RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 6 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
A.11
B.10
C.9
D.12
Answer: C.9
Explanation: Suppose they meet x hours after 6 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 9 a.m.
Answer: C
Question: 3889 + 12.952 - ? = 3854.002
A.47.59
B.48.95
C.49.85
D.47.95
Answer: D.47.95
Explanation: Let 3889 + 12.952 - x = 3854.002.
Then x = (3889 + 12.952) - 3854.002
= 3901.952 - 3854.002
= 47.95.
Answer is D.
Question: A car gets 20 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 180 kilometers?
A.8.5 gallons
B.9 gallons
C.6.5 gallons
D.5.5 gallons
Answer: B.9 gallons
Explanation: Each 20 kilometers, 1 gallon is needed. We need to know how many 20 kilometers are there in 180 kilometers?
180 / 20 = 9 * 1 gallon = 9 gallons correct answer B
Question: the probability of a student possessing a ball point pen in exam is 3/5 & possessing an ink pen is 2/3. find his probability of possessing at least one of them
A.10/15
B.11/15
C.12/15
D.13/15
Answer: D.13/15
Explanation: the probability of a student possessing a ball point pen in exam is 3/5 .
the probability of a student not possessing a ball point pen in exam is 2/5 & possessing an ink pen is 2/3.
& not possessing an ink pen is 1/3.
his probability of possessing none of them =2/5*1/3=2/15
his probability of possessing one of them =1-2/15 = 13/15
ANSWER:D
Question: Camel and carriage for Rs. 5000. He SP the camel at a gain of 20% and the carriage at a loss of 10%. If he gains 3% on the whole, then find the CP of the camel?
A.Rs.2166.67
B.Rs.2145.67
C.Rs.2157
D.Rs.2167.1
Answer: A.Rs.2166.67
Explanation: Now, in this numerical, there is no common loss and gain %.
Hence, solve it making equations.
Let cost price of camel be x.
As cost of camel and carriage = Rs 5000
Cost of carriage = Rs. (5000 – x)
After selling camel he gains 20% and on carriage a loss of 10%. But on the whole he gains 3%.
Therefore,
20% of x – 10 % of (5000 – x) = 3 % of 5000
20 × x – 10 × (5000 – x) = 3 × 5000
100 100 100
x – (5000 – x) = 150
5 10
10x – (5000 – x) × 10 = 150 × 10
5 10
2x-5000+x=1500
3x=1500+5000
x=2166.67
The cost of camel = Rs.2166.67
Option (A) is the correct answer
Question: The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 294. What is the rate of interest per annum?
A.18
B.12
C.9
D.14
Answer: D.14
Explanation: Explanation:
[15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 294
15000[(1 + R/100)2 - 1 - 2R/100] = 294
15000[(100 + R)2 - 10000 - 200R]/10000 = 294
R2 = (294 * 2)/3 = 196 => R = 14
Rate = 14%
Answer: Option D
Question: A certain sum of money is divided among A, B and C so that for each Rs. A has 80 paisa, B has 65 paisa and C 40 paisa. If C's share is Rs.40, find the sum of money?
A.Rs.185
B.Rs.410
C.Rs.285
D.Rs.385
Answer: A.Rs.185
Explanation: A:B:C = 80:65:40
= 16:13:8
8 ---- 40
37 ---- ? => Rs.185
ANSWER:A
Question: How many FIVE letter words are formed using the letters of the word LEADER?
A.860
B.720
C.230
D.460
Answer: B.720
Explanation: The number of letters in the given word is 6.
The number of FIVE letter words that can be formed using these four letters is 6P5=6*5*4*3*2=720
Answer:B
Question: 10 distinct integers are arranged in ascending order. The range of the first 7 is 25 and that of last 7 is 30. What is the maximum range M of the 10 numbers?
A.25
B.27
C.30
D.52
Answer: D.52
Explanation: Positions: 1 2 3 4 5 6 7 8 9 10
Given: 1st position = x; 4th position = a; 7th position = y; 10th position = b
y - x = 25
Let x be 0 and y = 25. We are asked to maximize the range and the integers are distinct.
b - a = 30 --> b = 30 + a
In order to increase the range, we have to maximize the value of 'b'.
'b' can be maximized by taking the max value of 'a'.
From the assumed values, maximum value of 'a' can be 22.
Therefore, b = 30 + 22 = 52
Range M= 52 - 0 = 52
Answer: D
Question: Keshav runs a factory in three shifts of eight hours each with 210 employees. In each shift minimum of 80 employees are required to run the factory effectively. No employees can be allowed to work for more than 16 hours a day. At least how many employees will be required to work for 16 hours every day?
A.30
B.40
C.50
D.60
Answer: A.30
Explanation: total 210 employees and There are 3 shifts of 8 hrs.
per each shift no of employees = 210/3 = 70.
But Per each shift 80 employees are required.
so employess need to work for 16 hrs =80-70=10.
for 3shifts,10*3=30
i.e 30 employees required to work 16 hrs every day.
ANSWER:A
Question: The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. Find out the average age of the team.
A.23 years
B.20 years
C.24 years
D.21 years
Answer: A.23 years
Explanation: Explanation:
Number of members in the team = 11
Let the average age of of the team = x
=> Sum of ages of all 11 members/11=x
=> Sum of the ages of all 11 members = 11x
Age of the captain = 26
Age of the wicket keeper = 26 + 3 = 29
Sum of the ages of 9 members of the team excluding captain and wicket keeper
=11x−26−29=11x−55
Average age of 9 members of the team excluding captain and wicket keeper
=11x−5/59
Given that 11x−55/9=(x−1)
⇒11x−55=9(x−1)
⇒11x−55=9x−9
⇒2x=46
⇒x=46/2 = 23 years
Answer: Option A
Question: A circle of radius 10 inches has its center at the vertex C of an equilateral triangle ABC and passes through the other two vertices. The side AC extended through C intersects the circle at D. The number of degrees of angle ADB is:
A.27
B.30
C.837
D.37
Answer: B.30
Explanation: Answer: B
Question: Jake remembers only the last three letters of his four-letter Klingon name. If he is sure that the first letter is neither "N" nor "X", and assuming that there are only 15 letters in the Klingon alphabet, what is the probability that he will give the correct name when asked for it by the space attendant?
A.A)8/100
B.B)9/100
C.C)1/8
D.D)1/13
Answer: D.D)1/13
Explanation: Total letters 15, out of which the first letter is anything of 10 but N or X...
So there are 13 possible letters for first place..
And only one of them is correct..
So 1/13
Answer: D
Question: ? x 12 = 173 x 240
A.3460
B.685
C.865
D.495
Answer: A.3460
Explanation: Let y x 12 = 173 x 240
Then y = (173 x 240) / 12
=3460
ANSWER :A
Question: A seller mixed 4 dozen bananas costing Rs.12 per dozen with 6 dozen bananas at Rs.8 per dozen then what is the cost price of mixed bananas per dozen?
A.Rs.6.40
B.Rs.10
C.Rs.9.6
D.Rs.10.2
Answer: C.Rs.9.6
Explanation: 4 dozens of bananas cost is rs12
then 4*12=48
6 dozens of bananas cost is rs8
then 6*8=48
48+48/4+6=96/10=9.6
ANSWER:C
Question: If 5^21 X 4^11 = 2x10^n. What is the value of n?
A.11
B.21
C.22
D.23
Answer: B.21
Explanation: If 5^21 x 4^11 = 2x10^n what is the value of n
4^11 = (2^2)^11 = 2^22
10^n = (5x2)^n = 5^n x 2^n
5^21 x 2^22 = 2x 2^n x 5^n = 2^n+1 x 5^n = 2^22 x 5^21
n = 21
Option B
Question: Find the least number that must be subtracted from 1387 so that the remaining number is divisible by 15.
A.1
B.5
C.7
D.9
Answer: C.7
Explanation: On dividing 1387 by 15 we get the remainder 7, so 7 should be subtracted. The answer is C.
Question: A 270 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.230m
B.240m
C.250m
D.260m
Answer: A.230m
Explanation: speed = (120 + 80)km/h (because direction is opposite hence relative velocity is added)= 500/9 m/s
time= 9sec
let the lenght of second train is x
total distance covered= 270 + x
therefore, D= speed*time
thus 270 + x = 500/9 * 9
x= 500-270=230 m
ANSWER:A
Question: The probabilities of solving a question by 3students A, B & C are 1/2,1/3 &1/4, respectively. The probability that the problem will be solved is?
A.2/3
B.3/4
C.3/5
D.3/7
Answer: B.3/4
Explanation: Sol. First, we find the probability of not solving the problem x PTO x = (1 — D x - D x - D
1 2 3 1 =iXiX71=4;
1 3 Required probability 3/4
B
Question: Celine worked for h hours each day for d consecutive days. If she earns $7.50 per hour, what is the total amount she earned?
A.7.50/d + h
B.7.50 + d + h
C.7.50 + dh
D.7.50dh
Answer: D.7.50dh
Explanation: H hours for d days.
Income each day = 7.5*h
Total income = 7.5*h*d
Correct option: D
Question: What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
A.6
B.9
C.24
D.20
Answer: C.24
Explanation: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
Number of such number =14
Required percentage =14	x 100	% = 20%
Answer:C
Question: A courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof. What could be the weight in grams of a package for which the charge is $1.95?
A.980
B.1170
C.1530
D.1720
Answer: C.1530
Explanation: The charge is 65 cents for the first 250 grams.
This leaves a charge of $1.95 - $0.65 = $1.30
The charge for the next 1200 grams is $1.20 which leaves a charge of $0.10
The weight is somewhere between 1450 and 1550.
The answer is C.
Question: A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 6 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?
A.480
B.487
C.720
D.729
Answer: C.720
Explanation: 1/x - 1/20 = -1/24
x = 120
120 * 6 = 720
Answer:C
Question: A person spent Rs. 6,040 from his salary on food and 8,000 on house rent. After that he was left with 70% of his monthly salary. What is his monthly salary ?
A.46,800
B.66,800
C.56,800
D.26,800
Answer: A.46,800
Explanation: Total money spent on food and house rent = 6,040+8,000 = 14,040
Which is 100 - 70 = 30% of his monthly salary
∴ His salary = 14040x100/30 = 46800
Answer : A
Question: Mary passed a certain gas station on a highway while traveling west at a constant speed of 40 miles per hour. Then, 15 minutes later, Paul passed the same gas station while traveling west at a constant speed of 60 miles per hour. If both drivers maintained their speeds and both remained on the highway for at least 2 hours, how long after he passed the gas station did Paul catch up with Mary?
A.1/2
B.2
C.1
D.4
Answer: A.1/2
Explanation: d = rt
M: r = 40 mph, t = t + 1/4hr
d = 40 (t + 1/4)
P: r = 60, t = t
d = 60t
since they went the same distance:
40t + 40/4 = 60t
20t = 40/4
t = 1/2 or 1/2 hr
A
Question: Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 3 ½ hours if they are walking in the same direction?
A.7 km
B.6 km
C.4 3/8 km
D.9 km
Answer: C.4 3/8 km
Explanation: RS = 5 ¾ - 4 ½ = 1 ¼
T = 3 ½ h.
D = 5/4 * 7/2 = 35/8
= 4 3/8 km
Answer:C
Question: In a particular gumball machine, there are 4 identical blue gumballs, 3 identical red gumballs, 2 identical green gumballs, and 1 yellow gumball. In how many different ways can the gumballs be dispensed, 1 at a time, if the 3 red gumballs are dispensed last?
A.105
B.210
C.315
D.420
Answer: A.105
Explanation: Since the red gumballs are being dispensed last they will not impact the number of permutations of the other gumballs, so we can effectively ignore them. (There is only one way for the three red gumballs to be dispensed last (RRR), so we will multiply the number of permutations of the other colours by 1).
The remaining gumballs are: 4 blue, 2 green, 1 yellow. 7 gumballs in total, so they can be arranged in 7! ways. But since the gumballs of each colour are identical, we must divide by the arrangements of each colour.
Total arrangements of the 7 gumballs = 7!/4!∗2!∗1!=7∗6∗5/2=105
So total arrangements of the 10 gumballs, with all 3 reds chosen last is 105 *1 = 105
Answer: A
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
A.35 km/hr
B.50 km/hr
C.45 km/hr
D.65 km/hr
Answer: B.50 km/hr
Explanation: 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 - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.
Answer: B
Question: What least number must be subtracted from 427398 so that remaining number is divisible by 15
A.3
B.5
C.7
D.9
Answer: A.3
Explanation: Explanation:
On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted
Answer: Option A
Question: A man gains 20% by selling an article for a certain price. If the sells it at double the price, the percentage of profit will be:
A.130
B.220
C.140
D.120
Answer: C.140
Explanation: C
140%
Let C.P. = $x.
Then, S.P. = $(12% of x) = $6x/5
New S.P. = 2 * 6x/5 = $12x/5
Profit = 12x/5 - x = $7x/5
Profit = 7x/5 * 1/x * 100 = 140%.
Question: The age of teacher is the same as the digit in the student's age, but in reverse order. In five years teacher will be twice as old as student will be then. what is the difference in their current age ?
A.18
B.12
C.25
D.13
Answer: A.18
Explanation: Teacher's age= 10x+y so student's age= 10y+x..
after 5 years , 10x+y+5=2*(10y+x+5)....
so 5+19y=8x... check for odd values of y, y=1 satisfies the eqn with x=3... so ages are 31 and 13 and ans as found correctly by u is A..18
Question: A farm has only chickens and pigs. When the manager of the farm counted the heads of the animals on the farm, the number totaled up to 80. When the number of legs was counted, the number totaled up to 218. How many more chickens than pigs are there on the farm? Note: Each pig has 4 legs and each chicken had 2 legs.
A.16
B.18
C.20
D.22
Answer: D.22
Explanation: Let x be the number of chickens.
Then 80-x is the number of pigs.
2x+4(80-x)=218
2x=102
x=51 (chickens)
70-x=29 (pigs)
There are 51-29=22 more chickens on the farm.
The answer is D.
Question: In what time will a train 400 meters long cross an electric pole, if its speed is 144 km/hr
A.5 seconds
B.4.5 seconds
C.10 seconds
D.2.5 seconds
Answer: C.10 seconds
Explanation: Explanation:
First convert speed into m/sec
Speed = 144*(5/18) = 40 m/sec
Time = Distance/speed
= 400/40 = 10 seconds
Answer: C
Question: If 2 cards are selected at random from the deck of 52 cards then What is the probability of one of the selected cards will be 10 and other will be Queen?
A deck of cards has a total of 52 cards, consisting of 4 suits; (spades(Black), hearts(Red), diamond(Red)s, and clubs(Black)); and 13 cards including 1 king, 1 queen and 1 jack in each suit
A.8/2652
B.1/2652
C.12/2652
D.18/2652
Answer: D.18/2652
Explanation: 2 possible cases:
10 - Queen or Queen -10 (4 kings and 4 queens).
Either way,
the total probability = 2( 10 -Queen) = 2 (4/52 * 4/51) = 18/2652. D is the correct answer.
Question: Simplify 64568 * 9999
A.645615432
B.236547892
C.289546354
D.558666666
Answer: A.645615432
Explanation: Explanation:
Although it is a simple question, but the trick is to save time in solving this.
Rather than multiplying it we can do as follows:
64568 * (10000 - 1) = 645680000 - 64568 = 645615432
Answer: Option A
Question: For integers x, y, and z, if (3^x) (4^y) (5^z) = 65,536,000,000 and x + y + z = 17, what is the value of xy/z?
A.0
B.1
C.3
D.5
Answer: A.0
Explanation: The number 65,536,000,000 is not divisible by 3. (We can verify this by adding the digits of the number to see that the sum is not a multiple of 3.)
Thus x = 0 and xy/z = 0.
The answer is A.
Question: A teacher gave the same test to three history classes: M, B, and C. The average (arithmetic mean) scores for the three classes were 65, 80, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined?
A.74
B.75
C.76
D.77
Answer: B.75
Explanation: Ans : B (75)
lets say class M indeed has 4 children, B has 6 children and C has 5 children.
now, if the average of class M is 65, hence total marks awarded in the class = 65*4=260
Similarly,
class B = 80*6 = 480
class C = 77*5 = 385
total marks provided = M+B+C = 260+480+385 = 1125
avg. marks = 1125 / 15 (total no. of students) = 75=B
Question: The C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%?
A.16 2/9%
B.16 2/4%
C.16 2/3%
D.16 2/1%
Answer: C.16 2/3%
Explanation: 10 CP = 12 SP
12 --- 2 CP loss
100 --- ? => 16 2/3%
Answer:C
Question: X and Y are both integers. If X/Y = 57.40, then what is the sum of all the possible two digit remainders of X/Y?
A.560
B.616
C.450
D.900
Answer: C.450
Explanation: Remainder = 0.40 --> 40/100 --> Can be written as (40/4) / (100/4) = 10/25
So remainders can be 10, 20, 30, 40, ..... 90.
We need the sum of only 2 digit remainders --> 10 + 20 + 30 + 40 + 50 + 60 + 70+ 80 + 90 =450
Answer: C
Question: In the xy plane line m has the equation 4x + y = w. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r?
A.-4/3
B.1/4
C.-4
D.3/4
Answer: A.-4/3
Explanation: The equation of line m is y=-4x+w. Now, since line n is perpendicular to line m, then its slope is negative reciprocal of the slope of line m, so the slope of n is 1/4. Next, as line n passes through the origin (0, 0) and has the slope of 1/4 then its equation is y=1/4*x.
Point (r, r+1) lies on line n means that (r+1)=1/4*r --> r=-4/3.
Answer: A.
Question: If in a box of dimensions 6 m * 5 m * 4 m smaller boxes of dimensions 60 cm * 50 cm * 40 cm are kept in it, then what will be the maximum number of the small boxes that can be kept in it?
A.2888
B.1000
C.2878
D.27878
Answer: B.1000
Explanation: 6 * 5 * 4 = 60/100 * 50/100 * 40/100 * x
1 = 1/10 * 1/10 * 1/10 * x => x = 1000
Answer:B
Question: By selling a book for 300, 20% profit was earned. What is the cost price of the book?
A.A)215
B.B)250
C.C)230
D.D)235
Answer: B.B)250
Explanation: SP = 120% of CP; :. CP = 300 × 100/120 = 250
Option 'B'
Question: How many of the following numbers are divisible by 21 ?
264, 396, 462, 792, 968, 2178, 5184, 6336
A.3
B.4
C.5
D.1
Answer: D.1
Explanation: By using your calculator you can calculate that the following numbers are divisible by 21 : 462
Required number of number = 1.
D
Question: Vishal invested 10% more than Trishul. Trishul invested 10% less than Raghu. If the total sum of their investments is Rs. 6069, how much amount did Raghu invest ?
A.1287
B.2887
C.2100
D.1129
Answer: C.2100
Explanation: Let money invested by Raghu = Rs. x
Money invested by Trishul = 9/10 x = 0.9x
Money invested by Vishal = 9/10x * 110/100 = 0.99x
Also, x+0.9x+0.99x = 6069
= x= 6069/2.89 = 2100
Therefore, amount invested by Raghu is Rs. 2100.
Answer: C
Question: If xy=4, x/y=16, for positive numbers x and y, y=?
A.1/2
B.2
C.1/3
D.3
Answer: A.1/2
Explanation: Very easy question. 2 variables and 2 easy equations.
xy=4 ---> x=4/y - (i)
x/y=16 ---> replacing (i) here ---> 4/(y^2)=16 ---> y^2=4/16=1/4 ---> y=1/2 or -1/2
The question states that x and y are positive integers. Therefore, y=1/2 is the answer.
Answer A.
Question: A theater box office sold an average (arithmetic mean) of 63 tickets per staff member to a particular movie. Among the daytime staff, the average number sold per member was 78, and among the evening staff, the average number sold was 60. If there are no other employees, what was the ratio of the number of daytime staff members to the number of evening staff members?
A.2:3
B.1:4
C.1:5
D.6:11
Answer: C.1:5
Explanation: Deviation from the mean for the daytime staff = 78 - 63 = 15.
Deviation from the mean for the evening staff = 63 - 60 = 3.
Thus, the ratio of the number of daytime staff members to the number of evening staff members is 3:15 = 1:5.
The answer is C.
Question: A boy has 9 trousers and 9 shirts. In how many different ways can he select a trouser and a shirt?
A.100
B.81
C.104
D.94
Answer: B.81
Explanation: The boy can select one trouser in nine ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 9 = 81 ways.
B
Question: When a jogger moves at an average speed of 6 kmph, they reach their destination on time. When their average speed becomes 4 kmph, they reach their destination 15 minutes late. Find the length of journey.
A.3 km
B.5 km
C.7 km
D.6 km
Answer: A.3 km
Explanation: Sol.
Difference between timings = 15 min = 1/4 hr.
Let the length of journey be x km.
Then, x/4 - x/6 = 1/4
â‡” 3x - 2x = 3
â‡” x = 3 km.
Answer A
Question: The average of 100,200,300 and x is 250 and the average of 300,150,100,x and y is 200. What is the value of y?
A.100
B.150
C.50
D.200
Answer: C.50
Explanation: We have : (100+200+300+x) /4 = 250
600+x = 1000
x = 400
(300+150+100+x+y)/5 = 200
550+400+y = 1000
y = 50
Answer is C
Question: An express traveled at an average speed of 200 km/hr, stopping for 3 min after every 125 kn. How long did it take to reach its destination 800 km from the starting point?
A.5 hrs 21 min
B.4 hrs 18 min
C.6 hrs 41 min
D.6 hrs 21 min
Answer: B.4 hrs 18 min
Explanation: B
4 hrs 18 min
Time taken to cover 800 km = 800/200 = 4 hrs.
Number of stoppages = 800/125 - 1 = 6
Total time of stoppages = 3 * 6 = 18 min
Hence, total time taken = 4 hrs 18 min.
Question: A rower whose speed is 6 km/hr in still water rows to a certain point upstream and back to the starting point in a river which flows at 3 km/hr. What is the rower's average speed (in km/hr) for the total journey?
A.3.9
B.4.2
C.4.5
D.4.8
Answer: C.4.5
Explanation: time upstream = d / 3
time downstream = d / 9
total time = d/3 + d/9 = 4d/9
average speed = 2d / (4d/9) = 4.5 km/hr
The answer is C.
Question: How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5 and 6 such that the numbers are divisible by 9?
A.1
B.2
C.4
D.6
Answer: C.4
Explanation: CONCEPT: A number will be divisible by 9 if sum of all the digits of the number is divisible by 9
Here the Possible sum of the two distinct digits can be 9 only in order to satisfy the given condition
If sum of Digits = 9, No. =36, 45, 54, 63 --- 4 Cases
Answer: option C
Question: In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole?
A.17 sec
B.14 sec
C.78 sec
D.10 sec
Answer: D.10 sec
Explanation: Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps.
The distance to be covered is equal to the length of the train.
Required time t = d/s = 100/10 = 10 sec.
Answer:D:
Question: A certain team consists of 4 professors and 6 teaching assistants. How many different teams of 3 can be formed in which at least one member of the group is a professor? (Two groups are considered different if at least one group member is different.)
A.48
B.100
C.120
D.288
Answer: B.100
Explanation: The groups can be formed as
PTT + PPT + PPP where P=professor and T=Teaching assistant
Number of different teams of 3 can be formed in which at least one member of the group is a professor
= 4C1* 6C2 + 4C2*6C1 + 4C3
= 4!/3! * 6*5/2 + 4*3/2 * 6 + 4
=60 +36 + 4
=100
Answer B
Question: What is the probability that the sum of two dice will yield a 7, and then when both are thrown again, their sum will again yield a 7? assume that each die has 6 sides with faces numbered 1 to 6.
A.1/144
B.1/36
C.1/12
D.1/6
Answer: B.1/36
Explanation: In order to get the sum of the two dices to be 7, there are six combinations that satisfy this requirement.
1+6=7
2+5=7
3+4=7
4+3=7
5+2=7
6+1=7
Each combination has 1/36 of probability of occurrence, or in total 6/36 for the six combinations, which is 1/6.
In order to get the probability of this occurring twice in a row we multiply 1/6 *1/6 and we get 1/36.
The answer is B.