RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 768 as interest at the end of the loan period, what was the rate of interest?
A.3.6
B.6
C.8
D.24
Answer: C.8
Explanation: Let rate = R% and time = R years.
Then, (1200 x R x R)/100 = 768
12R2 = 768
R2 = 64
R = 8.
Answer: Option C
Question: Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 13?
A.3
B.4
C.5
D.8
Answer: D.8
Explanation: i'm not sure i got the question right, if it is what i think it is, then 8 should be the right answer
0,1,2,3,4,5, will not have 2 slip sum of 13 add another (either 6,7,8 or 9) and we'll have a pair with sum 13
Ans:D
Question: Find the average of first 32 natural numbers.
A.A)12.6
B.B)16.5
C.C)15.9
D.D)17.5
Answer: B.B)16.5
Explanation: Sum of first n natural numbers = n(n+1)/2
sum of first 32 natural numbers = 32*33/2 =528
average = 528/32 = 16.5
Answer is B
Question: A train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 80 kmph. When and at what distance from Mumbai do the two trains meet?
A.87
B.279
C.80
D.278
Answer: C.80
Explanation: When the second train leaves Mumbai the first train covers 40 * 1 = 40 km
So, the distance between first train and second train is 40 km at 10.00am
Time taken by the trains to meet
= Distance / relative speed = 40 / (80 -40) = 1 hours
So, the two trains meet at 11 a.m. The two trains meet 1 * 80 = 80 km away from Mumbai.
Answer:C
Question: A cistern has two taps which fill it in 12 minutes and 15 minutes respectively. There is also a waste pipe in the cistern. When all the three are opened, the empty cistern is full in 20 minutes. How long will the waste pipe take to empty the full cistern ?
A.10 min
B.12 min
C.15 min
D.9 min
Answer: A.10 min
Explanation: Work done by the waste pipe in 1 minutes
= 1⁄20 - (1⁄12 + 1⁄15) = -1⁄10 [-ve sign means emptying]
∴ Waste pipe will empty the full cistern in 10 minutes.
Answer A
Question: The present worth of Rs.1014 due in 2 years at 4% per annum compound interest is
A.Rs.150.50
B.Rs.937.5
C.Rs.156.25
D.Rs.158
Answer: B.Rs.937.5
Explanation: Solution
Present Worth	= Rs.[1014/(1+4/100)²]
= Rs.(1014x25/26x25/26)
= Rs.937.5
Answer B
Question: emblem is coded as 216;
crude is coded as 125
parakeets will be ?
A.243
B.866
C.729
D.456
Answer: C.729
Explanation: coding follows (no. of letters)^3
emblem = 216 = 6^3
crude = 125 = 5^3
parakeets= 9^3 =729
ANSWER:C
Question: John buys 100 shares of par value Rs. 5 each, of a company, which pays an annual dividend of 12% at such a price that he gets 10% on his investment. Find the market value of a share.
A.2
B.4
C.5
D.6
Answer: D.6
Explanation: Face value of each share = Rs.5
Total dividend received by John = 100×5×12/100 = Rs.60
Let market value of 100 shares = Rs.x
x×10/100=60
x = 600
ie, Market value of 100 shares = Rs.600
Hence, Market value of each share = Rs.6
Answer is D.
Question: At a summer camp with 1,500 participants, 1/2 of the campers are aged 10 to 12. Next year, the number of campers aged 10 to 12 will increase by 1/3. After this change, what percentage of the total 1,500 campers will the 10 to 12-year-olds represent?
A.62
B.64
C.65
D.66 2/3%
Answer: D.66 2/3%
Explanation: Total - 1,500 participants
campers are aged 10 to 12 = (1/2)*1500 = 750
Next year, campers are aged 10 to 12 = (4/3)*750 = 1000
Percentage = (1000/1500)*100 = 66 2/3%
Answer: Option D
Question: If x and y are positive numbers and z = xy^2, a 50 percent increase in x and a 20 percent decrease in y would result in which of the following changes in z?
A.A decrease of 4%
B.A decrease of 14%
C.An increase of 4%
D.An increase of 20%
Answer: A.A decrease of 4%
Explanation: z= x*y^2
Now , since x increases by 50 % and y decreases by 20 %
z'=(3/2)x * (8/10)(8/10)y^2
= 192/200 * x*y^2
= 96/100 * x*y^2
= 96/100 * z
a decrease in 4 %
Answer A
Question: The soldiers in two armies when they met in a battle were in the ratio of 10 : 3. Their respective losses were as 20 : 3 and the survivors as 40 : 13. If the number of survivors in the larger army be 24,000, find the original number of soldiers in each army ?
A.28000, 8400
B.25000, 7500
C.29000, 2750
D.26000, 7800
Answer: A.28000, 8400
Explanation: Let the soldiers in the two armies be 10X, 3X and losses be 20Y, 3Y,
Then we have,
10X - 20Y = 24000 ...(i)
And 3X - 3Y = 24000 x 13/40 = 7800
Solving, we have 10X = 28000, 3X = 8400
ANSWER:A
Question: Ice-ColdIce-cream factory produces only tricolor ice-cream products, where each ice-cream has three stripes of different colors. The factory uses the colors pink, purple, orange, silver, blue and GREEN. How many different ice-cream products have at least one stripe out of the following colors: pink, purple or orange (assume that the order of the stripes in a single ice-cream does not matter)?
A.12
B.14
C.18
D.19
Answer: D.19
Explanation: IMO: D - 19
There are 6C3 = 20 ways to create different colored ice cream products. Out of these 20, only 1 (Silver, Blue, GREEN) will not contain at least one of the colors pink, purple, or orange. 20 - 1 = 19.
The other way would be to calculate the number of ice cream products that contain at least one of the colors pink, purple, or orange (PPO).
#1: Pick one out of PPO and two out of SBP: 3C1 * 3C2 = 3 * 3 = 9
#2: Pick two out of PPO and one out of SBP: 3C2 * 3C1 = 3 * 3 = 9
#3: Pick three out of PPO: 3C3 = 1
9 + 9 + 1 = 19
answer is D
Question: What percent of 11 is 11 percent of 1?
A. 1
B. 0.01
C. 0.1
D. 13
Answer: A. 1
Explanation: 11 % of 1 = (11/100) * 1 = 11/100
To determine what percentage of 11 this is :
[11][/100*11] *100 = 1%
Ans : A
Question: In how many ways a committee, Consisting of 5 men and 6 women can be formed from 8 men and 10 women?
A.266
B.86400
C.11760
D.5040
Answer: C.11760
Explanation: To choose Required number of ways to form a committee:
Select 5 men out of 8 men and 6 women out of 10 women.
That is 8C5 * 10C6.
8C5=8!/3!*5!
8C5=8*7*6*5!/(3*2*1)*5!=56
10C6=10!/6!*4!
10C6=10*9*8*7*6!/6!*(4*3*2*1)=210
The Required number of ways=210*56=11760
Question: If the price of 6 toys is Rs. 264.37, what will be the approximate price of 5 toys ?
A.Rs. 140
B.Rs. 100
C.Rs. 200
D.Rs. 220
Answer: D.Rs. 220
Explanation: Solution
Let the required price be Rs. x . Then, less toys, less cost
∴ 6 : 5 :: 264.37 : x ⇔ 6x = (5 × 264.37) ⇔ x = (5x264.37)/6 ⇔ x = 220.308.
∴ Approximate price of 5 toys = Rs. 220. Answer D
Question: if P represents the number of prime numbers between 1 and 102 then what is the value of P?
A.25
B.26
C.27
D.28
Answer: B.26
Explanation: Units digit of a prime number except 2 will always be odd ( 1,3 , 5 , 7 , 9 )
So start working around.
01 - 09 = 2, 3 ,5 , 7
10 - 19 = 11, 13 , 17 , 19
20 - 29 = 23 , 29
30 - 39 = 31 , 37
40 - 49 = 41 , 43 , 47
50 - 59 = 53 , 59
60 - 69 = 61 , 67
70 - 79 = 71 , 73 , 79
80 - 89 = 83 , 87 , 89
90 - 99 = 97
100 - 102 = 101
Count you will get 26 Prime numbers
ANSWER:B
Question: Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Six years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
A.Can't be determined
B.48
C.27
D.24
Answer: B.48
Explanation: Explanation:
Let the present ages of Sameer and Anand be 5x years and 4x years respectively.
Then, (5x+6)/(4x+6)=11/9
⇒ 45x + 54 = 44x + 66⇒ 9(5x + 6) = 11(4x + 6)
⇒ 45x - 44x = 66 - 54
⇒ x = 12.
Anand's present age = 4x = 48 years.
Answer: B
Question: Pipe A can fill a tank in 6 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled ?
A.2.5 hours
B.3.3 hours
C.3.5 hours
D.3 hours
Answer: B.3.3 hours
Explanation: Explanation:
Part filled by A in 1 hour = 1/6
Part filled by B in 1 hour = 1/10
Part filled by C in 1 hour = 1/30
Part filled by (A+B+C) in 1 hour =
1/6+1/10+1/30=9/30
So all pipes will fill the tank in 3.3 hours.
Option B
Question: If 5% more is gained by selling an article for Rs. 350 than by selling it for Rs. 345, the cost of the article is
A.289
B.231
C.100
D.288
Answer: C.100
Explanation: Explanation:
Let C.P. be Rs. x.
Then, 5% of x = 350 - 345 = 5
x/20 = 5 => x = 100
Answer: C
Question: How many digits 2^10 has?
A.3
B.35
C.50
D.99
Answer: A.3
Explanation: 2^10 = 1.024 * 10^3
therefore 3 digits would be my best guess
A
Question: A, B, C enter into a partnership investing Rs. 35,000, Rs. 45,000 and Rs. 55,000 respectively. The respective shares of A, B, C in annual profit of Rs. 40,500 are:
A.Rs. 10,500, Rs. 13,500, Rs. 16,500
B.Rs. 11,500, Rs. 13,000, Rs. 16,000
C.Rs. 11,000, Rs. 14,000, Rs. 15,500
D.Rs. 11,500, Rs. 12,500, Rs. 16,500
Answer: A.Rs. 10,500, Rs. 13,500, Rs. 16,500
Explanation: A:B:C = 35000 : 45000 : 55000 = 7:9:11
A's share = 40500 * 7/27 = Rs. 10500
B's share = 40500 * 9/27 = Rs. 13500
C's share = 40500 * 11/27 = Rs. 16500
ANSWER:A
Question: A certain bus driver is paid a regular rate of $12 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $976 in total compensation, how many total hours did he work that week?
A.60
B.68
C.65
D.64
Answer: D.64
Explanation: For 40 hrs = 40*12=480
Excess = 976-480=496
For extra hours =.75(12)=9+12=21
Number of extra hrs =496/21=23.62
Total hrs =40+23.62=63.62=64 approx.
Answer D 64
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes?
A.58
B.60 ways
C.64 ways
D.68
Answer: C.64 ways
Explanation: Ans.(C)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways
Question: The H.C.F. and L.C.M. of two numbers are 14 and 5040 respectively If one of the numbers is 144, find the other number
A.400
B.256
C.120
D.490
Answer: D.490
Explanation: Explanation:
Solve this question by using below formula.
Product of 2 numbers = product of their HCF and LCM
144 * x = 14 * 5040
x = (14*5040)/144 = 490
Option D
Question: Donovan took a math test and got 35 correct and 15 incorrect answers.
What was the percentage of correct answers? (Round to the nearest
hundredth)
A.57.78%
B.67.78%
C.70.00%
D.47.78%
Answer: C.70.00%
Explanation: 35 correct our of 50 total (35+15)
35/50
correct answer C
Question: 30 pens and 75 pencils were purchased for 690. If the average price of a pencil was 2.00, find the average price of a pen.
A.10
B.11
C.18
D.13
Answer: C.18
Explanation: Since average price of a pencil = 2
∴ Price of 75 pencils = 150
∴ Price of 30 pens = (690 – 150) = 540
∴ Average price of a pen = 540⁄60 = 18
Answer C
Question: What is the normal price of an article sold at $144 after two successive discounts of 10% and 20%?
A.$184
B.$192
C.$200
D.$208
Answer: C.$200
Explanation: 0.8*0.9*cost price = $144
cost price = $200
The answer is C.
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
A.246 m
B.240 m
C.257 m
D.577 m
Answer: B.240 m
Explanation: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train
= (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36
= 15 ==> x + 300 = 540
==> x = 240 m.
Answer: B
Question: Hannah has 5 apples and 7 bananas. If she wants to give each of her 9 friends 1 banana and 2 apples, how many more apples and bananas does she need?
A.2 bananas, 13 apples
B.5 bananas, 13 apples
C.8 bananas, 8 apples
D.13 bananas, 5 apples
Answer: A.2 bananas, 13 apples
Explanation: 9 friends = 9 bananas. 9 - 7 = 2 bananas needed. 9 friends = 18 apples (2 per friend). 18 - 5 = 13 apples needed. Hence, answer : A
Question: What quantity of water should be added to reduce 5 litres of 45% acidic liquid to 25% acidic liquid?
A.3litres
B.2litres
C.4litres
D.4.5litres
Answer: D.4.5litres
Explanation: Quantity of acid in 5litres =45*5/100 = 2.25litres
Let X litres of water is added to the solution, then there is 2.25litres of acid in (5+ X ) Litres of liquid.
25% of ( 5 + X ) = 2.25, 25/100* ( 5 + X ) = 2.25
X = 225-125/25 = 4
ANSWER:D
Question: 45 men working 8 hours per day dig 40 m deep. How many extra men should be put to dig to a depth of 50 m working 6 hours per day?
A.10
B.20
C.30
D.40
Answer: C.30
Explanation: (45 * 8)/40 = (x * 6)/50 => x =75
75 – 45 =30
ANSWER:C
Question: If a(a + 7) = 18 and b(b + 7) = 18, where a ≠ b, then a + b =
A. −48
B. −2
C. −7
D. 46
Answer: C. −7
Explanation: a(a + 7) = 18
=> we have a = 2 or -9
also b(b + 7) = 18
=> b = 2 or -9
given a ≠ b
1) when a =2, b= -9 and a + b = -7
1) when a = -9, b= 2 and a + b = -7
Answer choice C
Question: A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be:
A.22
B.24
C.26
D.28
Answer: C.26
Explanation: Let the number of hens be x and the number of cows be y.
Then, x + y = 48 .... (i)
and 2x + 4y = 140
x + 2y = 70 .... (ii)
Solving (i) and (ii) we get: x = 26, y = 22.
The required answer = 26.
Answer is C.
Question: In the xy-coordinate system, if (m, n) and (m + 2, n + k) are two points on the line with the equation x = 2y + 5, then k =
A.1/2
B.1
C.2
D.5/2
Answer: B.1
Explanation: The equation of the line can be re written as y = (1/2)x - 5/2.
Slope = 1/2, which means for every 1 unit increase in the y co-ordinate, x will increase by 2 units.
Hence k = 1.
ANSWER:B
Question: In a group of students, 65 play foot ball, 45 play hockey, 42 play cricket, 20 play foot ball and hockey, 25 play foot ball and cricket, 15 play hockey and cricket and 8 play all the three games. Find the number of students in the group.
A.100
B.65
C.75
D.86
Answer: A.100
Explanation: Let ,F Hand C represent the set of students who play foot ball, hockey and cricket respectively.
F= 65, H=45, C=42
F and H= 20
F and C=25
H and C=15
F, H and C=8
All= 65+45+42-20-25-15+8=100
ANSWER A
Question: Mr. Tom invested in Fund X and Fund Y. The total amount she invested, in both funds combined, was $100,000. In one year, Fund X paid 23% and Fund Y paid 17%. The interest earned in Fund Y was exactly $200 greater than the interest earned in Fund X. How much did Ms. Tom invest in Fund X?
A. $32,000
B. $36,000
C. $42,000
D. $44,000
Answer: C. $42,000
Explanation: X+Y=100,000
0.17Y=0.23A+200
Take away decimals first: 17Y=23X+20,000
Isolate first equation to solve for X (your goal): Y=100,000-Y
Plug in for B:
17(100,000-X)=23X+20,000
1,700,000-17X=23X+20,000
1,680,000=40X
1,680,000/40=X
X=42,000=Answer Choice C
Question: A 90 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
A.220 meter
B.225 meter
C.230 meter
D.410 meter
Answer: D.410 meter
Explanation: Explanation:
As trains are running in opposite directions so their relative speed will get added
So, Relative speed = 120 +80 = 200 kmph
= 200*(5/18) = 500/9 m/sec
Let the length of other train is x meter then
x+90 /9=500 /9
=>x+90=500
=>x=410
So the length of the train is 410 meters
Option D
Question: In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 46, the dividend is
A.5336
B.4306
C.4236
D.4336
Answer: A.5336
Explanation: Sol.
Divisor = ( 5 × 46 ) = 230.
Also, 10 × Q = 230
⇒ Q = 23. And, R = 46.
Dividend = (230 × 23 + 46 )
= 5336.
Answer A
Question: Thirty percent of Country Y's yearly exports come from fruit exports. One-sixth of all fruit exports from Country Y are orange exports. If country Y generates $50 million from its orange exports, how much money does it generate from its yearly total of exports?
A.$1000m
B.$25.5m
C.$106.25m
D.$127.5m
Answer: A.$1000m
Explanation: 30/100*1/6*(total) = 50
1/20*(total) = 50
(total) = 50*20 = 1000
Answer: A
Question: What must be added to each term of the ratio 2 : 3, so that it may become equal to 4 : 5?
A.2
B.4
C.6
D.9
Answer: A.2
Explanation: Let the number to be added be x, then (2 + x) : (3 + x) = 4 : 5
⇒ (2 + x)/(5 + x) = 4/5
5(2 + x) = 4(3 + x)
10 + 5x = 12 + 4x
5x - 4x = 12 - 10
x = 2
Answer:2
Question: A car after covering ½ of a journey of 100 km develops engine trouble and later travels at ½ of its original speed. As a result, it arrives 2 hours late than its normal time. What is the normal speed of the car is?
A.12
B.77
C.15
D.25
Answer: D.25
Explanation: [50/x + 50/(x/2)] – 100/x
= 2
x = 25
Answer: D
Question: The mean proportional between 4 and 9 is?
A.21
B.35
C.44
D.12
Answer: B.35
Explanation: 7/20 * 100
= 35
Answer: B
Question: Three partners A,B and C invest Rs.18000, Rs.22500 and Rs.27000 respectively in a business. If total profit is Rs.18750 then C's share is (in Rs.)
A.10000
B.6500
C.5000
D.7500
Answer: D.7500
Explanation: 18000:22500:27000
4:5:6
c share=18750*6/15=7500
ANSWER:D
Question: A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
A.6
B.8
C.7
D.4
Answer: B.8
Explanation: 30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2 = 8
Answer: B
Question: The product of a and b is equal to 12 more than twice the sum of a and b. If b = 10, what is the value of b - a?
A.2
B.5
C.7
D.6
Answer: D.6
Explanation: ab= 12 + 2(a+b)
10a= 12+2a +20
8a= 32
a=4
b-a= 10-4=6
D is the answer
Question: If x^2=x+3, then x^3=?
A.3x+2
B.3x-2
C.4x+3
D.2x-3
Answer: C.4x+3
Explanation: Given X^2 = X+3
X^3 = X*X^2 = x*(X+3)-- Substituted from above.
= X^2 + 3X = X+3+3X = 4X+3.
Hence C.
Question: A certain galaxy is known to comprise approximately 3 x 10^11 stars. Of every 50 million of these stars, one is larger in mass than our sun. Approximately how many stars in this galaxy are larger than the sun?
A.800
B.6,000
C.8,000
D.12,000
Answer: B.6,000
Explanation: Total no. of stars on galaxy = 3 * 10^11
Of every 50 million stars, 1 is larger than sun.
1 million = 10^6 therofore, 50 million = 50 * 10^6
total no. of stars larger than sun = 3 * 10^11 / 50 * 10^6
=30 * 10^3 /5
= 6000
therefore answer is B
Question: Four persons enter the lift of a nine storey building at the ground floor. In how many ways can they get out of lift on any floor other than ground floor
A.720
B.1296
C.1540
D.4096
Answer: D.4096
Explanation: Each person out of 4 has 8 floors (options) to get out of (since no one gets out on the ground floor), hence total ways is 8*8*8*8=8^4=4096.
Answer: D.
Question: In a games hour 4 different types of players came to the ground? cricket 11, hockey 15, football 21, softball 15. In these 4 people play both cricket and hockey, 3people play both softball and football. 6 people play both cricket and football. How many people play only cricket?
A.11
B.1
C.5
D.3
Answer: B.1
Explanation: people play only cricket = total players in cricket- both cricket and football- both cricket and hockey.
people play only cricket = 11-4-6 = 1
Answer is B
Question: If x is 11 percent greater than 90, then x =
A.99.9
B.91.0
C.88.0
D.70.9
Answer: A.99.9
Explanation: 11% of 90 = (90*0.11) = 9.9
11% greater than 90 = 90 + 9.9 = 99.9
Answer is clearly A.
Question: In what time will a train 130 m long cross an electric pole, it its speed be 144 km/hr?
A.2.5 sec
B.3.25 sec
C.5 sec
D.12.5 sec
Answer: B.3.25 sec
Explanation: Speed = 144 * 5/18 = 40 m/sec
Time taken = 130/40 = 3.25 sec.
ANSWER:B
Question: Dawson earns $100 a week from his job. His income increased and now makes $110 a week. What is the percent increase?
A.5%
B.10%
C.15%
D.20%
Answer: B.10%
Explanation: Increase = (10/100)*100 = (1/10)*100 = 10%.
B
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
A.48%
B.70%
C.40%
D.45%
Answer: C.40%
Explanation: The total CP = Rs. 16000 + Rs. 6250
= Rs. 22250 and SP
= Rs. 31150
Profit(%)
= (31150 - 22250)/22250 * 100
= 40%
Answer: C
Question: A, B, K start from the same place and travel in the same direction at speeds of 30 km/hr, 40 km/hr, 80 km/hr respectively. B starts two hours after A. If B and K overtake A at the same instant, how many hours after A did K start?
A.2
B.3
C.4
D.5
Answer: D.5
Explanation: In 2 hours, A travels 60 km.
B can catch A at a rate of 10 km/hr, so B catches A 6 hours after B starts.
So A and B both travel a distance of 240 km.
C needs 3 hours to travel 240 km, so C leaves 5 hours after A.
The answer is D.
Question: The speed of a car is 90 km in the first hour and 75 km in the second hour. What is the average speed of the car?
A.89 kmph
B.82.5 kmph
C.75 kmph
D.65 kmph
Answer: B.82.5 kmph
Explanation: S = (90 + 75)/2 = 82.5 kmph
B
Question: A train 330 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
A.5
B.6
C.7
D.18
Answer: D.18
Explanation: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 330 * 3/55 = 18 sec.
Answer: Option D
Question: Three shops that belonged to a chain were closed, and as a result the average (arithmetic mean) annual revenue per shop in the chain grew from $150,000 to $225,000. If the number of shops in the chain before the change was 8, approximately, what was the average annual revenue of the shops that were closed?
A.$25,000
B.$37,500
C.$58,333
D.$75,000
Answer: A.$25,000
Explanation: if the average annual revenue of the 5 shops which are still open is 225,000, it means that they make a total of 225,000∗5=1,125,000 $
let's call the average annual revenue of the 3 shops that have been closed x.
therefore, they make a total of 3∗x $
We know that the total revenue of the 8 shops that were open has to be 150,000
Thus (3x+1,125,000)/8=150,000
therefore x=25,000 answer A
Question: If Thursday was the day after the day before yesterday five days ago, What is the least number of days ago when Sunday was three days before the day after tomorrow?
A.Two
B.Three
C.Four
D.Five
Answer: A.Two
Explanation: Explanation :
Day after the day before yesterday is yesterday.
Now, five days ago, yesterday was Thursday.
So, five days ago, it was Friday.
Therefore today is Wednesday.
Now, three days before the day after tomorrow is yesterday.
Now, it is on Monday that we say Yesterday was Sunday.
Answer : A
Question: If n has 15 positive divisors, inclusive of 1 and n, then which of the following could be the number of divisors of 3n?
I. 20
II. 30
III. 40
A.II only
B.I and II only
C.I and III only
D.II and III only
Answer: B.I and II only
Explanation: n has 15 positive divisors --> n=p^14 (the # of factors (14+1)=15) or n=p^2q^4 (the # of factors (2+1)(4+1)=15).
If neither p nor q is 3, then:
3n=3p^14 will have (1+1)(14+1)=30 factors.
3n=3p^2q^4 will have (1+1)(2+1)(4+1)=30 factors.
If p = 3, then:
3n=3p^14 =3^15 will have (15+1)=16 factors.
3n=3p^2q^4 = 3^3 p^4 will have (3+1)(4+1)=20 factors.
If q = 3, then:
3n=3p^2 =q^4 will have(2+1) (5+1)=18 factors.
Answer: B.
Question: At an election 2 candidates are participated a candidate got 45% of votes and defeated by 9000 votes. 83 votes are invalid. Find the total polled votes?
A.100000
B.85236
C.89562
D.90083
Answer: D.90083
Explanation: winners votes = 100-45 = 55%
invalid votes = 83
polled votes = [(100*9000)/(2*55-100)]+83 = 90083
Answer is D
Question: John bought a 1-year, $30,000 certificate of deposit that paid interest at an annual rate of 10 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?
A.$3175
B.$3275
C.$3075
D.$3375
Answer: C.$3075
Explanation: 10 percent compounded semiannually --> 5% in 6 moths.
For the first 6 moths interest was 5% of $30,000, so $1500;
For the next 6 moths interest was 5% of $31,500, so $1575
Total interest for 1 year was $1500+$1575=$3075
Answer : C