RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: what is the least number by which 16,800 must be divided to get a number perfect square
A.21
B.42
C.24
D.40
Answer: B.42
Explanation: 16,800/42=400
400=(20)^2
Ans-42
ANSWER:B
Question: What is the value of (44444445*88888885*44444442+44444438/44444444^2)
A.88888883
B.88888884
C.88888885
D.88888886
Answer: A.88888883
Explanation: let x=44444444,then
44444445=x+1
88888885=2x-3
44444442=x-2
44444438=x-6
44444444^2=x^2
then substitute it in equation
(x+1)(2x-3)(x-2)+(x-6)/x^2
ans is 2x-5 i.e 88888883
ANSWER:A
Question: The concentration of spirit in three different vessels A, B and C are 45%, 30% and 25% respectively. If 4 litres from vessel A, 5 litres from vessel B and 6 litres from vessel C are mixed, find the concentration of spirit in the resultant solution.
A.32%
B.33%
C.34%
D.35%
Answer: A.32%
Explanation: Quantity of spirit in new solution=(4*45/100)+(5*30/100)+(6*25/100)=1.8+1.5+1.5=4.8 liters
So % concentration of spirit=100*4.8/(4+5+6)=32%
ANSWER:A
Question: If the average (arithmetic mean) of (2a+16) and (3a-8) is 89, what is the value of a?
A.25
B.30
C.28
D.34
Answer: D.34
Explanation: ((2a+16) + (3a-8)) / 2 = (5a+8)/2 = 89
a= 34
The answer is D.
Question: A regular nine side is inscribed in a circle. If A and B are adjacent vertices of the pentagon and O is the center of the circle, what is the value of ∠OAB ?
A.48 degrees
B.54 degrees
C.72 degrees
D.70 degrees
Answer: D.70 degrees
Explanation: its a regular nine side so divide the globe by 9.
= 360/9
= 40
40 would be the angle at O.
Angles at A and B are equivalent, so
40 + 2x = 180
2x = 140
x = 70
Angles OAB and OBA will be 70 degrees each.
D
Question: Find the greatest number which leaves the same remainder when it divides 25, 50 and 120.
A.18
B.5
C.12
D.16
Answer: B.5
Explanation: 120 - 50 = 70
50 - 25 = 25
120 - 25 = 95
The H.C.F of 25, 70 and 95 is 5.
ANSWER:B
Question: Ayesha's father was 28 years of age when she was born while her mother was 20 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
A.2 years
B.4 years
C.12 years
D.8 years
Answer: C.12 years
Explanation: Explanation:
Mother's age when Ayesha's brother was born = 20 years.
Father's age when Ayesha's brother was born = (28 + 4) years = 32 years.
Required difference = (32 - 20) years = 12 years.
Answer: C
Question: A can do a piece of work in 10 days and B alone can do it in 15 days. How much time will both take to finish the work ?
A.2 days
B.7 days
C.6 days
D.9 days
Answer: C.6 days
Explanation: C
6 days
Time taken to finish the job = XY / (X + Y)
= 10 x 15 / (10 + 15)
= 150 / 25
= 6 days
Question: What is the mass of the man, if a boat of length 4m, width 1.5m floating on a river sinks by 0.015 m when the man gets on the boat?
A.100kg
B.90kg
C.80kg
D.70kg
Answer: B.90kg
Explanation: SOLUTION :
Volume of water displaced = 4*1.5*0.015 = 0.09m3
Mass = volume of water displaced * density of water
Mass = 0.09 * 1000
Mass = 90kg
ANSWER IS B
Question: Which of the following is equal to 1(1/4)%?
A.0.012/100
B.0.12/100
C.1.25/100
D.12/100
Answer: C.1.25/100
Explanation: This notation may be confusing for some, since it looks like we're multiplying 1 and 1/4
How about adding a space:Which of the following is equal to (1 1/4)%
(1 1/4)% = 1.25% = 1.25/100
Answer:
C
Question: The H.C.F. of two numbers is 12 and their difference is 12. The numbers are :
A.66, 78
B.70, 82
C.94, 106
D.84, 96
Answer: D.84, 96
Explanation: Explanation:
Out of the given numbers, the two with H.C.F. 12 and difference 12 are 84 and 96.
ANSWER IS D
Question: A group of 3 CEOs and 2 employees recently frequented the Bohemian Ala Restaurant. The total bill for the meal, including 20% gratuity, came to $600. On average, how much did the meal of each individual cost before gratuity?
A.$160
B.$96
C.$90
D.$10
Answer: D.$10
Explanation: 3 CEOs and 2 employees - so total 5 people
The bill $600 includes 20% gratuity... so the actual cost of dinner was $500
Now, the cost per person will be $500/5 which is $10
Option D
Question: 4 dice are thrown simultaneously on the board. Find the probability show the same face.
A.1/115
B.2/113
C.1/216
D.3/114
Answer: C.1/216
Explanation: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let XX be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability,
=n(X)n(S)=664=n(X)n(S)=664
=1/216
C
Question: P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 50 days to complete the same work. then Q alone can do it in
A.30 days
B.25 days
C.20 days
D.15 days
Answer: B.25 days
Explanation: Work done by P and Q in 1 day = 1/10
Work done by R in 1 day = 1/50
Work done by P, Q and R in 1 day = 1/10 + 1/50 = 6/50
But Work done by P in 1 day = Work done by Q and R in 1 day . Hence the above equation can be written as
Work done by P in 1 day × 2 = 6/50
=> Work done by P in 1 day = 3/50
=> Work done by Q and R in 1 day = 3/50
Hence work done by Q in 1 day = 3/50 – 1/50 = 2/50 = 1/25
So Q alone can do the work in 25 days
Option B
Question: Sahil purchased a machine at Rs 10000, then got it repaired at Rs 5000, then gave its transportaƟon
charges Rs 1000. Then he sold it with 50% of profit. At what price he actually sold it
A.Rs. 22000
B.Rs. 24000
C.Rs. 26000
D.Rs. 28000
Answer: B.Rs. 24000
Explanation: Explanation:
Question seems a bit tricky, but it is very simple.
Just calculate all Cost price, then get 150% of CP.
C.P. = 10000 + 5000 + 1000 = 16000
150% of 16000 = 150/100 * 16000 = 24000
Answer: B
Question: In a kilometer race, A beats B by 48 meters or 12 seconds. What time does A take to complete the race?
A.238 sec
B.190 sec
C.667 sec
D.167 sec
Answer: A.238 sec
Explanation: Time taken by B run 1000 meters = (1000 * 12)/48 = 250 sec.
Time taken by A = 250 - 12 = 238 sec.Answer: A
Question: In how many ways Principal and a vice Principle can be elected from a team of 20 members?
A.480
B.380 ways
C.830
D.840
Answer: B.380 ways
Explanation: To do this, if captain is elected first, then we have 20 ways of doing this.
For election of vice-captain, we have only 19 ways left, Bcoz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 20*19 = 380ways.
Ans : B
Question: Set A of 8 positive integers may have the same element and have 36. And set B of 8 positive integers must have different elements and have 36. When m and n are the greatest possible differences between 36 and other elements’ sums in set A and set B, respectively, m-n=?
A.20
B.21
C.23
D.25
Answer: B.21
Explanation: This is maximum-minimum. Hence, 36-(1+1+1+1+1+1+1)=29 and 36-(1+2+3+4+5+6+7)=8. So, 29-8=21. The correct answer is B.
Question: John spent a total of $135 on baseball tickets. The price of a ticket is either $12 for the field seats or $5 for the balcony. What is the minimum amount Z of dollars he could have spent for the $12 tickets?
A.$48
B.$60
C.$84
D.$96
Answer: B.$60
Explanation: 60 ..... 12 *5 Z= 60. (min). Thus answer .B
Question: Find the largest 4 digit number which isexactly divisible by 88?
A.8560
B.8950
C.9944
D.10000
Answer: C.9944
Explanation: Largest 4 digit number is 9999
After doing 9999 ÷ 88 we get remainder 55
Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944
C
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green?
A.23/35
B.23/37
C.23/39
D.23/32
Answer: A.23/35
Explanation: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green
= (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7
= 46/70 = 23/35
Answer: A
Question: By selling a watch for Rs. 720/- a man loses 20% at what price should he sell it to gain 10%?
A.Rs.810/-
B.Rs.880/-
C.Rs.900/-
D.Rs.990/-
Answer: D.Rs.990/-
Explanation: Explanation:
80 % ------> 720 (80 * 9 = 720)
110 % ------> 880 (110 * 9 = 990)
= Rs.990/-
Answer: Option D
Question: 7, 10, 8, 11, 9, 12, ?
A.13
B.12
C.10
D.9
Answer: C.10
Explanation: This is a simple alternating addition and subtraction series. In the first pattern, 3 is added; in the second, 2 is subtracted.
Answer : C.
Question: An unbiased die is tossed.Find the probability of getting a multiple of 3.
A.1
B.4/3
C.1/3
D.2/3
Answer: C.1/3
Explanation: S = {1,2,3,4,5,6}
Let E be the event of getting the multiple of 3
Then, E = {3,6}
P(E) = n(E)/n(S) = 2/6 = 1/3
ANSWER:C
Question: To furnish a room in a model home an interior decorator is to select 2 chairs and 2 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables w are there in the warehouse?
A.6
B.8
C.10
D.15
Answer: A.6
Explanation: Total number of ways to choose 2 chairs from 5 w= 5C2=10
Total number of combination=150
That means we need get 15 combinations from the selection of tables....
Screening through the answers.... 6C2=15..... 15*10=150
Answer is 6... A
Question: The present worth of Rs.845 due in 2 years at 4% per annum compound interest is
A.Rs.150.50
B.Rs.154.75
C.Rs.781.25
D.Rs.158
Answer: C.Rs.781.25
Explanation: Solution
Present Worth	= Rs.[845/(1+4/100)²]
= Rs.(845x25/26x25/26)
= Rs.781.25
Answer C
Question: The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
A.0
B.1
C.10
D.19
Answer: D.19
Explanation: Average of 20 numbers = 0.
Sum of 20 numbers (0 x 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a).
Answer : D
Question: Two musicians, Maria and Perry, work at independent constant rates to tune a warehouse full of instruments. If both musicians start at the same time and work at their normal rates, they will complete the job in 45 minutes. However, if Perry were to work at thrice Maria’s rate, they would take only 20 minutes. How long would it take Perry, working alone at his normal rate, to tune the warehouse full of instruments?
A.1 hr 20 min
B.1 hr 7 min
C.2 hr
D.2 hr 20 min
Answer: B.1 hr 7 min
Explanation: Sol:
Lets Perry Rate be P and Rate of Maria be M
(rate)*(time)= Work or rate = work/time
first equation=> P+M = 1/45
converting it to hrs P+M= 1/(45/60) => 1/(3/4) =>4/3
second equation => M+3M =>1/20
converting it to hrs 4M=1/(20/60) =>1/(1/3) =>3
therefore M= 3/4 and P=7/12
Rate of Perry = 7/12
time= work/rate (work = 1 job)
Time= 1 hrs 7 mins
Answer : B
Question: A fair gold coin with sides marked heads and tails is to be tossed eight times. What is the probability that the coin will land tails side up more than five times?
A.A)37/256
B.B)56/256
C.C)65/256
D.D)70/256
Answer: A.A)37/256
Explanation: Landing on tails more than 5 times means tails has to hit 6, 7 or 8 times.
8!/6!2! = 7*4 = 28
8!/7!1! = 8
8!/8! = 1
28 + 8 + 1 = 37/256
ans:A
Question: Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one green marble. Suppose we are going to put them into three cups: a black cup, a white cup, and a purple cup. We could put all six in any cup and leave two cups empty; or we could put marbles in two cups and leave one cup empty; or we could put some marbles in each of the three cups. How many combinations are possible?
A.90
B.180
C.360
D.540
Answer: B.180
Explanation: # ways to distribute Blue marbles(3) is :
1 in each cup= 1
2 in one cup and 1 in other=6
all 3 in one cup = 3
total 1+6+3=10 possibilities
# ways to distribute Red marbles(2) is :
1 in each cup = 3 ways
all in one cup = 3ways
total 6ways.
# ways to distribute Green marbles(1) is :
3 ways
total number of ways = 10*6 *3 = 180 ANS:B
Question: A train running at the speed of 52 km/hr crosses a pole in 18 seconds. What is the length of the train?
A.120 metres
B.180 metres
C.260 metres
D.150 metres
Answer: C.260 metres
Explanation: Speed=52 x5/18m/sec=130/9	m/sec.
Length of the train = (Speed x Time).
Length of the train =	130/9 x 18m = 260 m.
ANSWER:C
Question: When a train travels at a speed of 60kmph,it reaches the destination on time.when the same train travels at a speed of 50kmph,it reaches its destination 15min late.what is the length of journey?
A.75km
B.50km
C.60km
D.85km
Answer: A.75km
Explanation: Let x be the time reached with the speed 60km/h
50km/h ----> x+15
Distance is equal so
60(km/h)× xhr = 50(km/h) × (x+15) hr
So
60 x = 50x + 750
So the would be in km
And x = 75
So
75km
ANSWER:A
Question: A jogger running at 9 kmph along side a railway track is 250 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?
A.3.6 sec
B.37 sec
C.36 sec
D.72 sec
Answer: B.37 sec
Explanation: Speed of train relative to jogger
= (45 – 9) km/h = 36 km/h
= (36 × 5⁄18) m/sec = 10 m/sec
Distance to be covered = (250 + 120) m = 370 m.
∴ Time taken = (370⁄10) sec = 37 sec.
Answer B
Question: What is the next number of the following sequence
7776,625,64,9,2
A.1
B.2
C.3
D.4
Answer: A.1
Explanation: 7776,625,64,9,2, x
7796 --> 6^5
625 --> 5^4
64 --> 4^3
9 --> 3^2
2 --> 2^1
x --> 1^0 ==> 1
ANSWER:A
Question: One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 35 minutes, then the slower pipe alone will be able to fill the tank in
A.144 mins
B.140 mins
C.136 mins
D.132 minw
Answer: B.140 mins
Explanation: Explanation:
Let the slower pipe alone fill the tank in x minutes
then faster will fill in x/3 minutes.
Part filled by slower pipe in 1 minute = 1/x
Part filled by faster pipe in 1 minute = 3/x
Part filled by both in 1 minute =
1/x+3/x=1/35
=>4/x=1/35
x=35∗4=140 mins
Option B
Question: In a division sum,the divisor is 10 times the quotient and 5 times the remainder.If the remainder is 46,what is the dividend ?
A.5336
B.5242
C.6524
D.3526
Answer: A.5336
Explanation: Divisor=(5*46)=230
10*quotient =230
quotient =230/10=23.
dividend =(divisor*quotient)+remainder
=(230*23)+46=(5290+46)=5336.
Answer is A
Question: If in a cricket one day match, there were no wide balls, no wides, no extras and no overthrows.
What is the maximum number of runs that a batsman can score in 30 overs in an ideal case scenario?
A.1020
B.993
C.985
D.996
Answer: B.993
Explanation: Solution:
993
Explanation:
For an ideal case, the batsman will hit a six on each ball. But if he hits six on the last ball of the over, the strike will change in the next over. Thus, the best he can do in the last ball is run 3 runs so that he retains the strike even in the next over. Thus the total runs that he can score in each over:
6 * 5 + 3 = 33
But this will have to go like it only till the 29th over. In the 30th over, he can hit a six in the last ball as well as that will be the last ball of his destination.
Thus runs for the 30th over will be 6 * 6 = 36.
Hence the maximum runs = 33 * 29 + 36 = 993
Answer B
Question: 3.5 can be expressed in terms of percentage as?
A.0.35%
B.3.5%
C.35%
D.350%
Answer: D.350%
Explanation: Answer: Option D
3.5 = 35/10 = (35/10 * 100) = 350%
Question: In what time a debt of Rs.7920 due may be cleared by immediate cash down
payment of Rs.3600 at 1/2% per month
A.10years
B.20years
C.30years
D.40years
Answer: B.20years
Explanation: Explanation:
PW=100x Amount/100+(RxT)
Answer: B
Question: Three grades of milk are 1 percent, 5 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 5 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 7 percent grade, what is x in terms of y and z?
A.-1y - 2z
B.(y +z) / 4
C.2y + 3z
D.3y + z
Answer: A.-1y - 2z
Explanation: Based on the given information, the following equation could be dervied: 1% * x + 5% * y + 3% * z = 7% * (x+y+z)
Then use algebra to figure out 6%*x = -2%*y - 4%*z. Thus, 3x = -1y - 2z.
A
Question: A tank is filled by 3 pipes A,B,C in 6 hours. Pipe C is twice as fast as B and B is twice as fast as A. How much will pipe A alone take to fill the tank ?
A.25hr
B.42hr
C.40hr
D.20hr
Answer: B.42hr
Explanation: Suppose pipe A alone take x hours to fill the tank
Then pipe B and C will take x/2 and x/4 hours respectively to fill the tank.
1/x + 2/x + 4/x = 1/6
7/x = 1/6
x = 42 hours
Answer is B
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 20 seconds. Find the length of the faster train?
A.270
B.277
C.200
D.257
Answer: C.200
Explanation: Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.
Distance covered in 27 sec = 20 * 10 = 200 m.
The length of the faster train = 200 m.
Answer: C
Question: If you roll one fair six-sided die, what is the probability that the number is even or less than 5?
A.3/4
B.5/6
C.1/2
D.2/3
Answer: B.5/6
Explanation: The numbers which satisfy the conditions are 1, 2, 3, 4, and 6.
The probability is 5/6
The answer is B.
Question: A person was asked to subtract 25% of a number from the original but he subtracted 25 from the number. His answer was 25 more than correct one. What was the original number?
A.160
B.170
C.180
D.200
Answer: D.200
Explanation: 25 + 25 = 50
25% ------ 50
100% ----- ? => 200
ANSWER:D
Question: The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 78 kg and 93 kg join the group. Find the initial number of members in the group?
A.26
B.28
C.23
D.28
Answer: C.23
Explanation: Let the initial number of members in the group be n.
Initial total weight of all the members in the group = n(48)
From the data,
48n + 78 + 93 = 51(n + 2) => 51n - 48n = 69 => n = 23
Therefore there were 23 members in the group initially.Answer: C
Question: Present ages of Sameer and Anand are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Anand's present age in years?
A.24 years
B.28 years
C.27 years
D.16 years
Answer: A.24 years
Explanation: Let the present ages of Sameer and Anand be 5x and 4x years respectively.
Then, (5x + 3)/(4x + 3) = 11/9
9(5x + 3) = 11(4x + 3) => x = 6
Anand's present age = 4x = 24 years.
Answer:A
Question: The ratio of the earnings of P and Q is 9 : 10. If the earnings of P increases by one-fourth and the earnings of Q decreases by one-fourth, then find the new ratio of their earnings?
A.3/6
B.3/2
C.3/9
D.3/1
Answer: B.3/2
Explanation: Let the earnings of P and Q be Rs. 9x and Rs. 10x respectively.
New ration = [9x + 1/4(9x)]/[10x - 1/4(10x)]
=> [9x(1 + 1/4)]/[10x(1 - 1/4)] = 9/10 * (5/4)/(3/4)
=> 3/2.
Answer: B
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 210 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
A.88
B.45
C.36
D.80
Answer: B.45
Explanation: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 210 = 450 m.
Time taken = 450/10 = 45 sec.
Answer: B
Question: Given that 100.48 = x, 100.70 = y and xz = y², then the value of z is close to
A.1.2
B.1.45
C.2.2
D.2.9
Answer: D.2.9
Explanation: Sol.
xz = y² ⇔ (10 0.48 )z(100.70)2 (10 0.48z) = 10(2×0.70) = 101.40
⇔ 0.48z = 1.40 ⇔ z= 140/48 = 35/12 = 2.9 (approx).
Answer D
Question: The probability that A speaks truth is 1/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
A.13/35
B.18/38
C.18/36
D.18/16
Answer: A.13/35
Explanation: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability
= 1/5 * 4/7 + 4/5 * 3/7
= 1/35 + 12/35
= 13/35
Answer: A
Question: A farm used two harvesting machines, H and K, to harvest 100 acres of wheat. Harvesting machine H, working alone at its constant rate, harvested 50 acres of wheat in 8 hours. Then harvesting machine K was brought in, and harvesting machines H and K, working together at their respective constant rates, harvested the remaining acres of wheat in 5 hours. Harvesting machine K harvested how many acres of wheat per hour?
A. 7
B. 5
C. 12
D. 13
Answer: B. 5
Explanation: Rate of H = 5 acres/hr
Remaining land to be harvested = 100 - 50 = 50
Rate of H and K = 50/5 = 10 acres/hr
Rate of K = 10 - 5 =5
Answer: B
Question: The average of ten numbers is 8. If each number is multiplied by 8, then what is the average of the new set of numbers?
A.8
B.16
C.64
D.80
Answer: C.64
Explanation: The sum of the ten numbers is 8*10 = 80
If each number is multiplied by 8, the new sum is 8*(80).
The average is then 8*8 = 64
The answer is C.
Question: If x is to be chosen at random from the set {1,2,3,4} and y is to be chosen at random from the set {7,8,9}, what`s the probability that xy will be even?
A.2/3
B.1/3
C.1/2
D.1/6
Answer: A.2/3
Explanation: The product to be even either one or both must be even, so:
P(x=even OR y=even)=P(x=even)+P(y=even)-P(x=even AND y=even)=2/4+1/3-2/4*1/3=2/3;
Or: P(xy=even)=1-P(xy=odd)=1-2/4*2/3=2/3, so basically we find the probability of the product to be odd (which happens when both x and y are odd) and subtract it from 1.
Answer: A.
Question: Find the solution set of the equation x2+x+2=0 in roster form
A.{1,-2}
B.{ }
C.{1,1}
D.{1}
Answer: A.{1,-2}
Explanation: (x+2)(x-1)=0
x=-2 or 1
ANSWER:A
Question: If an integer n is to be selected at random from 1 to 99, inclusive, what is probability n(n+1) will be divisible by 3?
A.1/4
B.1/3
C.1/2
D.2/3
Answer: D.2/3
Explanation: For n(n+1) to be a multiple of 3, either n or n+1 has to be a multiple of 3.
Thus n must be of the form 3k or 3k-1, but not 3k+1.
The probability is 2/3.
The answer is D.
Question: Find the compound interest on $ 56,000 at 20% per annum for 9 months, compounded quarterly
A.2532
B.2552
C.6524
D.8827
Answer: D.8827
Explanation: Principal = $ 56000; Time = 9 months =3 quarters;
Rate = 20% per annum = 5% per quarter.
Amount = $ [56000 x (1+(5/100))^3] = $ 64827.
CI. = $ (64827 - 56000) = $ 8827.
Answer D.
Question: A train overtakes two girls who are walking in the opposite direction in which the train is going at the rate of 3 km/h and 6km/h and passes them completely in 36 seconds and 30 seconds respectively. The length of the train is:
A.120m
B.150m
C.125m
D.None of these
Answer: B.150m
Explanation: Explanation:
Let the length of the train e x meter, and let the speed of train be y km/h, then
x = (y + 3)5/18 × 36 .........(1)
and x = (y + 6)5/18 × 30 .....(2)
From eq (1) and (2), we get
(y + 3) × 36 = (y + 6) × 30
y = 12 km/h
x = (y + 3) × 5/18 × 36
x = 150 m
Answer: B
Question: A set of data consists of the following 8 numbers: 0, 2, 4, 6, and 8. Which two numbers, if added to create a set of 7 numbers, will result in a new standard deviation that is close to the standard deviation for the original 5 numbers?
A.-1 and 9
B.4 and 4
C.3 and 5
D.2 and 6
Answer: B.4 and 4
Explanation: If you are in for some calculations , this is how I got to it
mean = 4
sd = \sqrt{8} = 2.8
Expected values for the SD to not change are - One value below SD from mean is (4 - 2.8) = 1.2 , and one value above SD is (4 + 2.8) = 6.8
This would mean , adding 1.2 ans 6.8 would have no impact on the SD . SD remains the same when these two numbers are added. Now for SD to change the least , we need to add two values that are closest to these two values.
Hence any two values that are closest to 1.2 and 6.8 would change the SD , the least.
1. -1 , 9
distance between (1,9) and (1.2 and 6.8) is 2.2 and 2.2
2. 4 , 4
distance etween (4,4) and (1.2 , 6.8) is 2.8 and 2.8
3. 3 , 5
Distance is - 1.8 and 1.8
4. 2 , 6
Distance is - 0.8 and 0.8
5. 0 , 8
Distnace is - 1.2 and 1.2
Hence from above , we see that adding 4 and 4 , results in a value that would change the SD to the least. Hence B