats to kill 100 rats.
1 cat can kill 1 rat in 3 minutes, so 100 cats can kill 100 rats in 3 minutes
Answer C
Answer: (C) 3 minutes
Question: If y exceeds x by 25%, then x is less than y by?
(A) 28%
(B) 21%
(C) 20%
(D) 30%
(E) 29%
Rationale: X=100	y=125
125--------25
100--------? => 20%
Answer:C
Answer: (C) 20%
Question: Difference of 2 parallel sides ofa trapezium is 4cm. perpendicular distance between them is 10cm. If the area of the trapezium is 250cm^2. Find the lengths of the parallel side?
(A) 20,25
(B) 21,25
(C) 27,23
(D) 28,25
(E) 30,25
Rationale: Let the two parallel sides of the trapezium be a cm and b cm.
Then, a-b = 4 ------ (1)
And, (1/2) x (a+b) x 10 = 475 =>(a+b) =((250 x 2)/10) => a + b = 50------- (2)
Solving 1 and 2, we get: a=27,b=23
So, the two parallel sides are 27 cm and 23 cm.
C
Answer: (C) 27,23
Question: If the cost price of 50 articles is equal to the selling price of 40 articles, then the gain or loss percent is?
(A) 33%
(B) 29%
(C) 25%
(D) 55%
(E) 39%
Rationale: C
25%
Given that, cost price of 50 article is equal to selling price of 40 articles.
Let cost price of one article = Rs. 1
Selling price of 40 articles = Rs. 50
But Cost price of 40 articles = Rs. 40
Therefore, the trader made profit.\Percentage of profit = 10/40 * 100 = 25%
Answer: (C) 25%
Question: In a straight highway 2 cars starts from the same point in opposite directions each travels for 8 Kms and take left turn then travel for 6 Kms what is the distance between them now.
(A) 16
(B) 20
(C) 25
(D) 10
(E) 15
Rationale: use pythagoras theorem
c^2=a^2+b^2
=8^2+6^2 =64+36
c^2=100
c=10
the distance between A and B is (10+10)=20
ANSWER:B
Answer: (B) 20
Question: The distance between two towns is 380 km. At the same moment, a passenger car and a truck start moving towards each other from different towns. They meet 4 hours later. If the car drives 5 km/hr faster than the truck, what are their speeds?
(A) 33
(B) 45
(C) 37
(D) 36
(E) 19
Rationale: The main idea used in this kind of problems is that the distance equals speed multiplied by time S=V⋅tS=V⋅t
V (km/hr)	t (hr)	S (km)
Car	x + 5	4	4(x +5)
Truck	X	4	4x
4(x+5)+4x=3804(x+5)+4x=380
4x+4x=380−204x+4x=380−20
8x=3608x=360
x=3608x=3608
x=45x=45
Therefore the truck's speed is 45 km/hr, and the car's speed is 50 km/hr.
Answer:B
Answer: (B) 45
Question: In a race with 5 competitors, the first-place finisher receives a gold medal, the second-place finisher receives a silver medal, and the third-place finisher receives a bronze medal. If there are no ties, in how many different ways may these three medals be awarded?
(A) 35
(B) 120
(C) 720
(D) 840
(E) 60
Rationale: Well in this case since there are 3 positions and they can be taken by 3 persons only ,so order matters over here .For gold there are 5 choices ,for silver 4 remain (one who got gold cannot be given silver) and for bronze 3 choices remain.
So total possibilities=5*4*3
Correct answer E=60
Answer: (E) 60
Question: A train 125 m long passes a man, running at 4 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
(A) 49 km/hr
(B) 50 km/hr
(C) 45 km/hr
(D) 65 km/hr
(E) 87 km/hr
Rationale: Speed of the train relative to man
= (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr
= 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed
= (x - 4) km/hr. x - 4 = 45 ==> x = 49 km/hr.
Answer: A
Answer: (A) 49 km/hr
Question: An article sold at a profit of 20% if both the cost price and selling price would be Rs.20/- the profit
would be 10% more. What is the cost price of that article?
(A) 40
(B) 50
(C) 60
(D) 70
(E) 80
Rationale: if both cost price and selling price would be Rs.20 less.
let c.p-x and s.p-1.2x
1.2x-20 = 1.3(x-20)
x = 60
ANSWER:C
Answer: (C) 60
Question: The sum of three consecutive multiples of 3 is 117. What is the largest number?
(A) 45
(B) 48
(C) 51
(D) 42
(E) 54
Rationale: Let the numbers be 3x, 3x + 3 and 3x + 6.
Then,
3x + (3x + 3) + (3x + 6) = 117
9x = 108
x = 12
Largest number = 3x + 6 = 42
Answer : D
Answer: (D) 42
Question: A train running at the speed of 30 km/hr crosses a pole in 12 seconds. What is the length of the train?
(A) 70
(B) 80
(C) 90
(D) 100
(E) 110
Rationale: Speed=(30 x(5/18)m/sec	=(25/3)m/sec.
Length of the train = (Speed x Time).
Length of the train =	((25/3)x 12)m = 100 m
D
Answer: (D) 100
Question: A man sells two articles for Rs.3600 each and he gains 25% on the first and loses 25% on the next. Find his total gain or loss?
(A) 9% loss
(B) 6.25% Loss
(C) 4000
(D) 324
(E) 8% LOSS
Rationale: (25*25)/100 = 6.25%loss
ANSWER:B
Answer: (B) 6.25% Loss
Question: The probability of shooting a target increases after a certain skill is enhanced and is equal to the new probability of NOT shooting the target. Given this fact, which of the following must be false?
(A) The new probability of shooting the target is greater than 0.5
(B) The original probability of shooting the target is less than 0.5
(C) The original probability of NOT shooting the target and the new probability of shooting the target are the same
(D) The original probability of shooting the target and that of NOT shooting the target are the same.
(E) The sum of the original and the new probabilities of shooting the target is ALWAYS equal to 1
Rationale: 1. Let p(i), q(i), be the initial probability of shooting and missing the target respectively and let p(n) and q(n) be the new probability of shooting and missing the target respectively.
Given:
1. p(i) + q(i) =1
2. P(n) + q(n) =1
3. p(n) > p(i)
4. p(i) = q(n)
Deductions:
5. q(n) + q(i) =1 ( from (1) and (4) )
6. p(n) + p(i) =1 ( from (2) and (4) ) - ( Choice E always true)
7. From ( 3) and (6), p(i) < 0.5 and p(n) > 0.5 - ( Choice A and Choice B always true)
8. From (1) and (6), q(i) = p(n) - ( Choice C always true)
9. From (3) and (8), q(i) > p(i) - ( choice D always false)
Therefore the answer is Choice D
Answer: (D) The original probability of shooting the target and that of NOT shooting the target are the same.
Question: A man can row downstream at the rate of 32 Kmph and upstream at 17 Kmph. Find the man’s rate in still water and rate of current?
(A) 7.5
(B) 8.0
(C) 9.5
(D) 9.0
(E) 8.25
Rationale: Rate of still water = 1/2 (down stream + upstream)
= 1/2 (32 + 17) = 24.5 Kmph
rate of current = 1/2 (down stream - upstream)
= 1/2 (32 - 17)
= 1/2 (15)
= 7.5 kmph
Answer is A.
Answer: (A) 7.5
Question: Edward earns $7.00 per hour for the first 40 hours he works per week, and twice this rate for overtime. If Michael earned $210 last week, how many hours did he work?
(A) 43
(B) 44
(C) 45
(D) 46
(E) 47
Rationale: $7*40 + $12*x = $210 --> x = 5 hours.
Total working hours = 40 + 5 = 45
Answer: C.
Answer: (C) 45
Question: The price of lunch for 10 people was $207 including a 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity?
(A) 11.73
(B) 12
(C) 13.8
(D) 14
(E) 18
Rationale: Clearly E is the answer
I used POE here
Lets consider option (E) 10*18= 180 now 180(115/100)=207 => possible ANSWER IMO E
Answer: (E) 18
Question: Which of the following inequalities is always true for any real number 'a' and 'b'?
(A) |a+b| >= |(|a|-|b|)|
(B) |a-b| <= |(|a|-|b|)|
(C) |a-b| = |(|a|-|b|)|
(D) |a-b| >= |(|a|-|b|)|
(E) |a-b| <= |a|-|b|
Rationale: The answer here is D. One of the fundamental properties of absolute value is subadditivity, and this is a reverse triangle inequality, which is equivalent to subadditivity. So this means that difference of two any elements is something (some number) which is greater than or equal to the difference of the each element taken on itself separately, i.e. |a-b| >= |(|a|-|b|)|
Answer: (D) |a-b| >= |(|a|-|b|)|
Question: S = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}
Two integers will be randomly selected from the sets above, one integer from set S and one integer from set B. What is the probability that the sum of the two integers will equal 9 ?
(A)  0.15
(B)  0.20
(C)  0.25
(D)  0.30
(E)  0.33
Rationale: The total number of pairs S,B possible is 4*5=20. Out of these 20 pairs only 4 sum up to 9: (2, 7); (3, 6), (4, 5) and (5, 4). The probability thus is 4/20=0.2.
Answer: B.
Answer: (B)  0.20
Question: What will come in place of the x in the following Number series? 5,28,57,88,125
(A) 123
(B) 143
(C) 166
(D) 190
(E) 210
Rationale: 28=23+5
57=29+28
88=31+57
125=37+88
166=41+125
=166
C
Answer: (C) 166
Question: One train is traveling 36 kmph and other is at 12.5 meters a second. Ratio of the speed of the two trains is?
(A) 5:4
(B) 5:6
(C) 5:0
(D) 5:4
(E) 4:5
Rationale: 36 * 5/18 = 12.5
20:25 => 4:5
Answer: E
Answer: (E) 4:5
Question: The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
(A) 40%
(B) 44%
(C) 50%
(D) 54%
(E) 60%
Rationale: Let original length = x metres and original breadth = y metres.
Original area = (xy) m2.
New length = 120 x m = 6 x m.
100 5
New breadth = 120 y m = 6 y m.
100 5
New Area = 6 x x 6 y m2 = 36 xy m2.
5 5 25
The difference between the original area = xy and new-area 36/25 xy is
= (36/25)xy - xy
= xy(36/25 - 1)
= xy(11/25) or (11/25)xy
Increase % = 11 xy x 1 x 100 % = 44%.
25 xy
B
Answer: (B) 44%