RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: How many ways can 3 friends be arranged around a circular dinner table?
A.A)16
B.B)2
C.C)96
D.D)120
Answer: B.B)2
Explanation: The number of arrangements of n distinct objects in a row is given by n!n!.
The number of arrangements of n distinct objects in a circle is given by (n−1)!(n−1)!.
The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:
n!n=(n−1)!n!n=(n−1)!.
So, the answer is (3 - 1)! = 2! = 2.
Answer: B.
Question: A dishonest milkman wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing Rs.35 per litre so as to make a profit of 20% on cost when he sells the resulting milk and water mixture for Rs.40 In what ratio should he mix the water and milk?
A.1:20
B.1:10
C.1:8
D.1:4
Answer: A.1:20
Explanation: water = w (liter)
Milk = m (liter)
==> Cost = Price x Quantity = 0.35m
==> Revenue = Price x Quantity = 0.40(m + w)
==> Profit =0.40(m+w) - 0.35m = 0.2*(0.35m)[20% of cost]
==> 0.40m + 0.40w - 0.35m = 0.07m
==> 0.02m = 0.40w
==> m/w = 0.40/0.02 = 20
--OR--
w/m = 1/20
A is correct.
Question: The incomes of two persons A and B are in the ratio 3:4. If each saves Rs.100 per month, the ratio of their expenditures is 1:2 . Find their incomes?
A.150,287
B.150,219
C.150,200
D.150,298
Answer: C.150,200
Explanation: The incomes of A and B be 3P and 4P.
Expenditures = Income - Savings
(3P - 100) and (4P - 100)
The ratio of their expenditure = 1:2
(3P - 100):(4P - 100) = 1:2
2P = 100 => P = 50
Their incomes = 150, 200
Answer:C
Question: The ratio of the radius of two circles is 1: 3, and then the ratio of their areas is?
A.1:8
B.1:6
C.1:9
D.1:3
Answer: C.1:9
Explanation: r1: r2 = 1: 3
Πr12: Πr22
r12: r22 = 1:9
Answer: C
Question: The probability that B can shoot a target two out of two times is 0.45. What is the probability that the target will be missed by B immediately after such two shots?
A.0.25
B.0.5
C.0.55
D.0.4
Answer: C.0.55
Explanation: Suppose there are total 'x' shots.
B shoots 2 out of 2 times. means out of x shots (x>2) B shots 2 out of 2 ----> B shots at least 2 out of x.
therefore, 2/x = 0.25 (given)
the target will be missed by B immediately after such two shots : this means he can shot just twice ...the third shot cannot happen which means he missed (x-2) shots.
thus, the probabilty of missing just after 2 shots is (x-2)/x.
(x-2)/x = 1 - 2/x
= 1 - 0.45
= 0.55
Answer : C
Question: The number 95 can be written as the sum of the squares of 4 different positive integers in two ways. Of the following, which can be the sum of these 4 integers
A.9
B.10
C.16
D.17
Answer: D.17
Explanation: The only possible sum for 4 different squares of an integer with total sum number is 95 are :
49 + 36 + 9 + 1 = 95 which are the square from numbers : 7, 6, 3, 1 (total sum number is 17)
or
81 + 9 + 4 + 1 = 95 which are the square from numbers : 9, 3, 2, 1 (total sum number is 15)
hence the answer is (D)
Question: If the arithmetic mean of seventy-five numbers is calculated, it is 35. if each number is increased by 5, then mean of new number is :
A.30
B.40
C.70
D.90
Answer: B.40
Explanation: Solution
A.M of 75 numbers = 35.
sum of 75 numbers = (75 × 35) = 2625.
total increase = (75 × 5) = 375 .
increased sum = (2625 + 375) = 3000.
increased average = 3000/75 =40 Answer B
Question: A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
A.270
B.227
C.268
D.198
Answer: A.270
Explanation: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 870 = 270
Answer:A
Question: There are 5 locks and 5 keys and each of the 5 keys matches each of the 5 locks. What is the minimum and the maximum trial numbers of attempts Q needed to confirm that each of the 5 keys matches each of the 5 locks?
A.5,15
B.4,15
C.5,10
D.4,10
Answer: D.4,10
Explanation: Assume you have locks 1-5 and keys A-E.
Minimum: assume you are lucky to find the correct key/combo on the first try. So, 1 -> A, 2 -> B, 3 ->C, and 4 -> D, then 5 must match with E. Therefore, you only need to try 4 combos at a minimum.
Maximum: assume that it takes as many guesses as possible. So, with the first key you try A, B, C, and D with no success, therefore E must be the match (so 4 attempts). For key 2 you no longer have E available so you try A, B, and C, with no success, therefore D must be the match (3 attempts). And so on for key 3 (2 attempts) and key 4 (1 attempt). Key 5 matches with the remaining lock for a total of Q=4 + 3 + 2 + 1 = 10 attempts.D
Question: In a class if 1 is absent the rest of them can be divided into 6 equal groups and if two are absent can be divided into 7 equal groups. Find the minimum number of students in the class
A.35
B.36
C.37
D.38
Answer: C.37
Explanation: Multiple of 6 and 7 with difference 1 are 36 and 35
So the number of students in the class is 37
ANSWER:C
Question: In one hour a boat goes 18 km long the stream and 14 km against the stream.The speed of the boat in still water is?
A.17
B.18
C.16
D.15
Answer: C.16
Explanation: Speed in still water A = ½ ( 18+14) km/hr A= 16 kmph
Answer: C
Question: A sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is?
A.33.5
B.33.4
C.33.3
D.33.1
Answer: C.33.3
Explanation: Let B = 100
A = 50
C * (150/100) = 50
3C = 100
C = 33.3 then 'C' Cheapest
Answer: C
Question: If a·b·c·d=270, where a, b, c and d are positive integers, and a<b<c<d, which of the following could be the value of d−a?
A.7
B.10
C.11
D.13
Answer: A.7
Explanation: prime factorize : 270 = 2*3*5*9
Hence a = 2 and d = 9 .
Hence answer is 9 - 2 = 7
Answer A
Question: Seven unbiased coin are tossed. What is the probability of getting almost
one head?
A.1/2
B.1/4
C.127/128
D.127/5
Answer: C.127/128
Explanation: Here n(S)= 2^7
Let E=event of getting atmost one head =
n(E)= 127
P(E)=n(E)/n(S)=127/128
Answer option C)
Question: Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
A.11 1/7
B.11 1/4
C.11 8/4
D.11 9/4
Answer: B.11 1/4
Explanation: 3/12 + x/15 = 1
x= 11 1/4
Answer:B
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
A.444 km
B.400 km
C.450 km
D.500 km
Answer: A.444 km
Explanation: 1h ----- 5
? ------ 60
12 h
RS = 16 + 21 = 37
T = 12
D = 37 * 12 = 444
ANSWER A
Question: A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they taken, if all the three work together?
A.2
B.4
C.5
D.67
Answer: B.4
Explanation: 1/7 + 1/14 + 1/28 = 7/28 = 1/4 => 4 days
Answer: B
Question: A tap can fill a tank in 4 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?
A.2 hr
B.2 hr 30 min
C.2 hr 50 min
D.2 hr 20 min
Answer: B.2 hr 30 min
Explanation: A tap can fill a tank in 4 hours
The tap can fill half the tank in 2 hours
Remaining part = 1/2
After half the tank is filled, three more similar taps are opened.
Hence, total number of taps becomes 4.
Part filled by one tap in 1 hour = 1/4
Part filled by four taps in 1 hour = 4×1/4=1
i.e., 4 taps can fill remaining half in 30 minutes
Total time taken = 2 hour + 30 minute = 2 hour 30 minutes
Answer is B
Question: Jony walks along Sunrise Boulevard daily. He starts walking at 07:00 from block 10 and walks to block 90 where he turns around and walks back to block 70, where he stops at 07:40. The blocks along the boulevard are numbered sequentially (1,2,3), and each block measures 40 meters. What is Jony's speed in meters per minute?
A.88
B.100
C.198
D.216
Answer: B.100
Explanation: Total distance from 10 to 90 =80 + from 90 to 70 =20
So the dist is 100×40(per block dist)
Speed = 4000mts/40min =100m/min
B is the answer
Question: Last year, a certain public transportation system sold an average (arithmetic mean) of 41,000 tickets per day on weekdays (Monday through Friday) and an average of 19,000 tickets per day on Saturday and Sunday. Which of the following is closest to the total number of tickets sold last year?
A.1 million
B.1.25 million
C.10 million
D.12.6 million
Answer: D.12.6 million
Explanation: If you type that into the calculator, it results in 12.7 mil
[D], 12.6 mil, is the correct answer... see 2 posts above for quick approx method
Question: A train covers a certain distance at a speed of 300kmph in 4 hours. To cover the same distance in 2 hours, it must travel at a speed of
A.600km/hr
B.700km/hr
C.800km/hr
D.900km/hr
Answer: A.600km/hr
Explanation: Explanation:
Distance = 300×4 = 1200km
Required speed = (1200/2) = 600km/hr
Answer: Option A
Question: The average of twelve numbers is 7. The average of first nine numbers is 6 and the average of last two numbers is 10. What is the middle number?
A.A)9
B.B)10
C.C)12
D.D)7
Answer: B.B)10
Explanation: The total of twelve numbers = 12X7 = 84
The total of first 9 and last 2 numbers is = 9 X 6+2 X 10 = 74
So, the middle number is (84 - 74 ) = 10
B
Question: If 37 /2% of a number is 900,then 62 1/2% of the number is ?
A.1200
B.1350
C.1500
D.540
Answer: C.1500
Explanation: Answer
Let 371/2% of A = 900
⇒ {(75/2) x A} x 100 = 900
∴ A = (900 x 2 x 100) / 75 = 2400
So, 621/2% of A = (125/2) x (1/100) x 2400 =1500
Correct Option: C
Question: P is the brother of Q and R. S is R's mother. T is P's father. Which of the following statements cannot be definitely true ?
A.Q is K's son
B.Q is L's son
C.Q is S's son
D.Q is T's son
Answer: D.Q is T's son
Explanation: Explanation:
P, Q, R are children of same parents. So. S who is R's mother and T, who is R's father will be mother and father of all three.
However, it is not mentioned whether Q is male or female So, D cannot be definitely true.
Answer: D) Q is T's son
Question: If Bella's income is Rs 27000, calculate her savings given that her income and expenditure are in the ratio 6:5.?
A.Rs.4300
B.Rs.4500
C.Rs.7500
D.Rs.2500
Answer: B.Rs.4500
Explanation: Let the income and the expenditure of the person be Rs.6x and Rs.5x respectively.
Income, 6x = 27000 => x = 4500
Savings = Income - expenditure = 6x - 5x = x
So, savings = Rs.4500
Answer: B
Question: The average number of shirts with Salman, Ambani and Dalmiya is 60, if all of them reached a shopping mall in Delhi and purchased 6 shirts each of them then average number of shirt each of them now has
A.66
B.63
C.62
D.64
Answer: A.66
Explanation: Required average
= Old average + New average
= 60 + 6 = 66
answer :A
Question: How many four-digit odd numbers do not use any digit more than once?
A.1728
B.2160
C.2240
D.2268
Answer: D.2268
Explanation: Let a 4-digit number be represented by ABCD
Here A can have any value between 1 to 9 - so total 9
B can have any value between 0 to 9, but not A - so total 9
C can have any value between 0 to 9, but not A or B - so total 8
D can have any value between 0 to 9, but not A, B or C - so total 7
No. of ALL possible 4-digit nos (without repeating any digit) = 9*9*8*7 = 4536
Half of these would be odd.
Therefor, no. of ODD possible 4-digit nos (without repeating any digit) = 4536 / 2 = 2268
Answer should be D.
Question: A rectangular lawn of length 200m by 120m has two roads running along its center, one along the length and the other along the width. If the width of the roads is 5m what is the area covered by the two roads?
A.400
B.1550
C.1575
D.1600
Answer: C.1575
Explanation: Area Covered by Road Along the Length = 5*200 = 1000 Square Meter
Area Covered by Road Along the Width = 5*120 = 600 Square Meter
Common Area in both Roads (where the roads intersect) = Square with Side 5 meter = 5*5 = 25
Total Area of the Roads = 1000+600-25 = 1575
Answer: option C
Question: In a certain group of 9 members, 4 members teach only French and the rest teach only Spanish or German. If the group is to choose 3-member committee, which must have at least 1 member who teaches French, how many different committee can be chosen ?
A.40
B.50
C.74
D.80
Answer: C.74
Explanation: Case 1
1french 2either German or Spanish: 4C1 * 5C2 = 40
Case 2
2french 1either German or Spanish: 4C2 * 5C1 = 30
Case 3
3french 4C3 = 4
Answer is C = 74
Question: 2+9=20
3+4=19
4+3=25
5+2=34
6+1=??
Solve it?
A.37
B.26
C.43
D.42
Answer: A.37
Explanation: x+y=x[y+(x-1)]=x^2+xy-x
2+9=2[9+(2-1)]=4+18-2=20
3+4=3[4+(3-1)]=9+12-2=19
4+3=4[3+(4-1)]=16+12-3=25
5+2=5[2+(5-1)]=25+10-4=34
6+1=6[1+(6-1)]=36+6-5=37
Answer :A
Question: Of the 80 researchers in a workgroup, 40 percent will be assigned to Team A and the remaining 60 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer?
A. 15
B. 17
C. 20
D. 25
Answer: C. 20
Explanation: I solved it by assuming 100 people and then dividing my answer in two to save time on calculations. (percentage equals number of people) In that case
40 will be in team A
60 will be in team B
The larger diff is
70 want team A so diff is 80-40=40. At least 30 people will NOT get their wish, so for 50 researchers the same number is 20.
Answer choice C
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
A.2.89 km
B.2.88 km
C.3.99 km
D.3.78 km
Answer: B.2.88 km
Explanation: M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
Answer:B
Question: 80% of a number is added to 20, the result is the same number. Find the number?
A.300
B.288
C.270
D.100
Answer: D.100
Explanation: (80/100) * X + 20 = X
4x+ 100 = 5 x
x=100
Answer :: D
Question: Initially, the men and women in a room were in the ratio of 4 : 5. Then, 2 men entered the room and 3 women left the room. Then, the number of women doubled. Now there are 14 men in the room. How many D women are currently in the room?
A.12
B.14
C.15
D.24
Answer: D.24
Explanation: the number of women doubled means that they have become 24 from 12..
and we have to tell the current strength so 24 is the answer..
let the number be 4x and 5x..
given 4x+2=14.. so x=3..
women number=5*3-3=12, then doubled=24..
ans D
Question: Two cubes of tire sides ratio 2 : 3. Find its cube volumes ratio?
A.2:27
B.3:27
C.1:27
D.8:27
Answer: D.8:27
Explanation: a(power3) : b(power3) = 2(power3) : 3(power3)
= 8 : 27
Answer is D.
Question: A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
A.250
B.882
C.772
D.512
Answer: A.250
Explanation: CP1 = 100 SP1 = 90
CP2 = 80 SP2 = 80 * (140/100) = 112
22 ----- 100
55 ----- ? => Rs.250
Answer: A
Question: How many numbers between 11 and 90 are divisible by 7 ?
A.23
B.11
C.22
D.32
Answer: B.11
Explanation: The required numbers are 14, 21, 28, 35, .... 77, 84.
This is an A.P. with a = 14 and d = (21 - 14) = 7.
Let it contain n terms.
Then, Tn = 84 => a + (n - 1) d = 84
=> 14 + (n - 1) x 7 = 84 or n = 11.
Required number of terms = 11
ANSWER B 11
Question: How many integer values Y are there for x such that 1 < 3x + 5 < 17?
A.Two
B.Three
C.Four
D.Five
Answer: D.Five
Explanation: 1 < 3x + 5 < 17
=> -4 < 3x < 12
=> -4/3 < x < 4
x can take integer values Y -1,0 , 1 , 2 , 3
Answer D
Question: A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount was offered?
A.60%
B.23%
C.30%
D.56%
Answer: C.30%
Explanation: Let C.P. be Rs. 100.
Then, S.P. = Rs. 123.50
Let marked price be Rs. x. Then, 95/100 x = 123.50
x = 12350/95 = Rs. 130
Now, S.P. = Rs. 130, C.P. = Rs. 100
Profit % = 30%.
Answer: C
Question: Which of the following points falls outside of the region defined by 2y≤6x−8?
A.(5, 1)
B.(3, -8)
C.(1, 0)
D.(2, 0)
Answer: C.(1, 0)
Explanation: Equation given is 2y<=6x-8
Simplifying this; y<=3x-4
Plug in the values provided in the options,
A. 1<=11
B. -8<=3
C. 0<=-1
D.0<=0
E. -14<=-12
Option C is the answer.
Question: A farmer has enough food to feed her 1000 cows for 50 days. After 10 days some of the cows run away and the food was now enough for the same period of 50 days as before. How many cows ran away?
A.300
B.200
C.500
D.400
Answer: B.200
Explanation: 1000 ---- 50
1000 ---- 40
x ---- 50
x*50 = 1000*40
x = 800
1000
-------
200
Answer = B
Question: Find the L.C.M of 15, 18, 28 and 30.
A.1800
B.1260
C.1460
D.1600
Answer: B.1260
Explanation: Explanation:
2 x 3 x 5 x 3 x 14 = 1260
Answer: Option B
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 36 years now, the son's age five years back was:
A.13
B.15
C.20
D.25
Answer: A.13
Explanation: Let the son's present age be x years. Then, (36 - x) = x
2x = 36.
x = 18.
Son's age 5 years back (18 - 5) = 13 years.
Answer: Option A
Question: A train 310 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
A.40
B.56
C.41
D.36
Answer: D.36
Explanation: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 310 + 140 = 450 m
Required time = 450 * 2/25 = 36 sec
Answer: Option D
Question: 9 3/4 + 8 2/17 - 9 1/15=?
A.7 719/1020
B.9 817/1020
C.9 719/1020
D.8 817/1020
Answer: D.8 817/1020
Explanation: Given sum=9+3/4+8+2/17-(9+1/15)
=(9+8-9)+(3/4+2/17-1/15)
=8+(765+120-68/1020
=8 817/1020
Answer is D
Question: There are 10 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played?
A.10
B.30
C.45
D.60
Answer: C.45
Explanation: 10 players are there.
two players play one game with one another.
so 10C2=10*9/2
=45
SO OPTION C is correct
Question: The sum of three consecutive even numbers is 42. Find the middle number of the three?
A.14
B.66
C.88
D.99
Answer: A.14
Explanation: Three consecutive even numbers (2P - 2), 2P, (2P + 2).
(2P - 2) + 2P + (2P + 2) = 42
6P = 42 => P = 7.
The middle number is: 2P = 14.Answer:A
Question: The ratio of 5 seconds to 4 hours
A.1:80
B.1:6000
C.1:3600
D.1:400
Answer: C.1:3600
Explanation: 1 hour =3600 sec
then 5 hours =5*3600=18000
so ,5:18000=1:3600
ANSWER:C
Question: The H.C.F. of two numbers is 12 and their L.C.M. is 600. If one of the numbers is 480, then the other is:
A.11
B.10
C.8
D.15
Answer: D.15
Explanation: Other number =	(12 x 600)/480 = 15.
ANSWER :D
Question: The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is?
A.7! * ⁷P₆
B.6! * ⁷P₆
C.8! * ⁷P₆
D.2! * ⁷P₆
Answer: B.6! * ⁷P₆
Explanation: We can initially arrange the six boys in 6! ways.
Having done this, now three are seven places and six girls to be arranged. This can be done in ⁷P₆ ways.
Hence required number of ways
= 6! * ⁷P₆
Answer: B
Question: The instructions state that Cheryl needs 3/8 square yards of one type of material and 1/3 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 15/40 square yards left that she did not use. What is the total amount of square yards of material Cheryl used?
A.1/12
B.1/9
C.2/3
D.1/3
Answer: D.1/3
Explanation: total bought = 3/8+1/3
left part 15/40--->3/8
so used part 3/8+1/3-3/8=1/3
Ans D
Question: In a family, a couple has a son and a daughter. The age of the father is three times that of his daughter and the age of the son is half of that of his mother. The wife is 9 years younger to her husband and the brother is seven years older than his sister. What is the age of the mother ?
A.40 years
B.45 years
C.50 years
D.60 years
Answer: D.60 years
Explanation: let daughter age x then father age will be 3x
let mother age is y then son age will be y/2
accor. to que.
3x-y=9 ....................1
y/2-x=7 =>2x-y = -14......2
solve the both eqe.
y=60
ANSWER:D
Question: In how many different number of ways 3 men and 2 women can sit on a shopa which can accommodate persons?
A.170
B.180
C.200
D.5
Answer: D.5
Explanation: Option 'D'
5p1 = 5 = 5
Question: Teas worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs 153 per Kg , the price of the third variety per Kg will be?
A.Rs. 147.50
B.Rs. 785.50
C.Rs. 175.50
D.Rs. 258.50
Answer: C.Rs. 175.50
Explanation: Explanation :
Since first and second varieties are mixed in equal proportions.
So, their average price =Rs. (126+135)/2.
=>Rs. 130.50.
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1.
We have to find x.
By the rule of alligation, we have:
Cost of 1 kg Cost of 1 kg
of 1st kind of 2nd kind
(Rs. 130.50) (Rs. x)
\ /
Mean Price
(Rs. 153)
/ \
x−153 22.50
=>x−(153/22.50)=1.
=>x−153=22.50.
=>x= 175.50 Rs.
Answer : C
Question: A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
A.81
B.66
C.55
D.42
Answer: A.81
Explanation: 4.5 km /hr = (4.5*5/18) = 5/4 m/sec = 1.25 m/sec
5.4 km/hr = (5.4*5/18) = 3/2 = 1.5 m/sec
speed = (x-1.25)*8.4=(x-1.5)*8.5
x=22.5
speed = 22.5*18/5 = 81 km/hr
ANSWER A
Question: A certain quantity of 55% concentration solution is replaced with 25% concentration solution such that the concentration of the combined amount is 35%.
What's the ratio of the amount of solution that was replaced to the amount of solution that was not replaced?
A.1:3
B.1:2
C.2:3
D.2:1
Answer: D.2:1
Explanation: 25% - - - - - - - - - 35% - - - - - - 55%
From 25 to 35 =10
From 35 to 55 = 20
So the ratio is 10/20 = 1 to 2
D it is
Question: Ram's age and Shyam's age are in the ratio 3:4. Seven years ago the ratio of their ages was 2:3. Find the ratio of their ages five years hence?
A.26/37
B.26/35
C.26/39
D.26/33
Answer: D.26/33
Explanation: Let ages of Ramu and Shyam be x and y respectively.
x/y = 3/4 => x = 3/4 y
(x- 7)/(y - 7) = 2/3
=> 3x - 21 = 2y - 14 => 3x = 2y + 7
But x = 3/4 y
3 * 3/4 y = 2y + 7
9y = 8y + 28 => y = 28years
=> x = 21 years
Ratio of their ages five years hence, (21 + 5)/(28 + 5) = 26/33.
Answer:D
Question: The average of 1st 3 of 4 numbers is 7 and of the last 3 are 5. If the sum of the first and the last number is 13. What is the last numbers?
A.4
B.5
C.3.5
D.7
Answer: C.3.5
Explanation: A + B + C = 21
B + C + D = 15
A + D = 13
A – D = 6
A + D = 13
2D = 7
D = 3.5
ANSWER:C
Question: Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 60 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?
A.480
B.96
C.160
D.192
Answer: B.96
Explanation: A:B:C:D=2x:3x:5x:6x, for some positive number x. Total time 2x+3x+5x+6x=16x.
If 2x = 60 then 16x = 480;
If 3x = 60 then 16x = 320;
If 5x = 60 then 16x = 192;
If 6x = 60 then 16x = 160;
Only answer choices which is not obtained is 96.
Answer: B.
Question: An object thrown directly upward is at a height of h feet after t seconds, where h = -15 (t-3)^2 + 150. At what height, in feet, is the object 2 seconds after it reaches its maximum height?
A.90
B.98
C.106
D.120
Answer: A.90
Explanation: We see that h will be a maximum h=150 when t-3=0, that is when t=3.
At t=5, h = -15(5-3)^2 + 150 = -15(4) + 150 = 90
The answer is A.