mathewhe/aqua_rat huggingface dataset:
Question: The weight of four dogs is determined to be 25 pounds, 31 pounds, 32 pounds and 28 pounds respectively. The weight of a fifth dog is determined to be y pounds. If the average (arithmetic mean) weight of the first four dogs is the same as that of all five dogs what is the value of y?
(A) 31
(B) 29
(C) 35
(D) 37
(E) 39
Rationale: Total weight of the 4 dogs = (25+31+32+28) = 132
Avg = 116/4 = 29
Total weight of 5 dogs = 116+y or 4(29)+y
Average of 5 dogs as per Question = 29
Equation:
4(29) + y = 5 (29), or y = 29.
Choose B
Answer: (B) 29
Question: List I: 3, 6, 14, 19
List II: x, 3, 14, 8, 19
(A)  6
(B)  7
(C)  8
(D)  9
(E)  10
Rationale: We start by calculating the median of the numbers of list I: 3, 6, 14, 19. We see that the numbers in the list are in order already and, since we have an even number of numbers, the median is the average of the two middle numbers.
median = (6 + 14)/2
median = 20/2
median = 10
The median of list I is 7.
Looking at list II: x, 3, 6, 14, 19, we see that we have an odd number of terms. Thus, when the list is ordered from least to greatest the median must be the middle term. Since the medians of the two lists must be equal, we know that the median of list II must be 10 and therefore x is 10.
The answer is E.
Answer: (E)  10
Question: If by selling an article for Rs.60, a person loses 1/7 of money, what would he have gained or lost % by selling it for Rs.77?
(A) 5%
(B) 10%
(C) 13%
(D) 14%
(E) 20%
Rationale: Sol. CP - = EC7 = 70 1-7 6 77-70 % Profit = 100 = 10%
B
Answer: (B) 10%
Question: In a certain math department, students are required to enroll in either Calculus or Trigonometry, each of which is offered in beginner and advanced courses. The number of students enrolled in Trigonometry is 50% greater than the number of students enrolled in Calculus, and 70% of Calculus students are enrolled in the beginner course. If 4/5 of students are in the beginner courses, and one student is selected at random, what is the probability that an advanced Trigonometry student is selected?
(A) 8%
(B) 16%
(C) 20%
(D) 24%
(E) 40%
Rationale: Let x be the number of students in calculus.
Then the number of students in trigonometry is 1.5x
The number of students on beginner calculus is 0.7x
The number of students in beginner trigonometry is 4/5*(2.5x) - 0.7x = 1.3x
The number of students in advanced trigonometry is 0.2x
The percentage in advanced trigonometry is 0.2x / 2.5x = 8%
The answer is A.
Answer: (A) 8%
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
(A) Rs.1014
(B) Rs.1140
(C) Rs.999
(D) Rs.1085
(E) Rs.1185
Rationale: a2 = 3136 => a = 56
56 * 4 * 3 = 672 – 6 = 666 * 1.5 = 999
ANSWER:C
Answer: (C) Rs.999
Question: When a merchant imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that the merchant paid was $94.50, what was the total value of the item?
(A) $2,350
(B) $2,850
(C) $3,250
(D) $3,400
(E) $3,750
Rationale: Let x be the value in excess of $1,000.
0.07x = 94.5
x = $1,350
The total value was $1,350 + $1,000 = $2,350.
The answer is A.
Answer: (A) $2,350
Question: A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container.
(A) 26.34 litres
(B) 27.36 liters
(C) 28 litres
(D) 29.16 litres
(E) cannot be determined
Rationale: Solution
Amount of milk left after 3 operations
[40 (1-4/40)3] litres = (40x9/10x9/10x9/10)= 29.16 litres
Answer D
Answer: (D) 29.16 litres
Question: If the average of 744, 745, 747, 748, 749, 752, 752, 753, 755 and x is 750, what is the value of x?
(A) 750
(B) 752
(C) 754
(D) 755
(E) 756
Rationale: Sum of the deviations of the numbers in the set from the mean is always zero
744, 745, 747, 748, 749, 752, 752, 753, 755
mean is 750
so the list is -6-5-3-2-1+2+2+3+5... this shud total to zero
but this is -5 , hence we need a number that is 5 more than the mean to get a +5 and make it zero
hence the answer is 750 + 5 =755
D
Answer: (D) 755
Question: Two bullet trains of equal lengths take 10 seconds and 30 seconds respectively to cross a telegraph post. If the length of each bullet train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
(A) 13 sec.
(B) 14 sec.
(C) 12 sec.
(D) 15 sec.
(E) 19 sec.
Rationale: Speed of the first bullet train = 120/10 m/sec = 12 m/sec.
Speed of the second bullet train = 120/30 m/sec = 4 m/sec.
Relative speed = (12 + 4) = 16 m/sec.
Required time = (120 + 120)/16 sec = 15 sec.
D
Answer: (D) 15 sec.
Question: What will be the length of the mini-train, if it crosses a pole in 3 sec while travelling at a speed of 75 kmph?
(A) 60 m
(B) 65 m
(C) 63.5 m
(D) 64 m
(E) 62.5 m
Rationale: Explanation:
D = 75 * 5/18 * 3 = 62.5 m
Answer: Option E
Answer: (E) 62.5 m
Question: 30 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780. The bigger part is :
(A) 33
(B) 34
(C) 26
(D) 10
(E) 19
Rationale: Explanation:
Let the two parts be (30- x) and x.
Then, 10 (30 - x) + 22x = 780
=> 12x = 480
=> x = 40.
Bigger part = (30- x) = 10.
Answer: D) 10
Answer: (D) 10
Question: Find the least number which when divided by 20,25,35,40 leaves remainder 14,19,29,34 respectively.
(A) 1394
(B) 1450
(C) 1245
(D) 2564
(E) 1256
Rationale: The difference of 20-14 = 6 , 25-19 = 6 , 35-29 = 6 , 40-34 = 6
LCM of 20,25,35,40 = 1400
Required number = 1400 - 6 = 1394
Answer is A
Answer: (A) 1394
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 180 m and they cross each other in 12 sec, then the speed of each train is?
(A) 54
(B) 31
(C) 36
(D) 25
(E) 24
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (180 + 180)/12 => x = 15
Speed of each train = 15 m/sec.
= 15 * 18/5 =54 km/hr.
Answer: Option A
Answer: (A) 54
Question: In a party, there are rows arranged with 12,20 and 30 chairs and there were 3 left in all the cases. When there were 11 rows. There were no chair left. If 30 chairs were added. Then what will be the reminder?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: LCM of 12,20,30 is 120.so the number is in the form of 120x+3 which is divisible by 11,by placing x=3, we get 363 which is divisible by 11 and the multiple of 120 when 3 is subtracted from 363.so the no. is 363.so when 30 is added to it and is divided by 11 we get remainder as 8
ANSWER:A
Answer: (A) 8
Question: David leaves home everyday at 4 p.m to pick his son from school and returns home at 6 p.m. One day, the school was over at 4 p.m and the son started walking home from school. David, unaware of this, starts from home as usual and meets his son on the way and returns home with him 15 minutes early. If the speed of David is 30 km\hr, find the speed of his son.
(A) 15km/hr
(B) 6 km/hr
(C) 4.28 km/hr
(D) 9 km/hr
(E) 4.12 km/hr
Rationale: David leaves home everyday at 4 p.m to pick his son from school and returns home at 6 p.m. One day, the school was over at 4 p.m and the son started walking home from school. David, unaware of this, starts from home as usual and meets his son on the way and returns home with him 15 minutes early. If the speed of David is 30 km\hr, find the speed of his son.
The distance from home to school is 30 km. The round trip distance = 60 km. Because he returns home 15 minutes early, I thought it might be easier to break his trip up into 8 identical 15 minute blocks, each of which he traveled at 7.5 km/hour.
Because we are dealing with a round trip here,David would have stopped 7.5 minutes short of the school. This means he traveled Distance=rate* time .5Km/hour*52.5 minutes or 26.25 KM. His son therefore traveled 3.75km/hour by the time he met his dad at 4:52.5. It took the son 52.5 minutes to travel 3.75 km. Because we are trying to find the son's rate per hour (i.e. 60 minutes) and we have his speed for 52.5 minutes it's best to convert to km/minute then multiply by 60 to get km/hour
3.75km/52.5 = .07 km/minute
.07km/minute*60 minutes = 4.28 km/hour.
Answer: C. 4.28 km/hr
Answer: (C) 4.28 km/hr
Question: If the time is currently 1:30pm, what time will it be in exactly 479 hours?
(A) 12:30am
(B) 1:30am
(C) 12:30pm
(D) 2:30pm
(E) 10:30pm
Rationale: Every 24 hours will bring us to the same 1:30pm. 480 is divisible by 24 (20*24=480), so if it were 480 hours we would have 1:30pm, but since it's 479 hours then it will be 1 hour less, so 12:30pm.
Answer: C.
Answer: (C) 12:30pm
Question: A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:
(A) 120 kmph
(B) 150 kmph
(C) 50 kmph
(D) 80 kmph
(E) 75 kmph
Rationale: Let speed of the car be x kmph.
Then, speed of the train =	150/100x	= 3/2 x	kmph.
75/x - 75/(3/2)x = 125/10 x 60
75/x	-50/x = 5/24
x =	25 x24/5	= 120 kmph.
answer :A
Answer: (A) 120 kmph
Question: The average of five consecutive odd numbers is 61. What is the difference between the highest and lowest numbers ?
(A) 7
(B) 8
(C) 5
(D) 4
(E) 2
Rationale: Let the numbers be x, x + 2, x + 4, x + 6 and x + 8.
Then [x + (x + 2) + (x + 4) + (x + 6) + (x + 8) ] / 5 = 61.
or 5x + 20 = 305 or x = 57.
So, required difference = (57 + 8) - 57 = 8
Answer: B
Answer: (B) 8
Question: Given that 1.75 x 10(power 8), Which of the following options is equal to it?
(A) 171000000
(B) 172000000
(C) 176000000
(D) 175000000
(E) 177000000
Rationale: = 1.75 x 10(power 8)
= 1.75 x 100000000
= 175000000.
Answer is D.
Answer: (D) 175000000
Question: The length of a rectangular landscape is 4times its breadth. There is a playground in it whose area is 1200 square mtr & which is 1/3rd of the total landscape. What is the length of the landscape?
(A) 110
(B) 115
(C) 120
(D) 130
(E) 145
Rationale: Sol. x * 4x = 3 * 1200
x = 30
Length = 4 * 30 = 120
C
Answer: (C) 120
Question: Two positive integers differ by 4, and sum of their reciprocals is 2. Then one of the numbers is
(A) a) 3
(B) 2
(C) c) 5
(D) d) 21
(E) e) 28
Rationale: Algebraic approach:
Let n be the smaller integer => 1/n + 1/(n+4) = 2
or ((n+4)+n)/n(n+4) =2 or (n^2+4n)*2 =2n+4 or n=2 as n cannot be -negative
Solve for n => n=2. Hence,
B
Answer: (B) 2
Question: A Hotel has 6 employees; there are 5 female employees and 1 male employee. In how many ways can a 3-person committee be created if the committee must include the male employee?
(A) 10
(B) 12
(C) 15
(D) 24
(E) 30
Rationale: A Hotel has 6 employees;for male 1C1 = 1 ........ A
foe female = 5C2 = 10.........B
total = 10*1
= 10 - answer=A
Answer: (A) 10
Question: The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?
(A) 9
(B) 9.2
(C) 10
(D) 11.5
(E) 12
Rationale: Explanation:
1 to 11 = 11 * 10.9 = 119.9
1 to 6 = 6 * 10.5 = 63
6 to 11 = 6 * 11.4 = 68.4
63 + 68.4 = 131.4 – 119.9 = 11.5
6th number = 11.5
D)
Answer: (D) 11.5
Question: If r and s are positive integers and r-s=6, which of the following has the greatest value W?
(A) 2r
(B) 2s
(C) r +s
(D) 2r-s
(E) 2s-r
Rationale: The simplest way to do this is to assume values.
We are told that r and s are positive integers W.
Also, r-s = 6 => r = 6+s
Hence r is 6 more than s.
Let s be 10. Hence r = 16.
Option A: 2r = 2*16 = 32
Option B: 2s = 2 * 10 = 20
Option C: r + s = 16 + 10 = 26
Option D: 2r - s = 2(16) - 10 = 32 - 10 = 22
Option E: 2s - r = 2(10) - 16 = 20 - 16 = 4
Hence option A is the greatest.
Answer: (A) 2r
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
(A) 6
(B) 7
(C) 8
(D) 4
(E) 2
Rationale: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer: C
Answer: (C) 8
Question: In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 80 questions and secures 120 marks, the number of questions he attempts correctly, is:
(A) 35
(B) 46
(C) 42
(D) 30
(E) 40
Rationale: Let the number of correct answers be x.
Number of incorrect answers = (80 â€“ x).
4x â€“ 1(80 â€“ x) = 120 or 5x = 200 or x = 40.
ANSWER:E
Answer: (E) 40
Question: In a hostel, there is a meal for 120 men or 200 boys. If 150 boys have taken the meal, how many men will be catered to with remaining meal?
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: Explanation :
There is a meal for 200 boys. 150 boys have taken the meal.
Remaining meal is to be catered to 50 boys.
Now, 200 boys 120 men.
So 50 boys => 120 x 50/200 = 30 men.
Answer : B
Answer: (B) 30
Question: If the average (arithmetic mean) of a and b is 160, and c – a = 200, what is the average of b and c?
(A) 260
(B) 250
(C) 150
(D) 225
(E) 325
Rationale: a+b/2 = 160
=> a+b = 320
a = c - 200...sub this value
c-200+b =320
=>c+b = 520
=>c+b/2 = 260
Answer : A
Answer: (A) 260
Question: Find the ratio in which rice at Rs.7.10 a kg be mixed with rice at Rs.5.70 a kg to produce a mixture worth Rs.6.30 a kg?
(A) 1 : 3
(B) 2 : 3
(C) 3 : 4
(D) 4 : 5
(E) None of these
Rationale: Solution
Required ratio = 60 : 80 = 3 : 4
Answer C
Answer: (C) 3 : 4
Question: Share Rs.4800 among John, Jose & Binoy in the ration 2 : 4 : 6.Find the amount received by John?
(A) 900
(B) 980
(C) 1600
(D) 1240
(E) 1400
Rationale: Amount received by sanjay.
4 / 12 X 4800 = 1600= ( related ratio / sum of ratio ) x Total amount
So, the Amount received by sanjay is 1600.
C
Answer: (C) 1600
Question: A computer can perform c calculations in s seconds. How many minutes will it take the computer to perform m calculations?
(A) 60ms/c
(B) ms/c
(C) ms/60c
(D) 60c/ms
(E) m/60cs
Rationale: As 'thick' as this question might look, it's actually a fairly straight-forward Rate question and can be solved by TESTing VALUES.
We're told that a computer can perform C calculations in S seconds.
Let's TEST....
C = 2
S = 3
2 calculations every 3 seconds =
40 calculations every 1 minute
We're asked how many MINUTES it will take to perform K calculations.
Since we already know that the computer can perform 40 calculations in 1 minute, let's TEST...
m = 80
So we're looking for an answer that = 2 when C = 2, S = 3 and K = 80
Answer A: 60mS/C = 60(80)(3)/2 = 7200 This is NOT a match
Answer B: mS/C = (80)(3)/2 = 120 This is NOT a match
Answer C: mS/60C = (80)(3)/(60)(2) = 2 This IS a match
Answer D: 60C/mS = 60(2)/(80)(3) = 1/2 This is NOT a match
Answer E: m/60CS = 80/(60)(2)(3) = a fraction. This is NOT a match
C
Answer: (C) ms/60c
Question: If −y ≥ x, and −x < −9, then which of the following must be true?
(A) y = −9
(B) y > −9
(C) −y > 9
(D) y ≤ −9
(E) y ≥ −9
Rationale: −y ≥ x, and −x < −9
y <= -x < -9
As '-x' is less than '-9' and Y is less than or equal to '-x'
we have y < -9 which is similar to -y > 9.
C) -y > 9
Answer: (C) −y > 9
Question: When x is divided by y, the quotient is u with remainder r. What is x in terms of r, y, and u?
(A) y + r + u
(B) yu + r
(C) x/y+r
(D) y/u+r
(E) ru + y
Rationale: (x/y) = u + r
solve for x
x=(u*y)+r
Ans B.
Answer: (B) yu + r
Question: A computer store offers employees a 20% discount off the retail price. If the store purchased a computer from the manufacturer for $1000 dollars and marked up the price 20% to the final retail price, how much would an employee save if he purchased the computer at the employee discount (20% off retail price) as opposed to the final retail price.
(A) $1,000
(B) $960
(C) $240
(D) $200
(E) $150
Rationale: Cost price=1000
Profit=20% =20% of 1000=200
selling price=CP+ Profit
SP=1200
a Discount of 20% to employees means 20% off on 1200
so 20% of 1200= 240
so a employee thinks he saved 240..
Answer: C
Answer: (C) $240
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
(A) 28%
(B) 20%
(C) 80%
(D) 70%
(E) 30%
Rationale: 900 ---- 180
100 ---- ? => 20%
Answer: B
Answer: (B) 20%
Question: If two times A is equal to three times of B and also equal to four times of C, then A:B:C is
(A) 2:3:4
(B) 3:4:2
(C) 4:6:3
(D) 6:4:3
(E) None
Rationale: Solution: 2A = 3B;
Or, B = (2/3)A; And, 2A = 4C;
Or, C = (1/2)A;
Hence, A:B:C = A:2A/3:A/2 = 1:2/3:1/2 = 6:4:3
Answer: Option D
Answer: (D) 6:4:3
Question: if p/q=3/4
then3p+5q=?
(A) 25/4
(B) 29/4
(C) 20/4
(D) 35/4
(E) 25/3
Rationale: 3p+5q=?
Divided by q,
3(p/q)+5=x
3*(3/4)+5=29/4
ANSWER:B
Answer: (B) 29/4
Question: Harkamal purchased 9kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
(A) A)1120
(B) B)1065
(C) C)1070
(D) D)1075
(E) E)1080
Rationale: Cost of 9 kg grapes = 70 × 9 = 630.
Cost of 9 kg of mangoes = 55 × 9 = 490.
Total cost he has to pay = 630 + 490 = 1120
A
Answer: (A) A)1120
Question: A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
(A) 3.2 km
(B) 3 km
(C) 2.4 km
(D) 3.6 km
(E) None of these
Rationale: Explanation :
Speed in still water = 5 kmph
Speed of the current = 1 kmph
Speed downstream = (5+1) = 6 kmph
Speed upstream = (5-1) = 4 kmph
Let the requited distance be x km
Total time taken = 1 hour
=> x/6 + x/4 = 1
=> 2x + 3x = 12
=> 5x = 12
=> x = 2.4 km. Answer : Option C
Answer: (C) 2.4 km
Question: A certain list of 100 data has an average (arithmetic mean) of 9 and a standard deviation of d, where d is positive. Which of the following pairs of data, when added to the list, must result in a list of 108 data with standard deviation less than d?
(A) -9 and 0
(B) 0 and 0
(C) 0 and 9
(D) 0 and 18
(E) 9 and 9
Rationale: Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.
So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller.
According to the above adding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount.
Closest to the mean are 9 and 9 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD.
Answer: E.
Answer: (E) 9 and 9
Question: A miniature roulette wheel is divided into 10 equal sectors, each bearing a distinct integer from 1 to 10, inclusive. Each time the wheel is spun, a ball randomly determines the winning sector by settling in that sector. If the wheel is spun five times, approximately what is the probability that the product of the five winning sectors’ integers will be even?
(A) 50%
(B) 67%
(C) 85%
(D) 91%
(E) 97%
Rationale: The only way to have an odd product is if all 5 integers are odd.
P(odd product) = 1/2*1/2*1/2*1/2*1/2 = 1/32
P(even product) = 1 - 1/32 = 31/32 which is about 97%
The answer is E.
Answer: (E) 97%
Question: If the given two numbers are respectively 8% and 16% of a third number, then what percentage is the first of the second ?
(A) 20%
(B) 25%
(C) 18%
(D) 50%
(E) none of these
Rationale: Here, l = 8 and m = 16
Therefore, first number = l/m x 100% of second number = 8/16 x 100% of second number = 50% of second number
ANSWER:D
Answer: (D) 50%
Question: What should come in place of the question mark (?) in the following equation?
6 5⁄6 × 5 1⁄3 + 17 2⁄3 × 1⁄2 = ?
(A) 112 1⁄3
(B) 663
(C) 240
(D) 116 2⁄3
(E) None of these
Rationale: ? = 41⁄6 × 16⁄3 + 53⁄3 × 9⁄2 = 41×16+53×9×3 /6×3
= 656+1431 /18=2087/18=11517/18
Answer E
Answer: (E) None of these
Question: After decreasing 24% in the price of an article costs Rs.912. Find the actual cost of an article?
(A) 226
(B) 255
(C) 1200
(D) 2771
(E) 332
Rationale: CP* (76/100) = 912
CP= 12 * 100 => CP = 1200
Answer:C
Answer: (C) 1200
Question: A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability E that the team will have exactly 2 women?
(A) 1/14
(B) 1/7
(C) 2/7
(D) 3/7
(E) 1/2
Rationale: 5C2 * 3C2 -> it gives combination of exactly 2 women and 2 men.
8C4 -> gives total possibilities of 4 people from 5 women and 3 men.
Probability = 5C2*3C2 / 8C4 = 3/7
SECOND METHOD:
Probability of two women -> 5/8 * 4/7.
probability of two men -> 3/6 * 2/5.
Probability: (5/8 * 4/7) * (3/6 * 2/5) = 1/14.
Answer: (D) 3/7
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
(A) 110 km/hr
(B) 80 km/hr
(C) 60 km/hr
(D) 50 km/hr
(E) 120 km/hr
Rationale: Answer: Option C
Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/8 = 3x => x = 25/3.
So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr.
Answer: (C) 60 km/hr
Question: An urn contains 10 balls, numbered from 1 to 10. If 2 balls are selected at random with replacement from the urn, what is the probability B that the sum of the 2 numbers on the balls will be even?
(A) 25%
(B) 37.5%
(C) 50%
(D) 62.5%
(E) 75%
Rationale: Correct Answer: C
Since there are 5 even numbered balls and 5 odd numbered balls, the probability B of selecting either an even or an odd is 5/10= 1/2. In order for the sum of the numbers on the two balls to be even, either both numbers must be even or both numbers must be odd; one even and one odd number would add to an odd number. The probability of selecting two even numbers is:
1/2 * 1/2= 1/4
The probability of selecting two odd numbers is also:
1/2 * 1/2= 1/4
Adding both probabilities gives 1/4+1/4= 1/2 , or 50%, as the probability that the sum of the numbers will be even. Thus, the correct answer is (C).
Answer: (C) 50%
Question: If a car went the first third of the distance at 80 kmh, the second third at 24 kmh, and the last third at 30 kmh, what was the average speed of the car for the entire trip?
(A) 36 kmh
(B) 40 kmh
(C) 42 kmh
(D) 44 kmh
(E) 34 kmh
Rationale: Assume D/3 = 240 (this number is convenient because it is divisible by 80, 24 and 30)
So:
240 = 80*T1 = 3 hrs
240 = 24*T2 = 10 hrs
240 = 30*T3 = 8 hrs
T = T1 + T2 + T3 = 21 hrs
D = RT
(240*3) = R*21
R = 34
ANSWER: E
Answer: (E) 34 kmh
Question: What is the rate percent when the simple interest on Rs.900 amount to Rs.160 in 4 Years?
(A) 4.44
(B) 5.44
(C) 6.44
(D) 7.44
(E) 8.44
Rationale: 160 = (900*4*R)/100
R = 4.44%
Answer: A
Answer: (A) 4.44
Question: When a number is divided by 4 &then multiply by 12 the answer is 9 what is the no.?
(A) 3
(B) 5
(C) 5.6
(D) 5.7
(E) 6.5
Rationale: if $x$ is the number, x/4 * 12 = 9
=> 3x = 9
=> x = 3
A
Answer: (A) 3
Question: Last year, the price of a vacation package was P. At the beginning of this year, the price went up 50%. Lucas used a travel voucher to purchase the vacation package at 30% off this year’s price. In terms of P, how much did Lucas pay?
(A)  P + 10
(B)  1.1*P
(C)  0.50*P
(D)  0.05*P
(E)  1.05*P
Rationale: Last year price = P;
This year price = 1.5P;
Lucas used a travel voucher to purchase the vacation package at 30% off this year’s price, thus he paid (1 - 0.3)*1.5P = 0.98P.
Answer: E.
Answer: (E)  1.05*P
Question: A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
(A) 250
(B) 276
(C) 976
(D) 267
(E) 287
Rationale: CP1 = 100 SP1 = 90
CP2 = 80 SP2 = 80 * (140/100) = 112
22 ----- 100
55 ----- ? => Rs.250
Answer:A
Answer: (A) 250
Question: A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old id the mother at present?
(A) 46
(B) 49
(C) 40
(D) 21
(E) 19
Rationale: Let the mother's present age be x years. Then, the person's present age = 2/5 x years.
(2/5 x + 8) = 1/2 (x + 8)
2(2x + 40) = 5(x + 8) => x = 40
Answer:C
Answer: (C) 40