RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Jim is twice as old as Stephanie, who, four years ago, was three times as old as Kate. If, five years from now, the sum W of their ages will be 51, how old is Stephanie ?
A.6
B.10
C.14
D.20
Answer: B.10
Explanation: 1) take C (14y.o.), so mean that S=14, J=28, their sum itself is 42+10 years from now is 52, it is over the 51,
so eliminate C,D,E
2) take B (10y.o.),W= meaning S=10,J=20, so 20+10+10=40 and for K=10-4/3=2+9=11, finally 40+11=51. It is correct
B
Question: If a 5-digit numerical with local value of digits 3 is 300, 4 is 40000, 5 is 50, 6 is 6 and 7 is 7000, is multiplied by 7 then the difference between local value of 4 in the new numerical and the face value of 3 is
A.397
B.2997
C.49997
D.697
Answer: A.397
Explanation: According to the given local values of the 5-digit number the number is 47356
Multiplying it with 7,
47356 x 7 = 331492
(Local value of 4 in 331492) - (Face value of 3) = 400 - 3 = 397
A
Question: A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast?
A.7500
B.2888
C.2666
D.2999
Answer: A.7500
Explanation: 35%-----------L
65%-----------W
------------------
30%----------2250
100%---------? => 7500
Answer:A
Question: 6 friends are living in 6 different flats of an apartment. Each of them was allotted a parking spot to park their cars in the ground floor. But they used to park their cars randomly in any of the 6 parking spots. In how many ways can they park their cars so that exactly 4 people park their cars in the spots allotted to them?
A.15
B.21
C.35
D.42
Answer: A.15
Explanation: 6C4 = 15
The remaining 2 people in each case will be parked in each other's parking spots.
The answer is A.
Question: Which of the following is not the square of an integer?
A.275625
B.385641
C.190096
D.432562
Answer: D.432562
Explanation: The square of an integer (n^2) can have only the following units digit:
0, if the units digit of n is 0;
1, if the units digit of n is 1 or 9;
4, if the units digit of n is 2 or 8.
5, if the units digit of n is 5;
6, if the units digit of n is 6 or 4;
9, if the units digit of n is 3 or 7.
The square of an integer cannot have the units digit of 2, 3, 7, or 8.
The answer is D.
Question: Rary spent 2⁄5 of her money on new clothes and then deposited 1⁄2 of what remained into her savings account. If she then had $21 left, how much did she have at the start?
A.$30
B.$35
C.$70
D.$105
Answer: C.$70
Explanation: Rary spent 2⁄5 of her money on new clothes but if you see 21 is half of 3/5 money so 210 is too huge to be correct..
solution..
let the money be x..
2/5 is used...
1/2 of remaining 3/5 is put in savings account and remaining half is 21..
so 1/2 * 3/5 *x=21..
x=21*2*5/3=70..
C
Question: three men invested sum. and their ratio is 5:7:6. profit is 5400.then b's share
A.2000
B.2100
C.2200
D.2300
Answer: B.2100
Explanation: b's share =7/18*5400=2100
ANSWER:B
Question: The ratio between the radii of two spheres is 1:3. Find the ratio between their volumes?
A.1:28
B.1:27
C.1:18
D.1:21
Answer: B.1:27
Explanation: r1 : r2 = 1:3
r13 : r23 = 1:27
Answer: B
Question: The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 424 different signs. If the company used 422 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 424 signs?
A.246
B.248
C.1692
D.15,128
Answer: C.1692
Explanation: # of 2-letter codes possible from 424 different signs = 424*424.
# of 2-letter codes possible from 422 different signs = 422*422.
The difference = 424^2 - 422^2 = (424 - 422)(424 + 422) = 1692.
Answer: C.
Question: A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
A.299
B.278
C.289
D.108
Answer: D.108
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 * 12
= 108 ways.
Answer: D
Question: A, B and C are partners in a business. Their capitals are respectively, Rs.5000, Rs.6000 and Rs.4000. A gets 30% of the total profit for managing the business. The remaining profit is divided among three in the ratio of their capitals. In the end of the year, the profit of A is Rs.200 more than the sum of the profits of B and C. Find the total profit.
A.3008
B.3006
C.3004
D.3000
Answer: D.3000
Explanation: A:B:C = 5:6:4
Let the total profit = 100 - 30 = 70
5/15 * 70 = 70/3
A share = 70/3 + 30 = 160/3
B + C share = 100 - 160/3 = 140/3
A-(B+C) = 160/3 - 140/3 = 20/3
20/3 ---- 200
100 ---- ? => 3000
Answer: D
Question: Three pipes of same capacity can fill a tank in 8 hours. If there are only two pipes of same capacity, the tank can be filled in.
A.22
B.12
C.88
D.99
Answer: B.12
Explanation: The part of the tank filled by three pipes in one hour = 1/8
=> The part of the tank filled by two pipes in 1 hour = 2/3 * 1/8 = 1/12.
The tank can be filled in 12 hours.
Answer:B
Question: Look at this series: 201, 202, 204, 207, ... What number should come next?
A.211
B.205
C.224
D.267
Answer: A.211
Explanation: In this addition series, 1 is added to the first number; 2 is added to the second number; 3 is added to the third number; 4 is added to the fourth number; and go on.
ANSWER A
Question: A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability W that out of the two, one is white and one is blue?
A.15/56
B.41/56
C.13/28
D.15/28
Answer: D.15/28
Explanation: The required probability W= probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls.
Ways to select 6 out of total 8 = 8C6
Ways to select 4 out of 5 white balls = 5C4
Ways to select 2 out of 3 blue balls = 3C2
Thus the required probability = (5C4*3C2)/8C6 = 15/28.
D is thus the correct answer.
Question: The second angle of a triangle is double the first(110). The third angle is 40 less than
the first(15). Find the first angle.
A.35
B.45
C.55
D.65
Answer: C.55
Explanation: First x With nothing given about the firstwemake that x
Second 2x The second is double the first,
Third x−40 The third is 40 less than the first
F +S +T =180 All three angles add to 180
(x)+(2x)+(x−40)=180 Replace F , S, and T with the labeled values.
x+2x+x−40=180 Here the parenthesis are not needed.
4x−40=180 Combine like terms, x+2x+x
+40 +40 Add 40 to both sides
4x=220 The variable ismultiplied by 4
4 4 Divide both sides by 4
x=55 Our solution for x
First 55 Replace xwith 55 in the original list of angles
Second 2(55)=110 Our angles are 55, 110, and 15
Third (55)−40=15
correct answer C
Question: If six persons sit in a row, then the probability that three particular persons are always together is
A.1/5
B.1/8
C.1/5
D.1/3
Answer: C.1/5
Explanation: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5.Answer: C
Question: In how many ways the letters of the word MOUSE be arranged?
A.140
B.150
C.160
D.120
Answer: D.120
Explanation: Total ways of arranging the letters = 5! = 120 ways.
D)
Question: find the number, difference between number and its 3/5 is 58.
A.140
B.143
C.144
D.145
Answer: D.145
Explanation: Explanation:
Let the number = x,
Then, x-(3/5)x = 58,
=> (2/5)x = 58 => 2x = 58*5,
=> x = 145
Answer: Option D
Question: Two trains started at the same time, one from A to B and the other from B to A . If they arrived at B and A respectively 9 hours and 16 hours after they passed each other the ratio of the speeds of the two trains was
A.2:1
B.3:2
C.4:3
D.5:4
Answer: C.4:3
Explanation: Explanation:
Note : If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then: (A's speed) : (B's speed) = (b : a)
Therefore, Ratio of the speeds of two trains = = 4 : 3. Answer: C
Question: Excluding stoppages, the speed of a bus is 60 kmph and including stoppages, it is 50 kmph. For how many minutes does the bus stop per hour?
A.10 min
B.15 min
C.12 min
D.8 min
Answer: A.10 min
Explanation: Due to stoppages, it covers 10 km less.
Time taken to cover 10 km = (10/60 x 60) min = 10 min
Answer : A
Question: The sum of the first 70 positive even integers is 4,970. What is the sum of the first 70 odd integers?
A.4500
B.4600
C.4300
D.4900
Answer: D.4900
Explanation: Sum of first n even numbers = n(n+1) =4970
Sum of first n odd numbers = n^2 = 70*70 = 4900 (here n=70)
Answer : D
Question: In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together ?
A.10080
B.4989600
C.120960
D.250035
Answer: C.120960
Explanation: In the word 'MATHEMATICS' we treat the vowels AEAI as one letter.
Thus, we have MTHMTCS (AEAI).
Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.
Number of ways of arranging these letters = 8!/(2!)(2!) = 10080.
Now, AEAI has 4 Letters in which A occurs 2 times and the rest are different.
Number of ways of arranging these letters = 4!/2! = 12.
∴ Required number of words = (10080 * 12) = 120960.
Answer is C
Question: When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/6 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year?
A.3/10
B.2/5
C.1/2
D.2/3
Answer: C.1/2
Explanation: Say, the tree grows by x feet every year.
Then, 4 + 6x = (1+1/6)(4+4x)
or, x = 1/2
Answer C
Question: Suppose you work for a manufacturing plant that pays you $12.50 an hour plus $0.16 for each widget you make. How many widgets must you produce in a 40 hour week to earn $620 (before payroll deductions)?
A.670
B.710
C.750
D.790
Answer: C.750
Explanation: total pay = 40*$12.50 + $0.16*x = 620
x = 120 / 0.16 = 750
The answer is C.
Question: The three competitors in a race have to be randomly chosen from a group of four men and five women. How many different such trios contain at least one woman?
A.50
B.60
C.70
D.80
Answer: D.80
Explanation: The total number of ways to choose three runners 9C3 = 84
The number of trios with only males is 4C3 = 4
The number of trios which include at least one woman is 80.
The answer is D.
Question: Find the face value of 5 in 5432100
A.50
B.5
C.50000
D.500000
Answer: B.5
Explanation: Face value is the value of digit itself
face value of 5 = 5
Answer : B
Question: An analyst will recommend a combination of 2 industrial stocks, 3 transportation stocks, and 3 utility stocks. If the analyst can choose from 6 industrial stocks, 3 transportation stocks, and 4 utility stocks, how many different combinations of 9 stocks are possible?
A.12
B.19
C.60
D.180
Answer: C.60
Explanation: 6C2 * 3C3 * 4C3 = 15*1*4 = 60.
Answer: C
Question: In a certain encryption pattern, HARD is coded as 1357 and SOFT is coded as 2468, What will 21448 stand for?
A.SHAFT
B.SHORT
C.SHOOT
D.SHART
Answer: C.SHOOT
Explanation: on the behlaf of order like
h =1
a=3
r=5 and so on.
so 21448 is SHOOT
ANSWER:C
Question: A palindrome is a word or a number that reads the same forward and backward. For example, 2442 and 111 are palindromes. If 5-digit palindromes are formed using one or more of the digits 1, 2, 3, and 4, how many palindromes are possible?
A.32
B.64
C.96
D.128
Answer: B.64
Explanation: There are 4 choices for each of the first three digits.
The number of possible palindromes is 4^3=64.
The answer is B.
Question: f the LCM of two integers a, b (where b> a and a>1) is a*b, then which of the following can not be true?
A.Both a and b can be Prime Numbers.
B.Both a and b can be consecutive integers.
C.All Prime factors of a must be Prime factors of b.
D.a and b do not share any Prime factors.
Answer: C.All Prime factors of a must be Prime factors of b.
Explanation: Say a = 2; b = 3; only option C contradicts
All Prime factors of a must be Prime factors of b
Answer = C
Question: A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?
A.1350
B.1357
C.1328
D.1329
Answer: A.1350
Explanation: Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 2 = Rs.1350
Answer:A
Question: Which of the following numbers doesn't belong to the group?
A.14
B.16
C.20
D.28
Answer: A.14
Explanation: All of the numbers are multiples of 2. But only one is not a multiple of 4: 14.
Answer: 14
Question: In a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 10,290,000, how many red beads were removed?
A.2
B.3
C.4
D.5
Answer: B.3
Explanation: 10,290,000
= 2^4 * 5^4 * 1029
= 2^4 * 3 * 5^4 * 343
= 2^4 * 3 * 5^4 * 7^3
The answer is B.
Question: If the area of circle is 706 sq cm then its circumference?
A.21
B.88
C.66
D.94
Answer: D.94
Explanation: 22/7 r2 = 706 => r = 15
2 * 22/7 * 15 = 94
Answer: D
Question: Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train catches and completely passes the slower train in 54 seconds. What is the length of each train (in meters)?
A.45
B.55
C.65
D.75
Answer: D.75
Explanation: The relative speed = 46 - 36 = 10 km/hr = 10 * 5/18 = 25/9 m/s
In 54 seconds, the relative difference in distance traveled is 54 * 25/9 = 150 meters
This distance is twice the length of each train.
The length of each train is 150/2 = 75 meters
The answer is D.
Question: Which of the following fractions is greater than 3/4 and less than 5/6?
1. 3/4 2. 5/6 3. 1/2 4. 2/3 5. 4/5 6. 9/10
A.4/5
B.1/2
C.9/10
D.5/6
Answer: A.4/5
Explanation: 3/4 = 0.75, 5/6 = 0.833, 1/2= 0.5, 2/3= 0.66, 4/5= 0.8, 9/10= 0.9.
Clearly, 0.8 lies between 0.75 and 0.833.
Therefore, 4/5 lies between 3/4 and 5/6.
Answer is A.
Question: Find the sum of prime numbers lying between 58 and 72?
A.198
B.258
C.252
D.272
Answer: B.258
Explanation: Solution
Required sum	= 59 + 61 + 67 + 71)
= 258.
Answer B
Question: If a and b are different positive integers and a + b = ab(a + b), then which of the following must be true?
I. a = 1
II. b = 1
III. a < b
A.I only
B.II only
C.III only
D.I and II
Answer: A.I only
Explanation: Number picking might not be the best way to solve MUST BE TRUE questions.
The question asks which of the followingMUSTbe true, or which of the following isALWAYStrue no matter what set of numbers you choose. For such kind of questionsif you can prove that a statement is NOT truefor one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.
So the set you chose just proves that II is not always true and hence it's not a part of a correct choice. As for I and III: they might be true for this particular set of numbers but not true for another set, so you can not say that I and III are always true just based on one set of numbers (it just happens to be that I and III are always true).
As forCOULD BE TRUEquestions:
The questions asking which of the followingCOULDbe true are different:if you can prove that a statement is truefor one particular set of numbers, it will mean that this statement could be true and hence is a correct answer.
A
Question: A car travels uphill at 30 km/hr and downhill at 50 km/hr. It goes 100 km uphill and 50 km downhill. Find the average speed of the car?
A.32kmph
B.33kmph
C.34kmph
D.35kmph
Answer: D.35kmph
Explanation: avg speed=total distance/total time.
total distance traveled=100+50=150km;
time taken for uphill journey=100/30=10/3;
time taken for down hill journey=50/50=5/5;
avg speed=150/(10/3+5/5)=35kmph
ANSWER:D
Question: A circle passes through two adjacent vertices of a square and is tangent to one side of the
square. If the side length of the square is 2, what is the radius of the circle?
A.3/2
B.4 /3
C.5 /4
D.6 /5
Answer: C.5 /4
Explanation: Let A and B be the vertices through which the circle passes. LetM be the midpoint
of the line segment AB. The center C of the circle is on the line joining M to the midpoint of
the opposite side, which is also on the circle (see diagram below). Let r be the radius of the
circle. The length of the line segment joiningM to C is r-(2r-2) = 2-r as shown below.
Then 12+(2-r)2 = r2 by the Pythagorean Theorem. This gives 1+4-4r+r2 = r2, which
simplifies to 5- r = 0, so r = 5/4
correct answer C
Question: n is a positive integer and k is the product of all integers from 1 to n inclusive. If k is a multiple of 1800, then what is the smallest possible value of n?
A.8
B.10
C.12
D.15
Answer: B.10
Explanation: 1800=2^3*3^2*5^2
5^2 means that n must be at least 10. That is, We need 5 and 10.
The answer is B.
Question: One hour after Yolanda started walking from X to Y, a distance of 80 miles, Bob started walking along the same road from Y to X. If Yolandaâs walking rate was 8 miles per hour and Bobâs was 9 miles per hour, how many miles had Bob walked when they met?
A.38.07
B.40
C.42
D.39
Answer: A.38.07
Explanation: Let t be the number of hours that Bob had walked when he met Yolanda. Then, when they met, Bob had walked 4t miles and Yolanda had walked 8(t + 1) miles. These distances must sum to 80 miles, so 9t + 8(t + 1) = 80, which may be solved for t as follows
9t + 8(t + 1) = 80
9t + 8t + 8 = 80
17t = 72
T = 4.23 (hours)
Therefore, Bob had walked 9t = 9(4.23) = 38.07 miles when they met. The best answer is A.
Question: Timothy leaves home for school, riding his bicycle at a rate of 9 miles per hour. Fifteen minutes after he leaves, his mother sees Timothy’s math homework lying on his bed and immediately leaves home to bring it to him. If his mother drives at 33 miles per hour, how far (in terms of miles) must she drive before she reaches Timothy?
I think is a 700 level problem but I tag it as 600/700, let me know. Either way I hope in an explanationThanks
A.1/3
B.3
C.27/8
D.9
Answer: C.27/8
Explanation: In 15 mins, Timothy travels=9/4 miles.
Now, let his mother takes x hours to reach him, traveling at 31mph.
So, 33x=9x+9/4
x=3/32 hrs.
Thus, the distance traveled by his mother to reach= 36*3/32=27/8 miles. Ans C
Question: There are deer and peacocks in a zoo. By counting heads they are 80. The number of their legs is 200. How many peacocks are there ?
A.20
B.30
C.50
D.60 peacocks
Answer: D.60 peacocks
Explanation: Explanation:
Let x and y be the number of deer and peacocks in the zoo respectively. Then,
x + y = 80 ...(i) and
4x + 2y = 200 or 2x + y = 100 ...(ii)
Solving (i) and (ii), we get) x = 20, y = 60.
Answer: D
Question: What is the two-digit number? I. Sum of the digits is 7. II. Difference between the number and the number obtained by interchanging the digits is 9. III. Digit in the ten's place is bigger than the digit in the unit's place by 1.
A.I and II
B.II and III
C.I and III
D.I and II as well as I and III
Answer: D.I and II as well as I and III
Explanation: Explanation:
Let the tens and units digit be x and y respectively.
I. x + y = 7.
II. (10x + y) - (10y + x) = 9 x - y = 1.
III. x - y = 1.
Thus, I and II as well as I and III give the answer.
Correct answer is (D).
Question: Car A travels at three times the average speed of car B. Car A started to travel at 12:00 o'clock, car B started to travel at 16:00 o'clock. What is the speed of car B (in Km/h) if the total distance that both cars traveled until 18:00 was 3000 Km?
A.100.
B.25.
C.30.
D.150.
Answer: D.150.
Explanation: Total distance= Distance travelled by A +Distance travelled by car B
Distance= speed*time
Distance of A= 3x * 6
Distance of B= x*2
(3x * 6) + (x*2) = 3000
x= 150 KM/hr
D is the answer
Question: Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even ?
A.1/4
B.3/4
C.4/7
D.4/11
Answer: B.3/4
Explanation: Total number of cases = 6*6 = 36
Favourable cases = [(1,2),(1,4),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,2),(3,4),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,2),(5,4),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)] = 27
So Probability = 27/36 = 3/4
B)
Question: 55th word of SHUVANK in dictionary??
A.AHSNKUV
B.AHNKSVU
C.AHNKUSV
D.AHNKUVS
Answer: A.AHSNKUV
Explanation: First of all write letters in the alphabetical order : A,H,K,N,S,U,V
Then we fix the in order AHK_ _ _ _=> we get 4! means 24 words.
After Next letter in alphabetical order is AHN_ _ _ _=> we get 4! means 24 words
Now we get total 48 words.. Then
In order to Next word is AHSK_ _ _ => Filling this we can fill in 3! Ways means 6.
Now we get total 54 words then next Word is AHSNKUV
ANSWER:A
Question: If the price of a book is first decreased by 25% and then increased by 20%, then the decrease in the price will be?
A.20%
B.10%
C.25%
D.18%
Answer: B.10%
Explanation: Let the original price be $100
New final price = 120% of (75% of $100)
= 120/100 * 75/100 *100 = $90
Decrease is 10%
Answer is B
Question: A person covers a distance in 21 minutes. If runs at a speed of 12 km per hour on an average. Find the speed at which he must run to reduce the time of journey to 5 minutes.
A.18 m/s
B.4 m/s
C.14 m/s
D.10 m/s
Answer: C.14 m/s
Explanation: Explanation:
T = 21 m
Spees = 12 kmph
= 12 x 5/18 = 10/3 m/s
Let new speed be "x"
21 x (10/3) = 5x
x = 14 m/s
Answer: Option C
Question: Barbara has 10 shirts and 8 pants. How many clothing combinations does Barbara have, if she doesn’t wear 2 specific shirts with 3 specific pants?
A.41
B.66
C.36
D.70
Answer: D.70
Explanation: Total no of combinations available is= 10 shirts X 8 pants = 80
Eliminate the 2shirts X 3 pants combo = 6 which gives.......>> 80-6=74
ANSWER: D
Question: A dishonest shopkeeper professes to sell pulses at the cost price, but he uses a false weight of 960gm. for a kg.His gain is …%.
A.4.16%
B.5.36%
C.4.26%
D.6.26%
Answer: A.4.16%
Explanation: His percentage gain is 100*40/960 as he is gaining 40 units for his purchase of 960 units.
so 4.16%.
ANSWER:A
Question: The average age of a group of persons going for picnic is 16 years. Twelve new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for picnic is
A.5
B.10
C.12
D.40
Answer: C.12
Explanation: Solution
Let the initial number of persons be x. Then
16x + 12 x 15 = 15.5(x+20)
= 0.5x = 6
x = 12.
Answer C
Question: What percent is 36 paisa's of 12 rupees?
A.2 %
B.3 %
C.4 %
D.5 %
Answer: B.3 %
Explanation: 12 Rupees = 1200 paisa's
36/1200 × 100 = 3/12
12/3 = 3 %
B
Question: 9C2 + 9C3 +10C4=?
A.300
B.330
C.360
D.390
Answer: B.330
Explanation: 36+84+210=330
ANSWER:B
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when No boy gets more than one prize?
A.10
B.15
C.17
D.24
Answer: D.24
Explanation: Sol. In this case, repetitions are not allowed. So, the first prize can be given in 4 ways. The second in 3 ways and the third in 2 ways. But fundamental principle, (4 x 3 x 2) ways = 24 ways
4: Or 4p = — 4:- 4X3X2X1- 24 ways
D
Question: In 12 pumps can raise 1218 tons of water in 11 days of 9 hrs each, how many pumps will raise 2030 tons of water in 12 days of 11 hrs each?
A.12
B.15
C.18
D.21
Answer: B.15
Explanation: Explanation:
pumps work time
12 1218 99
x 2030 132
=> 1218/(912*99) = 2020/(x × 132)
=> x = 15 pumps
Answer: Option B
Question: What is the difference between the C.I. on Rs. 7000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly?
A.s.2.04
B.s.2.08
C.s.2.02
D.s.2.86
Answer: D.s.2.86
Explanation: C.I. when interest is compounded yearly
= [7000 * (1 + 4/100) * (1 + (1/2 * 4)/100]
= 7000 * 26/25 * 51/50 = Rs. 7425.6
C.I. when interest is compounded half-yearly
= [7000 * (1 + 2/100)2]
= (7000 * 51/50 * 51/50 * 51/50)
= Rs. 7428.46 Difference
= (7428.46 - 7425.6)
= Rs.2.86.
Answer: D