RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A solid yellow stripe is to be painted in the middle of a certain highway. If 1 gallon of paint covers an area of q square feet of highway, how many gallons of paint will be needed to paint a stripe of t inches wide on a stretch of highway m miles long? (1 mile = 5,280 feet and 1 foot = 12 inches)
A.(5,280 mt) / 12 q
B.(5,280 pt) / 12m
C.(5,280 pmt) /12
D.(5,280)(12m) / pt
Answer: A.(5,280 mt) / 12 q
Explanation: Given that: 1 gallon of paint covers an area ofqsquare feet. Question:how many gallonsof paint will be needed ...
In any case you will have:(total area in square feet)/(gallons per feet)=(total area in square feet)/q, so q must be in the denominator: eliminate all but A and D.
Now, lets see where should be t: (area in square feet)=(width in feet)*(length in feet) --> width=tinchesas1 feet=12 inchesthent inches=t/12 feet, so (area in square feet)=(t/12) * (length in feet), so t must be in the nominator: only A is left.
Answer: A.
Question: Two twins sisters Sita and Geeta were standing back to back and suddenly they started running in opposite direction for 4 miles and then turn to left and run for another 3 miles.
what is the distance between the the two twins when they stop ?
A.11 miles
B.10 miles
C.9 miles
D.12 miles
Answer: B.10 miles
Explanation: B
10 miles
Question: In the biology lab of "Jefferson" High School there are 0.037*10^5 germs, equally divided among 148000*10^(-3) Petri dishes. How many germs live happily in a single dish?
A.10
B.25
C.35
D.40
Answer: B.25
Explanation: 0.037*10^5 can be written as 3700
148000*10^(-3) can be written as 148
Required= 3700/148= 25
ANSWER:B
Question: The bankerâ€™s gain on a sum due 3 years hence at 12% per annum is Rs. 180. The bankerâ€™s discount is
A.Rs.960
B.Rs.840
C.Rs.1020
D.Rs.680
Answer: D.Rs.680
Explanation: Solution
T.D	=(B.G x 100 / R x T)
= Rs.(180x100/12 x 3)
= Rs.500.
B.D
=Rs(500+ 180)
= Rs.680.
Answer D
Question: A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
A.39
B.27
C.30
D.288
Answer: C.30
Explanation: US = 25
DS = 35
M = (35 + 25)/2 = 30
Answer: C
Question: An entrepreneurship competition requires registering teams to have 3 team members, at least one of which must be a technology co-founder. If all team members must come from the auditorium during the meet and greet event which has 4 technologists and 9 businessmen, how many possible team submissions are possible?
A.76
B.100
C.162
D.198
Answer: D.198
Explanation: P(at least one Tech)= p(total) - P( no tech)
=13c3 - 9c3
=198 (Ans :D )
Question: If the cost price of 65 chocolates is equal to the selling price of 50 chocolates, the gain percent is :
A.35%
B.10%
C.20%
D.30%
Answer: D.30%
Explanation: Explanation :
Solution: Let C.P. of each chocolate be Re. 1. then, C.P. of 50 chocolates = Rs. 50;
S.P. of 50 chocolates =Rs. 65.
.'. Gain% = 15*100/50 = 30%
Answer : D
Question: A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?
A.2:6
B.2:9
C.2:3
D.2:2
Answer: C.2:3
Explanation: Let the principal be P and rate of interest be R%.
Required ratio = [(P * R * 6)/100] / [(P * R * 9)/100] = 6PR/9PR = 6/9 = 2:3
Answer: C
Question: If 0 < Z < Y, Z is an odd number and Y is a prime number, which of the following can be the value of Z + Y ?
A.11.
B.13.
C.17.
D.10.
Answer: D.10.
Explanation: If Z is odd ,implies Z(odd)+y(odd/even prime)=(Even/Odd)
If Y is even, the 2 is the even prime , therefore y=2z=1 since 0<Z<Y therefore Z+Y =3. But 3 is not an option
which implies y is odd,
Now Z(odd)+Y(odd)=Even
10 is the only option that is even=D
Question: on dividing a N by 9,remainder is 8. the quotient obtained when divided by 11,leaves remainder 9. now the quotient when divided by 13,leaves remainder 8. find the remainder when when the N is divided by 1287
A.871
B.881
C.891
D.904
Answer: B.881
Explanation: take from the last step division
suppose no. is n which is divided by 13 and remainder 8 = 13n+8
now 13n+8 will be the no. which is divided by 11 and remainder is 9
= [11*(13n+8)]+9
now this no. is used for the very first step which is divider is 9 and remainder is 8
={9*[11*(13n+8)]+9}+8 solve and ans is 881
ANSWER:B
Question: If the current in a circuit equals 0 A, it is likely that the
A.22
B.37
C.36
D.28
Answer: D.28
Explanation: Answer: Option D
Question: I have a basket of 500 apples.
I want to divide them equally into 20 places.
How long will it take to divide if for each 25 apples counted i spent 5 minutes ?
A.199
B.100
C.60
D.5
Answer: B.100
Explanation: 500 apples divided by 20 is 25. If it takes 5 minutes to sort out 25 apples then it would take 100 minutes to perform the same task 20 times
Answer is B
Question: The number of permutations of the letters of the word 'MESMERISE' ?
A.9!/(2!)2 3!
B.9!/(2!)2 8!
C.9!/(2!)2 6!
D.9!/(9!)2 3!
Answer: A.9!/(2!)2 3!
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 'MESMERISE' consists of 10 letters of which there are 2M's, 3E's, 2S's and 1I and 1R.
Number of arrangements = 9!/(2!)2 3!
Answer: A
Question: A carton contains 25 bulbs, 8 of which are defective. What is the probability that if a sample of 4 bulbs is chosen, exactly 2 of them will be defective ?
A.(8/25) x (7/24) x (17/23) x (16/22)
B.(4C2) x (8/25) x (7/24) x (17/23) x (16/22)
C.(8/26) x (8/24) x (17/33) x (16/22)
D.None of these
Answer: B.(4C2) x (8/25) x (7/24) x (17/23) x (16/22)
Explanation: Explanation :
The probability that exactly two bulbs are defective and exactly two are not defective will be given by
(4C2) x (8/25) x (7/24) x (17/23) x (16/22)
Answer : B
Question: If 2994 Ã· 14.5 = 171, then 29.94 Ã· 1.45 = ?
A.17.1
B.17.3
C.17.5
D.17.7
Answer: A.17.1
Explanation: 29.94/ 1.45 = 299.4/14.5
= (2994/14.5) x 1/10) [ Here, Substitute 171 in the place of 2994/14.5 ]
= 171/10
= 17.1
Answer is A.
Question: Solve(0.76 × 0.76 × 0.76 − 0.008)/(0.76 × 0.76 + 0.76 × 0.2 + 0.04)
A.0.56
B.0.71
C.0.45
D.0.67
Answer: A.0.56
Explanation: Option 'A'
Question: The perimeter of a rectangular yard is completely surrounded by a fence that measures 36 meters. What is the length of the yard if the area of the yard is 40 meters squared?
A.12
B.10
C.8
D.14
Answer: C.8
Explanation: Perimeter of rectangular yard = 2(l + b) = 36 --> l + b = 18
Area = l * b = 40
b = 18 - l
l(18 - l) = 40
18l - l^2 = 40
l^2 - 18l + 40 = 0
Upon simplifying we get l = 5 or 8. Only 8 is there in the answer choice.
Answer: C
Question: A train 110 m long is running with a speed of 56 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
A.5
B.6.4
C.7
D.8
Answer: B.6.4
Explanation: Speed of train relative to man = 56 + 6 = 62 km/hr.
= 62 * 5/18 = 155/9 m/sec.
Time taken to pass the men = 110 * 9/155 = 6.4 sec.
Answer: Option B
Question: A person starting with Rs.64 and making 6 bets, wins three times and loses 3times, the wins and loses occurring in random order. The chance for a win is equal to the chance for a loss. If each wager is for half the money remaining at the time of the bet, then the final result is?
A.Rs.37
B.Rs.40
C.Rs.45
D.Rs.47
Answer: A.Rs.37
Explanation: As the win leads to multiplying the amount by 1.5 and loss leads to multiplying the amount by 0.5, we will multiply initial amount by 1.5 thrice and by 0.5 thrice (in any order).
The overall resultant will remain same.
So final amount with the person will be (in all cases):
=64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)==64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)= Rs 2727
Hence the final result is:
64−27=3764−27=37:
A loss of Rs.37
A
Question: The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?
A.16 2/3% loss
B.16 7/3% loss
C.18 2/3% loss
D.16 2/9% loss
Answer: A.16 2/3% loss
Explanation: 15 CP = 18 SP
18 --- 3 CP loss
100 --- ? => 16 2/3% loss
Answer:A
Question: A woman buys two articles for Rs.1980 each and he gains 10% on the first and loses 10% on the next. Find his total gain or loss percent?
A.10%
B.1%
C.-1%
D.-10%
Answer: B.1%
Explanation: B
Question: If 2/a + 3/a + 7/a is an integer, which of the following must also be an integer?
A.12/a
B.3/a
C.6/a
D.9/a
Answer: A.12/a
Explanation: 2/a + 3/a + 7/a
=12/a
Answer A
Question: The average of 30 results is 20 and the average of other 20 results is 30 . what is the average of all the results?
A.24
B.25
C.48
D.50
Answer: A.24
Explanation: Answer
Sum of 50 result = sum of 30 result + sum of 20 result.
= 30 x 20 + 20 x 30
= 1200
Correct Option: A
Question: Fresh dates contain 90% water while dry dates contain 28% water . How many kg of dry dates can be obtained from 36kg of fresh dates ?
A.5Kg
B.10Kg
C.12 Kg
D.16Kg
Answer: A.5Kg
Explanation: 36 kilograms of fresh dates contain 0.1*36=3.6 kilograms of non-water.
Dry dates obtained from these fresh dates will contain the same amount of non-water and we are told that this amount should be 72% of the dry dates, thus x*0.72=3.6 --> x=5 kilograms.
Answer: A.
Question: Can you find the smallest non fractional number such that
If the number gets divided by 13 , we get the remainder of 1;
If the number gets divided by 14 , we get the remainder of 2
If the number gets divided by 15 , we get the remainder of 3;
If the number gets divided by 16 , we get the remainder of 4.
A.55321
B.30238
C.58020
D.44141
Answer: B.30238
Explanation: B
30238.
As we know LCM of the numbers 13 14 15 & 16 is 30240
So if i divide 30240 by any of the four number , it gives remainder as 0.
Now to get reminder as desired, is should be 2 short of 30238. (3-1,4-2,5-3,6-4 )
Ans:option B
Question: The difference between the place values of 7 and 3 in the number 527435 is
A.4
B.5
C.45
D.6970
Answer: D.6970
Explanation: Sol.
= (Place value of 7) – (place Value of 3)
= (700 - 30)
= 6970
Answer D
Question: In a group of 160 people, 90 have an age of more 30 years, and the others have an age of less than 20 years. If a person is selected at random from this group, what is the probability the person's age is less than 20?
A.0.44
B.0.55
C.0.65
D.0.75
Answer: A.0.44
Explanation: Number of people whose age is less than 20 is given by
160 - 90 = 70
Probability P that a person selected at random from the group is less than 20 is gieven by
70 / 160 = 0.4375 ~ 0.44
correct answer A
Question: Find the missing couple of letters in the following series:
AZ, GT, MN, ? , YB
A.SE
B.SM
C.SO
D.SH
Answer: D.SH
Explanation: D
SH
If you look closely, you will see that the first letter of every set is moving 6 alphabets forward while the second one is moving six alphabets backwards.
Question: The market value of a 10.5% stock, in which an income of Rs. 756 is derived by investing Rs. 7500, brokerage being 1/4%, is:
A.103.92
B.114
C.114.75
D.124
Answer: A.103.92
Explanation: Face Value = Rs. 7500.
Dividend = 10.5%.
Annual Income = Rs. 756.
Brokerage per Rs. 100 = Rs. 0.25.
Dividend is always paid on the face value of a share.
Face Value * Dividend / (Market Value + Brokerage per Rs. 100) = Annual income.
= 7500 * 10.5 / 756 = Market Value of Rs. 100 stock + Brokerage per Rs. 100.
= Market Value of Rs. 100 stock + Brokerage per Rs. 100 = Rs. 104.17
= Market Value of Rs. 100 stock = Rs. 104.17 - Re. 0.25.
= Market Value of Rs. 100 stock = Rs. 103.92.
answer : A
Question: A man two flats for $675958 each. On one he gains 13% while on the other he loses 13%. How much does he gain or lose in the whole transaction?
A.1.69%
B.2.56%
C.3.12%
D.4.65%
Answer: A.1.69%
Explanation: In such a case there is always a loss
Loss% = (13/10)^2 = 120/71 = 1.69%
Answer is A
Question: Calculate the HCF of 69, 561, 963
A.4
B.5
C.22
D.3
Answer: D.3
Explanation: Explanation:
Lets solve this question by factorization method.
The factors of 69 are: 1, 3, 23, 69
The factors of 561 are: 1, 3, 11, 17, 33, 51, 187, 561
The factors of 963 are: 1, 3, 9, 107, 321, 963
Then the greatest common factor is 3.
Answer: Option D
Question: A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 1 students left over. What is the sum of the two smallest possible values of n?
A.33
B.62
C.49
D.53
Answer: B.62
Explanation: 4x+1 = 5y+ 1...........ie: 4x-5y = 2
x,y must be >1 and y is even ie ( 2,4,6,..etc)
if y = 2 thus x = fraction (not possible)
if y = 4 thus x =5 n =21
if y = 6 thus x = not possible fraction
if y =8 thus x = 10 n =41
21+41 = 62.....
B
Question: A pupil's marks were wrongly entered as 73 instead of 65. Due to the average marks for the class got increased by half. The number of pupils in the class is?
A.18
B.82
C.16
D.27
Answer: C.16
Explanation: Let there be x pupils in the class.
Total increase in marks
= (x * 1/2) = x/2
x/2 = (73 - 65) => x/2
= 8 => x = 16.
Answer: C
Question: Tammy climbed a mountain in two days. She spent a total of 14 hours climbing the mountain. On the second day, she walked at an average speed that was half a kilometer per hour faster, but 2 hours less than what she walked on the first day. If the total distance she climbed during the two days is 52 kilometers, how many R kilometers per hour did Tammy walk on the second day?
A.3
B.3.5
C.4
D.4.5
Answer: C.4
Explanation: Ans: C
Total time = 14 hrs
Let time traveled during 1st day = x
Let time traveled during 2nd day = x-2
Total time =14
x+x-2 = 14
x=8
speed * time = distance
s*8 + (s+0.5)(8-2) = 52
solving s = 4.5
now speed for 2nd day is 0.5 less than the 1st day which is 4.5
Thus speed for 2nd day = 4
Its simple algebra for s*8 + (s+0.5)(8-2) = 52 but for some reason Im getting 3.5 and not 4.5.
8s+6s+3=52
14s=49
s=3.5
Question: The three sides of an acute angled triangle (all in cms) are 12, 19 and h. How many integer values can h take?
A.23
B.22
C.15
D.8
Answer: D.8
Explanation: In acute angle triangles all angles in the triangle should be less than 90.
The maximum length of h can be when it is the hypotenuse of the triangle.
So, h= sqrt(12^2 + 19^2) = 22.5 (approx)
The maximum length of h can be when side of length 12 is the hypotenuse of the triangle.
So, h = sqrt (19^2 - 12^2) = 14.7 (approx)
So, h>14.7 and h<22.5.
Hence, possible values for h can be 15,16,17,18,19,20,21 and 22. Total 8 values.
Answer D.
Question: A boat takes 3 hours to travel from place M to N down stream and back from N to M upstream. If the speed of the boat instill water is 4 km/hr, what is the distance between the two places?
A.8 km
B.12 km
C.6 km
D.Data inadequate
Answer: D.Data inadequate
Explanation: Let the distance between M and N and the speed of current in still water be d km and x km/hr respectively.
According to the question, d/4+x+d/4−x=3
In the above equation we have only one equation but two variables, hence, can’t be determined.
Answer D
Question: The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 23hrs. How much distance will the car cover in 4hrs if the speed of the bike is twice speed of the tractor?
A.300 km
B.320 km
C.360 km
D.420 km
Answer: C.360 km
Explanation: Sol. Average speed of a tractor = 25 km / h
The speed of a bus in an hour = 25 × 2 = 50 km
The speed of a car in an hour = 9/5 * 50 = 90 km
So, the distance covered by car in 4 h is
90 × 4 = 360 km
Ans.(C)
Question: A alone can finish a work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of a total wages of Rs.3300, A will get:
A.Rs.1200
B.Rs.1500
C.Rs. 1980
D.Rs.2000
Answer: C.Rs. 1980
Explanation: Explanation:
Ratio of working days of A : B = 10 : 15
Therefore, their wages ratio = reverse ratio = 15 : 10
Therefore, A will get 15 units of ratio
Total ratio = 25
1 unit of ratio =3000/25 = 132
So, A’s amount = 120 × 15 = Rs.1980.
Answer: Option C
Question: Find the missing figures: 0.75% of ? = 0.06
A.4
B.6
C.8
D.10
Answer: C.8
Explanation: Let 0.75% of x = 0.06. Then , 0.75*x/100 = 0.06
X= [(0.06*100)/0.75] = 8.
Answer is C.
Question: How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
A.20 sec
B.10 sec
C.30 sec
D.40 sec
Answer: C.30 sec
Explanation: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters
Answer:C
Question: Two clocks begin to strike 12 together. One strikes in 33 seconds and the other in 22 secs. What is the interval between the 6th
stroke of the first and the 8th
stroke of the second?
A.11 secs
B.12 secs
C.10 secs
D.13 secs
Answer: A.11 secs
Explanation: Time of 6th strike of first clock = 5*33= 165 secs after 1200 hrs
Time of 8th strike of 2nd clock = 7*22= 154 secs after 1200 hrs
Time interval between the 6th stroke of the first and the 8th stroke of the second = 165-154=11 secs
ANSWER:A
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 $1.85?
A.1680
B.1420
C.1120
D.970
Answer: B.1420
Explanation: The charge is 65 cents for the first 250 grams.
This leaves a charge of $1.85 - $0.65 = $1.20
The charge for the next 1100 grams is $1.10 which leaves a charge of $0.10
The weight is somewhere between 1350 and 1450.
The answer is B.
Question: The sector of a circle has radius of 35 cm and central angle 135o. Find its perimeter?
A.91.5 cm
B.92.2 cm
C.152.5 cm
D.29.2 cm
Answer: C.152.5 cm
Explanation: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 35) + 2(35)
= 82.5 + 70 = 152.5 cm
Answer:C
Question: The ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 28 years. The ratio of their ages after 5 years will be
A.22 : 17
B.9 : 11
C.5 : 4
D.4 : 5
Answer: A.22 : 17
Explanation: Let Mini’s age = 4x and Minakshi’s age = 3x
Then 4x + 3x = 28
x = 4
Mini’s age = 16 years
And Minakshi’s age = 12 years
Ratio of their ages after 8 years = (16 + 5) : (12 + 5) = 22 : 17
ANSWER:A
Question: Today Katherine, who is 40 years old, and her daughter, who is 10 years old, celebrate their birthdays. How many years will pass before Katherine’s age is twice her daughter’s age?
A.22
B.20
C.23
D.24
Answer: B.20
Explanation: Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.
After x years passes Katherine’s age will be (40+x) years old, and her daughter’s age will be (10+x) years old. Since the Katherine’s age is twice her daughter’s age (40+x)= 2 * (10+x) ---> 40+x=20+2x ---> x= 20.
The answer is (B).
Question: A Coach is filling out the starting lineup for his indoor soccer team. There are 10 boys on the team, and he must assign 6 starters to the following positions: 1 goalkeeper, 2 on defence, 2 in midfield, and 1 forward. Only 2 of the boys can play goalkeeper, and they cannot play any other positions. The other boys can each play any of the other positions. How many different groupings are possible?
A.60
B.210
C.2580
D.3360
Answer: D.3360
Explanation: 2C1 select 1 goalkeeper from 2 boys;
8C2 select 2 defense from 8 boys (as 2 boys can only play goalkeeper 10-2=8);
6C2 select 2 midfield from 6 boys (as 2 boys can only play goalkeeper and 2 we've already selected for defense 10-2-2=6);
4C1 select 1 forward from 4 boys (again as 2 boys can play only goalkeeper, 4 we've already selected for defense and midfield 10-2-4=4)
Total # of selection=2C1*8C2*6C2*4C1=3360
Answer: D.
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
A.6
B.6.25
C.6.5
D.7
Answer: A.6
Explanation: equired run rate = 282 - (3.2 x 10)/40 =	250/40 = 6.25
ANSWER A
Question: A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
A.22 days
B.20 days
C.67 days
D.17 days
Answer: B.20 days
Explanation: C = 1/2 - 1/4 - 1/5 = 1/20
=> 20 days
Answer:B
Question: The ratio of investments of two partners A and B is 7:5 and the ratio of their profits is 7:10. If A invested the money for 5 months, find for how much time did B invest the money ?
A.25 months
B.11 months
C.16 months
D.10 months
Answer: D.10 months
Explanation: 7x5: 5xk = 7:10
k = 10 months
Answer: D
Question: Ramu bought an old car for Rs. 42000. He spent Rs. 15000 on repairs and sold it for Rs. 64900. What is his profit percent?
A.13.8
B.77
C.18
D.99
Answer: A.13.8
Explanation: Total CP = Rs. 42000 + Rs. 15000 = Rs. 57000 and SP = Rs. 64900
Profit(%) = (64900 - 57000)/57000 * 100 = 13.8%
Answer: A
Question: John want to buy a $100 Trouser at the store, but he think it’s too expensive. Finally, it goes on sale for $60. What is the percent decrease?
A.20%
B.30%
C.40%
D.50%
Answer: C.40%
Explanation: The is always the difference between our starting and ending points. In this case, it’s 100 – 60 = 40. The “original” is our starting point; in this case, it’s 100. (40/100)*100 = (0.4)*100 = 40%.
C
Question: A number when divided by 221 gives a remainder 43, what remainder will be obtained by dividing the same number 17?
A.7
B.6
C.9
D.2
Answer: C.9
Explanation: Explanation:
221 + 43 = 264/17 = 9 (Remainder)
Answer: C
Question: The sum of 3 hours 45 minutes and 2 hours 55 minutes is approximately what percent of a day?
A.14%
B.16%
C.24%
D.28%
Answer: D.28%
Explanation: Since the question is asking for an approximate percentage
3:45+2:55 ~ 7 hours
% of day = 7*100/24 ~ 7*100/25= 28%
Answer is D.
Question: Current ages of Rahim and Thomas are in the ratio of 5 : 4 correspondingly. 0.3 decades hence, the ratio of their ages will become 11 : 9 correspondingly, What is Thomas’s current age in years?
A.24 years
B.44 years
C.34 years
D.64 years
Answer: A.24 years
Explanation: A
24 years
If current ages of Rahim and Thomas be 5A years and 4A years correspondingly
Then, 5A + 3 = 11
4A + 3 = 9
9(5A + 3)=11(4A + 3)
A = 6
Thomas’s current age = 4A
= 24 years.
Question: Three years ago the average age of a class of six members was 21 years. A boy have been added, the average age of the class is the same today. What is the age of the boy?
A.A)1
B.B)2
C.C)3
D.D)4
Answer: C.C)3
Explanation: 6 * 24 = 144
7 * 21 = 147
`3
C
Question: The average runs scored by a batsman in 20 matches is 40. In the next 30 matches the batsman scored an average of 20 runs. Find his average in all the 50 matches?
A.31
B.46
C.28
D.13
Answer: C.28
Explanation: Total score of the batsman in 20 matches = 800.
Total score of the batsman in the next 30 matches = 600.
Total score of the batsman in the 50 matches = 1400.
Average score of the batsman = 1400/50 = 28.
Answer:C
Question: What is the least value of p, so that 123p578 is divisible by 11
A.7
B.8
C.6
D.5
Answer: B.8
Explanation: Explanation:
123p578
1 + 3 + 5 + 8 = 17
2 + p + 7 = 17
=> 9 + p = 17
=> p = 17 - 9
=> p = 8
Answer: Option B
Question: A firm has 4 senior partners and 6 junior partners. How many different groups F of 3 partners can be formed in which at least one member of the group is a senior partner. (2 groups are considered different if at least one group member is different)
A.48
B.100
C.120
D.288
Answer: B.100
Explanation: What seems to work as well, though its tougher to come up with this solution:
(10*9*8) * 2/3 + (10*9*4)*1/3 = 600. Divided by all possible permutations (=3!) yields 100.
Explanation: For the first spot you have 10 possible canditates, for the 2nd 9. For the 3rd spot you need to differentiate if a senior partner has been picked for one of the first 2 spots or not. If yes, then you can pick one of the 8 remaining guys, so 10*9*8. If no senior partner has been picked yet, you need 10*9*4.
Now you need to weight the 2 cases with the corresponding probabilities: probability of no senior partner being picked in the first 2 draws = 6/10*5/9=1/3, so you weight 10*9*4 with 1/3. For the complementary case (senior partner was picked in the first 2 draws) you just take the complementary prob (1-1/3)= 2/3 and weight 10*9*8 with it.
Now you just need to divide the answer (600) by the number of different positions (=3!) and get F=600/6=100.B