RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: What is the sum of the multiples of 6 from 48 to 72, inclusive?
A.500
B.600
C.700
D.300
Answer: D.300
Explanation: The formula we want to use in this type of problem is this:
Average*Total Numbers=Sum
First, find the average by taking the sum of the F + L number and divide it by 2:
A = (F + L)/2
Second, find the total numbers in our range by dividing our F and L numbers by 7 and add 1.
(72/6) - (48/6) + 1
Multiply these together so what we show Average*Total Numbers=Sum
(48 + 72)/2 * (72/6) - (48/6) + 1 = Sum
60 * 5 = 300
D
Question: A steel vessel has a base of length 60 cm and breadth 30 cm. Water is poured in the vessel. A cubical steel box having edge of 30 cm is immersed completely in the vessel. How much will the water rise?
A.7.5 cm rise
B.10 cm rise
C.15 cm rise
D.30 cm rise
Answer: C.15 cm rise
Explanation: Explanation:
Volume of Cube=a3=a*a*a
60cm*30cm*H=30cm*30cm*30cm
H=15cm
ANSWER IS C
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 60 kg. What might be the weight of the new person?
A.56 kg
B.80 kg
C.85 kg
D.Data inadequate
Answer: B.80 kg
Explanation: B
80 kg
Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (60 + 20) kg = 80 kg.
Question: The sum of all the digits of the integers from 18 to 21 inclusive is 24 (1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24). What is the sum T of all the digits of the integers from 0 to 99 inclusive?
A.450
B.810
C.900
D.1000
Answer: C.900
Explanation: We want the sum of the digits from 0 to 99, so I approximated:
0-9 ->45-> (9+0)*10/2
40-49 ->85(13+4)*10/2
90-99 ->135(18+9)*10/2
We can see at a glance that theweightgoes up as the numbers go up (meaning the difference between 85 and 45 is 40, while 135-85 is 50, this means that the second part of this sequence carries more weight for our result), so we know that the final answer has to be more than 850 (85*10) but close to it, and that's just T=900:the answer is C.
Question: A certain list consists of 21 different numbers. If n is in the list and n is 2 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?
A.1/20
B.1/12
C.1/5
D.4/21
Answer: B.1/12
Explanation: series : a1, a2....a20,n
sum of a1+a2+...+a20 = 20*x (x = average)
so, n = 2*x
Hence, a1+a2+..+a20+n = 22x
So, the fraction asked = 2x/22x = 1/12
B
Question: if the ratio of two number is 2:5 and LCM of the number is 160 then what is the number.
A.15
B.20
C.16
D.30
Answer: C.16
Explanation: product of two no = lcm *hcf
2x*5x=160*x
x=16
ANSWER:C
Question: A batsman scored 150 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
A.45(4/11) %
B.60 %
C.45(5/11) %
D.44(5/11) %
Answer: B.60 %
Explanation: Explanation :
Total runs scored = 150
Total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60
Total runs scored by running between the wickets = 150 - 60 = 90
Required % = (90/150) × 100 =60%
Answer : Option B
Question: The average monthly salary of 20 employees in an organisation is Rs. 1600. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary ?
A.3700
B.3890
C.88798
D.2789
Answer: A.3700
Explanation: Explanation:
Manager's monthly salary Rs. (1700 * 21 - 1600 * 20) = Rs. 3700.
Answer: A) 3700
Question: If k is an integer and 2 < k < 6, for how many different values of k is there a triangle with sides of lengths 2, 6, and k?
A.0
B.1
C.2
D.3
Answer: B.1
Explanation: (6-2) < k < (6+2)
4 < k < 8
thus k = 5, 6, 7
Since 2 < k < 6, then k can be 5.
The answer is B.
Question: A fill pipe can fill 1/2 of cistern in 20 minutes. In how many minutes, it can fill 1/2 of the cistern?
A.5min
B.10min
C.15min
D.20min
Answer: D.20min
Explanation: Required time = 20*2*1/2 = 20 minutes
Answer is D
Question: A bag contains 4 red balls, 5 green balls and 6 white balls. A ball is drawn at
random from the box. What is the probability that the ball drawn is either red or green?
A.2/5
B.3/5
C.1/5
D.7/15
Answer: B.3/5
Explanation: Total number of balls = (4 + 5 + 6) = 15.
Therefore, n(S) = 15.
Let E1 = event of drawing a red ball.
and E2 = event of drawing a green ball.
Then, E1 n E2 = f.
P (E1 n E2) = P(E1) + P(E2) = (4/15 + 5/15) = 9/15 = 3/5.
ANSWER:B
Question: The number of permutations of the letters of the word 'BUBBLEGUM' is?
A.9!/(2!)2
B.9!/2!
C.9!/3! 2!
D.8!/3! 2!
Answer: C.9!/3! 2!
Explanation: n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways.
The letter pattern 'BUBBLEGUM' consists of 9 letters of which there are 3B's, 2U's, 1L, 1G and 1M.
Number of arrangements = 9!/3! 2!
Answer: C
Question: A shop sells two variants of chocolates - one that costs $3 and the other that costs $5. If the shop sold $112 chocolates on a given day, how many different combinations of (number of $3 sold, number of $5 sold) exist?
A.6
B.7
C.8
D.12
Answer: B.7
Explanation: $112 = 20*$5 + 4*$3
We can find other combinations by reducing the $5 chocolates by 3 (which is -$15)and increasing the $3 chocolates by 5 (which is +$15).
The number of $5 chocolates can be 20, 17, 14,...,2 for a total of 7 combinations.
The answer is B.
Question: A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?
A.3:9
B.3:4
C.3:2
D.3:1
Answer: B.3:4
Explanation: Explanation:
They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
6000 : 8000 => 3:4
Answer:B
Question: A retailer sells 10 shirts. The first 3 he sells for $20,$22 and $25. If the retailer wishes to sell the 10 shirts for an overall average price of over $20, what must be the minimum average price of the remaining 7 shirts?
A.$14.00
B.$16.00
C.$17.00
D.$19.00
Answer: D.$19.00
Explanation: First 3 shirts are sold for $20,$22 and $25=$67.
To get average price of $20,total sale should be 10*$20=$200
So remaining 7 shirts to be sold for $200-$67=$133
Answer should be 133/7=$19.00 that is D
Question: Uncle Bruce is baking chocolate chip cookies. He has 36 ounces of dough (with no chocolate) and 20 ounces of chocolate. How much chocolate is left over if he uses all the dough but only wants the cookies to consist of 10% chocolate?
A.18
B.20
C.16
D.22
Answer: C.16
Explanation: First, you must find the total weight of the mixture given that 80% of it will be dough.
90%*Total = 36 => (9/10)Total=36=> Total=360/9 => Total=40 oz,
From there, you must find 10% of the total 40 oz of the mixture.
10%*Total => (1/10)(40)= 4 oz choclate used,
Not forgetting that the question asks how much chocolate is left over we must subtract the chocolate used from the initial chocolate. 20-4 = 16 oz chocolate left over.
Answer : C
Question: If 4 men can color 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in
A.1 day
B.2 days
C.3 days
D.4 days
Answer: A.1 day
Explanation: The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 6 = 1 day.
A
Question: A certain no. when divided by 20 leaves a remainder 25, what is the remainder if the same no.be divided by 15?
A.3
B.4
C.6
D.8
Answer: A.3
Explanation: Explanation:
20 + 25 = 45/15 = 3 (Remainder)
A
Question: Kim has 7 pairs of shoes; each pair is a different color. If Kim randomly selects 2 shoes without replacement from the 14 shoes, what is the probability that she will select 2 shoes of the same color?
A.1/13
B.1/15
C.11/9
D.1/10
Answer: A.1/13
Explanation: Can be tackled in this way as well: Probability of selecting any 1 out of 14 shoes = 14/14 = 1
Probability of selecting the next shoe (out of 14 available) having the same color = 1/14 (as after selecting the 1st one, there is only 1 another shoe left with the same color).
Thus the total probability = 1*1/13=1/13.
A is the correct answer.
Question: A train 225 m in length crosses a telegraph post in 15 seconds. The speed of the train is?
A.37 kmph
B.34 kmph
C.32 kmph
D.38 kmph
Answer: C.32 kmph
Explanation: S = 225/25 * 18/5
= 32 kmph
Answer: C
Question: A trader owes a merchant $10000 due 1 year hence. The trader wants to settle the account after 2 months. If the rate of interest 12% per annum, how much cash should he pay?
A.$9090.90
B.$9010.90
C.$7090.90
D.$8090.90
Answer: A.$9090.90
Explanation: Required money	= P.W. of $10000 due 10 months hence
= $((10000*100) / 100+ (12*10/12) )
= $9090.90
ANSWER:A
Question: Each of the 20 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and the average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 15 pounds by removing some of the 20-pound boxes, how many 20-pound boxes must be removed?
A.10
B.12
C.14
D.16
Answer: B.12
Explanation: If the average of 10-pound and 20-pound boxes is 18, the ratio of 10-pound boxes:20-pound boxes is 1:4.
So out of 20 boxes, 4 are 10-pound boxes and 16 are 20-pound boxes.
If the average of 10 and 20-pound boxes is to be 15, the ratio of 10-pound boxes:20-pound boxes should be 1:1.
The number of 10 pound boxes remains the same so we still have 4 of them.
To get a ratio of 1:1, the number of 20-pound boxes must be 4.
We need to remove 12 of the 20-pound boxes.
The answer is B.
Question: The cash realised on selling a 14% stock is Rs.104.25, brokerage being 1/4% is?
A.104
B.106
C.102
D.192
Answer: A.104
Explanation: Cash realised= Rs. (104.25 - 0.25)
= Rs. 104.
Answer: A
Question: The triplicate ratio of 2:5 is?
A.1:0
B.8:125
C.1:7
D.1:2
Answer: B.8:125
Explanation: 23: 53 = 8:125
Answer: B
Question: There are 2000 students in a school and among them 10 % of them attends chess class. 50% of the students who are in the chess class are also enrolled for swimming. No other students are interested in swimming so how many will attend the swimming class if all enrolled attends?
A.1
B.10
C.100
D.50
Answer: C.100
Explanation: 10% of 2000 gives 200. so 200 attends chess and 50% of 200 gives 100
so 100 enrolled for swimming
Answer: C
Question: If y is an integer, then y(y - 1)( y- k) must be evenly divisible by three when k is any of the following values EXCEPT
A.-4
B.-6
C.-1
D.2
Answer: B.-6
Explanation: if we put k=-1 we get:
y(y-1)(y+1) rearrange:(y-1)y(y+1)
so it looks like a sequenc,
if we assume that y=2 and put number from the answer then we get:
(y – 1)y(y – k)
k=5 =1.2.-3
k=2 =1.2.0
k=-1 =1.2.3
k=-4 =1.2.6
but when we put
k=-6 =1.2.8 not satisfied
so,the answer is B
Question: The grocer ordered deliveries of apples on each weekday. The numbers of apples he ordered per day were 80, 30, 100, 90 and x. If the median apple delivery was 10 apples larger than the average (arithmetic mean) number of apples delivered, which of the following could be x?
A.50
B.55
C.60
D.65
Answer: A.50
Explanation: Look at the options available
Value of x seems to 50 < = x < = 70
A. 50
B. 55
C. 60
D. 65
E. 70
So position of x is second
30 , x , 80 , 90 , 100
Median = 80
Median number of apples was 10 points higher than the average, so average = 70
30 + x + 80 + 90 + 100 = 350
x = 50 = Answer = A
Question: There are 3 teams each with 6 basket players. How many combinations are there if we were to pick 2 players from the 3 teams such that no team was picked twice?
A.50
B.23
C.108
D.28
Answer: C.108
Explanation: There are altogether three arrangements, which are we can select two members each from team A and B, each from team A and C, and each from team B and C. For each arrangement, there are altogether 36 possibilities (6*6) since each team has 6 players. So there are a total of 108 possibilities (36*3). I hope this method is easier for you to understand.
Question: In a group of 86 students, each student is registered for at least one of three classes – History, Math and English. Twenty-eight students are registered for History, twenty-three students are registered for Math, and forty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?
A.3
B.10
C.9
D.8
Answer: A.3
Explanation: A U B U C = A + B + C - AB-BC-AC + ABC
86 = 28 + 23+ 44 -AB-BC-AC +3 => AB+BC+AC = 12
Exactly Two classes = AB+BC+AC - 3ABC = 12 -3*3 = 3
Hence A
Question: If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is
A.50 km
B.56 km
C.70 km
D.80 km
Answer: A.50 km
Explanation: Let the actual distance travelled be x km.
Then x/10=(x+20)/14
--> 14x = 10x + 200
--> 4x = 200
--> x = 50 km.
Answer : A.
Question: A test paper has 10 questions each worth 4 marks. While taking the test, a student realises that he has attempted questions worth 16 marks. Assuming that whatever question he attempts is completely correct, how many more questions should he attempt so that he is able to secure 90 percent marks?
A.4
B.5
C.6
D.7
Answer: B.5
Explanation: Since the test paper has 10 questions each worth 4 marks, the maximum marks he can get is 40.
His aim is to secure 90 % marks, this means he wants to secure 90% of 40 = 36 marks.
Out of the 36 marks, he has already attempted questions worth 16 marks, so he should attempt questions worth 36 - 16 = 20 more marks.
As every question is worth 4 marks, so to secure 20 more marks he should attempt (20/4) = 5 more questions.
Ans B
Question: The average age of three boys is 48 years and their ages are in proportion 2:5:5. What is the age in years of the youngest boy?
A.30
B.23
C.24
D.26
Answer: C.24
Explanation: 2x + 5x + 5x = 144
x =12
2x = 24
Answer: C
Question: The cash realised on selling a 14% stock is Rs.106.25, brokerage being 1/4% is
A.123
B.106
C.100
D.156
Answer: B.106
Explanation: Explanation:
Cash realised= Rs. (106.25 - 0.25)
= Rs. 106.
Answer: B
Question: A jogger running at 9 kmph along side a railway track is 270 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.18 sec
C.36 sec
D.39 sec
Answer: D.39 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 = (270 + 120) m = 390 m.
∴ Time taken = (390⁄10) sec = 39 sec.
Answer D
Question: Find the average of all prime numbers between 80 and 100
A.88
B.60
C.80
D.89.6
Answer: D.89.6
Explanation: Prime numbers between 80 and 100 are 83, 89, 97
Required average = (83+ 89+ 97)/3 = 269/3 = 89.6
Answer is D
Question: In a birthday party, every person shakes hand with every other person. If there was a total of 28 handshakes in the party, how many persons were present in the party?
A.6
B.7
C.8
D.9
Answer: C.8
Explanation: Suppose there are nn persons present in a party and every person shakes hand with every other person. Then, total number of handshakes
= nC2=n(n−1)/2
n(n−1)=28×2n(n−1)=56
n=8
ANSWER C 8
Question: A train passes a man standing on the platform. If the train is 180 meters long and its speed is 72 kmph, how much time it took in doing so?
A.6 ½ sec
B.4 ½ sec
C.9 sec
D.8 sec
Answer: C.9 sec
Explanation: D = 180
S = 72 * 5/18 = 20 mps
T = 180/20 = 9 sec
Answer: C
Question: The average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by3 months. Find the age of the teacher.
A.22 years
B.23 years
C.24 years
D.25 years
Answer: D.25 years
Explanation: avg of 39 student = 15 yrs
Total age of 39 students=39*15= 585 yrs
Avg age of 39 students + teacher =15+3/12=15.25 yrs
so the total age of (39 student+1 teacher) or 40 persons=
40*15.25=610 yrs
so age of teacher=610-585=25 years
ANSWER:D
Question: A boat running downstream covers a distance of 44 km in 8 hours while for covering the same distance upstream, it takes 10 hours. What is the speed of the boat in still water?
A.5 kmph
B.4.95 kmph
C.6 kmph
D.7 kmph
Answer: B.4.95 kmph
Explanation: Explanation:
Speed downstream = 44/8 = 5.5 kmph
Speed upstream = 44/10 = 4.4 kmph
Speed of the boat in still water = (5.5+4.4)/2 = 4.95 kmph
Answer: Option B
Question: Two numbers are in the ratio 3 : 4. If the sum of numbers is 63, find the numbers.
A.27 and 36.
B.25 and 30.
C.23 and 44.
D.63 and 12.
Answer: A.27 and 36.
Explanation: Sum of the terms of the ratio = 3 + 4 = 7
Sum of numbers = 63
Therefore, first number = 3/7 × 63 = 27
Second number = 4/7 × 63 = 36
Therefore, the two numbers are 27 and 36.
Answer is A
Question: The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 50 with him, what was the average amount with the group before his joining the group?
A.17
B.26
C.15
D.97
Answer: C.15
Explanation: Total members in the group = 7
Average amount = Rs. 20
Total amount with them = 7 * 20
= Rs. 140
One number has Rs. 50. So, the amount with remaining 6 people
= 140 - 50 = Rs. 90
The average amount with them = 90/6
= Rs.15.
Answer:C
Question: There are 10 orators A, B, C, D, E, F, G, H, I and J. In how many ways can the arrangements be made so that A always comes before B and B always comes before C.
A.10! / 3!
B.8! / 6!
C.5! x 3!
D.8! / (5! x 3!)
Answer: A.10! / 3!
Explanation: Select any three places for A, B and C. They need no arrangement amongst themselves as A would always come before B and B would always come before C.
The remaining 7 people have to be arranged in 7 places.
Thus, 10C3 x 7! =10! / 3!
ANSWER:A
Question: A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?
A.37 1/2 days
B.22 days
C.31 days
D.22 days
Answer: A.37 1/2 days
Explanation: Work done by A in 20 days = 80/100 = 8/10 = 4/5
Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1)
Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)
Work done by A and B in 1 day = 1/15 ---(2)
Work done by B in 1 day = 1/15 – 1/25 = 2/75
=> B can complete the work in 75/2 days = 37 ½ days
Option A
Question: The present average age of a family of five members is 26 years. If the present age of the youngest member in the family is ten years, then what was the average age of the family at the time of the birth of the youngest member ? (Assume no death occurred in the family since the birth of the youngest)
A.22 years
B.25 years
C.20 years
D.28 years
Answer: C.20 years
Explanation: Present total age of the members = 26(5) = 130 years.
Present age of the youngest member = 10 years
Present total age of the remaining four members = 130 -10 = 120 years
Their average age at the time of the birth of the youngest member = [120 - (4 * 10)] / 4 = 30 - 10 = 20 years.
Answer: C
Question: 8597 - ? = 7429 - 4358
A.3567
B.6424
C.6835
D.5526
Answer: D.5526
Explanation: D
7429-4358=3071
Let 8597 - x = 3071
Then, x = 8597 - 3071 = 5526
Question: In an increasing sequence of 8 consecutive integers, the sum of the last 4 integers is 822. What is the sum of the first 4 integers in the sequence?
A.800
B.808
C.806
D.802
Answer: C.806
Explanation: Solution:
In solving this problem we must first remember that when we have 8 consecutive integers we can display them in terms of just 1 variable. Thus, we have the following:
Integer 1: x
Integer 2: x + 1
Integer 3: x + 2
Integer 4: x + 3
Integer 5: x + 4
Integer 6: x + 5
Integer 7: x + 6
Integer 8: x + 7
We are given that the sum of the first 4 integers is 570. This means that:
x+7+ x+6 + x+5 + x+4 = 822
4x + 22 = 822
4x = 800
x = 200
The sum of the last 4 integers can be expressed and simplified as:
x+ x+1 + x+2+ x+3 = 4x + 6
Substituting 141 for x yields:
(4)(200) + 6 = 806
Answer: C
Question: A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 11/5 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
A.(a) 7/16
B.(b) 7/15
C.(c) 10/21
D.(d) 22/37
Answer: D.(d) 22/37
Explanation: A simpler way i guess would be to think that in total 5 cups were sold. Out of which 3 are small and 2 are large. Now let the small ones cost $5. so the large ones would cost $11.
So,
3*5=15 and 2*11=22.
Total revenue was 15+22=37
and Large cup sales as found above is 22
Therefore answer is 22/37
D
Question: Find the area of the quadrilateral of one of its diagonals is 40 cm and its off sets 11 cm and 9 cm?
A.100 cm2
B.150 cm2
C.333 cm2
D.400 cm2
Answer: D.400 cm2
Explanation: 1/2 * 40(11 + 9)
= 400 cm2
Answer: D
Question: The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is
A.35.2
B.36.1
C.36.5
D.39.1
Answer: C.36.5
Explanation: Sol.
Therefore correct sum
= ( 36 × 50 + 48 – 23)
= 1825.
Therefore correct mean
= 1825 / 50
= 36.5.
Answer C
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?
A.76 m
B.17 m
C.88 m
D.55 m
Answer: B.17 m
Explanation: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 867
3b2 = 867
b2 = 289 = 172 (b > 0)
b = 17 m.
Answer:B
Question: In seven given numbers,the average of first four numbers is 4 and that of last four numbers is also 4. if the average of these seven numbers is 3, the fourth number is?
A.3
B.4
C.7
D.11
Answer: D.11
Explanation: let 7 numbers are a,b,c,d,e,f,g.
given avg of first 4 nums are 4...i.e (a+b+c+d)/4=4
a+b+c+d=16
given avg of last 4 nums are also 4..i.e.(d+e+f+g)/4=4
d+e+f+g=16
e+f+g=16-d
given avg of 7 nums are 3....i.e (a+b+c+d+e+f+g)/7=3
a+b+c+d+e+f+g=21
16+16-d=21
d=32-21
d=11
ANSWER:D
Question: A code is to be made by arranging 7 letters. Three of the letters used will be the letter A, two of the letters used will be the letter B, one of the letters used will be the letter C, and one of the letters used will be the letter D. If there is only one way to present each letter, how many different codes are possible?
A.42
B.210
C.420
D.840
Answer: C.420
Explanation: we have 7 letters out of which 3 are of one kind, 2 are of another kind..
so total ways = 7!/3!2!=420
ans C
Question: How many times are the hands of a clock at right angle in a day?
A.44
B.21
C.22
D.41
Answer: A.44
Explanation: A
44
In 12 hours, they are at right angles 22 times.
In 24 hours, they are at right angles 44 times.
Question: An amount of Rs.1638 was divided among A, B and C, in the ratio 1/2 : 1/3 : 1/4. Find the share of A?
A.656
B.456
C.756
D.745
Answer: C.756
Explanation: Let the shares of A, B and C be a, b and c respectively.
a : b : c = 1/2 : 1/3 : 1/4
Let us express each term with a common denominator which is the last number divisible by the denominators of each term i.e., 12.
a : b : c = 6/12 : 4/12 : 3/12 = 6 : 4 : 3.
Share of A = 6/13 * 1638 = Rs. 756
Answer: C
Question: Find the total number of distinct vehicle numbers that can be formed using two letters followed by two numbers. Letters need to be distinct.
A.60000
B.65000
C.70000
D.75000
Answer: B.65000
Explanation: Solution:
Out of 26 alphabets two distinct letters can be chosen in 26P2 ways.
Coming to numbers part, there are 10 ways (any number from 0 to 9 can be chosen) to choose the first digit and similarly another 10 ways to choose the second digit.
Hence, there are totally 10 *10 = 100 ways.
Combined with letters there are,
26P2 *100 = 65000 ways to choose vehicle numbers.
Answer: Option B
Question: If a letter is picked randomly from the alphabet, what are the odds of it being in the first 10 letters or being a vowel (a, e, i, o, u, y)?
A.6/13
B.1/2
C.15/26
D.11/26
Answer: B.1/2
Explanation: P(10á´œV) = P(10) + P(V) - P(10âˆ©V), where 10 denotes the first ten letters, and V denotes a vowel.
P(10á´œV) = 10/26 + 6/26 - 3/26
= 1/2
Answer: B
Question: Seed mixture X is 40% ryegrass and 60% bluegrass by weight; seed mixture Y is 25% ryegrass and 75% fescue. If a mixture of X and Y contains 31% ryegrass, what percent of the weight of the mixture is from mixture X?
A.20%
B.30%
C.40%
D.50%
Answer: C.40%
Explanation: 31% is 6%-points above 25% and 9%-points below 40%.
Thus the ratio of mixture Y to mixture X is 3:2.
The percent of mixture X is 2/5 = 40%.
The answer is C.