RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A number is doubled and 5 is added. If the resultant is trebled, it becomes 135. What is that number?
A.12
B.29
C.20
D.15
Answer: C.20
Explanation: Explanation:
Let the number be x.
Therefore,
3(2x + 5) = 135
6x + 15 = 135
6x = 120
x = 20
ANSWER:C
Question: If M = s% of t and N = t% of s, then which of the following is true?
A.M is equal to N
B.M is smaller than N
C.M is greater than N
D.none of these
Answer: A.M is equal to N
Explanation: Explanation :
Solution: s% of t = (s/100 * t)
=> (t/100 * s) = t% of s
=> M = N
Answer : A
Question: The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is?
A.8
B.7
C.6
D.5
Answer: A.8
Explanation: 2x * x = 128 => x= 8
Answer: A
Question: Distance between 2 places A and B is given. A man P starts from place A at 9 pm and another man Q goes from B at 10pm . Speed of Q is double of that of P. Both cover 1/4 dist in the same time interval. then A travels the entire dist in time
A.8hrs
B.9hrs
C.10hrs
D.11hrs
Answer: A.8hrs
Explanation: let speed of p and q are x, 2x
time taken by A to cover 1/4 distance =t
x*t = 2x*(t-1)
t=2 for 1/4 of total distance
A travels the entire dist in time 2*4=8hrs
ANSWER:A
Question: The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?
A.1:96
B.1:99
C.1:95
D.1:12
Answer: A.1:96
Explanation: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x2 = 6912
x2 = 576 = 4 * 144 = 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x
=1:96.
Answer:A
Question: In the game of Dubblefud, red chips, blue chips and green chips are each worth 1,2 and 5 points respectively. In a certain selection of chips, the product of the point values of the chips is 15, 000. If the number of blue chips in this selection equals the number of green chips, how many red chips are in the selection?
A.10
B.20
C.30
D.40
Answer: C.30
Explanation: this is equivalent to :-
x * 2y * 5z = 15000
y
= z (given)
x * 2y * 5y = 15000
x * y^2 = 15000/10
2x * y^2 = 1500
now from options given we will figure out which number will divide 800 and gives us a perfect square :-
which gives us x = 30 as
2* 30 * y^2 =1500
y^2 = 25
y =5
Number of red chips = 30 hence C
Question: Zinc and copper are melted together in the ratio 9 : 11. What is the weight of melted mixture, if 28.8 kg of zinc has been consumed in it?
A.58 kg
B.60 kg
C.64 kg
D.70 kg
Answer: C.64 kg
Explanation: Sol.
For 9 kg Zinc, mixture melted = (9+11) kg.
For 28.8 kg Zinc, mixture, melted = [20/9 x 28.8] kg
= 64 kg.
Answer C
Question: If x+y=10, x-y=18, for integers of x and y, x=?
A.14
B.15
C.25
D.13
Answer: A.14
Explanation: x+y =10
x-y = 18
2x = 28
x = 14
Answer is A
Question: (1^2+2^2+3^2+.....+7^2)=?
A.330
B.345
C.365
D.140
Answer: D.140
Explanation: formula is (1^2+2^2+3^2+....+n^2=1/6 n(n+1)(2n+1)
n=7
=(1/6x7x8x15)
=140
Answer is D.
Question: If a - b = 3 and a2 + b2 = 29, find the value of ab?
A.10
B.12
C.14
D.17
Answer: A.10
Explanation: 2ab = (a2 + b2) - (a - b)2
= 29 - 9 = 20
ab = 10
A)
Question: An empty fuel tank with a capacity of 200 gallons was filled partially with fuel A and then to capacity with fuel B. Fuel A contains 12% ethanol by volume and fuel B contains 16% ethanol by volume. If the full fuel tank contains 22 gallons of ethanol, how many gallons of fuel A were added?
A.160
B.150
C.250
D.80
Answer: C.250
Explanation: Say there are A gallons of fuel A in the tank, then there would be 200-A gallons of fuel B.
The amount of ethanol in A gallons of fuel A is 0.12A;
The amount of ethanol in 200-A gallons of fuel B is 0.16(200-A);
Since the total amount of ethanol is 22 gallons then 0.12A+0.16(200-A)=22 --> A=250.
Answer: C.
Question: There are some pigeons and hares in a zoo. If heads are counted, there are 200. If legs are counted, there are 780. The number of hares in the zoo is?
A.190
B.199
C.77
D.66
Answer: A.190
Explanation: 200*2 = 400
780
-----
380
1----2
?----380 = 190
Answer:A
Question: How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 30 m long and 16 1/2 m board?
A.90
B.99
C.97
D.95
Answer: B.99
Explanation: 30 * 33/2 = 5/2 * 2 * x => x = 99
ANSWER B
Question: A boy has five trousers and 15 shirts. In how many different ways can he select a trouser and a shirt?
A.75 ways
B.87 ways
C.66 ways
D.108 ways
Answer: A.75 ways
Explanation: Explanation:
The boy can select one trouser in five ways.
The boy can select one shirt in 15 ways.
The number of ways in which he can select one trouser and one shirt is 5 * 15 = 75 ways.
Answer: A
Question: Three candidates contested an election and received 1000, 2000 and 4000votes respectively. What percentage of the total votes did the winning candidate got?
A.30%
B.50%
C.57%
D.62%
Answer: C.57%
Explanation: Total number of votes polled = (1000 + 2000 + 4000) = 7000
Required percentage = 4000/7000 * 100 = 57% (approximately)
Answer: Option C
Question: A, B, K start from the same place and travel in the same direction at speeds of 30 km/hr, 40 km/hr, 120 km/hr respectively. B starts two hours after A. If B and K overtake A at the same instant, how many hours after A did K start?
A.3
B.4
C.6
D.8
Answer: C.6
Explanation: In 2 hours, A travels 60 km.
B can catch A at a rate of 10 km/hr, so B catches A 6 hours after B starts.
So A and B both travel a distance of 240 km.
C needs 2 hours to travel 240 km, so C leaves 6 hours after A.
The answer is C.
Question: Including Cara and Dan, there are five members on the board of directors for a company. If the board is to be split up into a three-person subcommittee, what fraction of all the possible subcommittees that include Cara, also include Dan?
A.2/3
B.1/2
C.1/3
D.2/4
Answer: B.1/2
Explanation: The number of possible subcommittees with Cara is 4C2=6.
The number of possible subcommittees with Cara and Dan is 3C1=3.
The fraction of Cara's subcommittees which include Dan is 3/6=1/2.
The answer is B.
Question: There is 60% increase in an amount in 6 years at S.I. What will be the C.I. of Rs. 12,000 after 3 years at the same rate?
A.Rs. 3932
B.Rs. 3972
C.Rs. 3372
D.Rs. 3942
Answer: C.Rs. 3372
Explanation: Explanation:
Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.
R = (100 * 60)/(100 * 6) = 10% p.a.
Now, P = Rs. 12000, T = 3 years and R = 10% p.a.
C.I. = [12000 * {(1 + 10/100)3 - 1}]
= 12000 * 331/1000 = Rs. 3972
Answer: Option C
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
A.18%
B.19%
C.68%
D.19%
Answer: A.18%
Explanation: 1500 ---- 270
100 ---- ? => 18%
Answer:A
Question: Two pipes A and B can fill a tank in 15 min and 27 min respectively. Both the pipes are opened together but after 4 min, pipe A is turned off. What is the total time required to fill the tank?
A.14 min 19 sec
B.14 min 42 sec
C.18 min 24 sec
D.14 min 40 sec
Answer: C.18 min 24 sec
Explanation: :
Part filled in 4 minutes = 4(1/15 + 1/20) = 7/15
Remaining part = 1 - 7/15 = 8/15
Part filled by B in 1 minute = 1/27
1/27 : 8/15 :: 1 ; x
x = 8/15 * 1 * 27 = 14 2/5 min = 14 min 24 sec.
The tank will be full in (4 min. + 14 min. 24 sec) = 18 min 24 sec.Answer: C
Question: Lake A has a duck population of 30 females and 35 males. Lake B’s duck population consists of the same ratio of females to males. If 6 new female ducks are added to Lake B and no other ducks are added or removed, the new total duck population of Lake B could be which of the following?
A.144
B.105
C.78
D.51
Answer: C.78
Explanation: Lake A has a duck population of 30 females and 35 males --> the ratio is F:M = 30:35 = 6:7.
Lake B’s duck population consists of the same ratio of females to males --> F:M = 6:7.
C
Question: Which of the following numbers is between 2⁄5 and 1⁄4?
A..45
B..35
C..23
D..22
Answer: B..35
Explanation: Isn't it B?
2/5 = .40
1/4 = .25
The only answer between that is B, .35.
Question: In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 18 years is replaced by a new boy. The age of the new boy is ?
A.14 years 8 months
B.15 years
C.16 years 4 months years
D.17 years 10 months years
Answer: A.14 years 8 months
Explanation: Answer
Total decrease
= ( 20 X 2 ) months
= 3 years 4 month
∴ Age of the new boy
= ( 18 years ) – ( 3 years 4 months)
= 14 years 8 month
Correct Option: A
Question: If d is the mean of x, y, and z, what is the mean x - 5, y - 5, z - 5 ?
A.d
B.3d
C.15d
D.d - 5
Answer: D.d - 5
Explanation: If we add or subtract a constant to each term in a set:
Mean will increase or decrease by the same constant.
SD will not change.
If we increase or decrease each term in a set by the same percent (multiply by a constant):
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.
So in our case mean will decrease by 5, as we are subtracting 5 from each term in a set --> Mean =d - 5.
Answer: D.
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.180
B.270
C.360
D.500
Answer: B.270
Explanation: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 870 = 270
ANSWER B
Question: what is the remainder when 45820 is divided by 45
A.8
B.15
C.25
D.10
Answer: D.10
Explanation: 45820 / 45
45820 / 9*5
9164 / 9 => rem = 2
we have cancelled it by 5
reqd remainder = 5*2 = 10
ANSWER:D
Question: Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 6 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?
A.$10,350
B.$10,494
C.$10,500
D.$11,500
Answer: B.$10,494
Explanation: the amount at the end of first year will become the principle for 2nd year, applying this trick and calculating we get the amount at the end of third year to be 10494. So the answer is (B).
Question: A, B and C enter into a partnership by investing Rs. 15000, Rs.21000 and Rs.27000 respectively. At the end of 8 months, B receives Rs.1260 as his share. Find the share of A.
A.Rs. 600
B.Rs. 1620
C.Rs. 1080
D.Rs. 900
Answer: D.Rs. 900
Explanation: Explanation:
Ratio of capital of A, B and C
= 15000 : 21000 : 27000
= 5 : 7 : 9
Let the total profit be Rs. x.
Then, B's share = Rs. 7x/21 = Rs. x/3
But x/3 = 1260
=> x = 3780
Hence, the total profit = Rs. 3780
A's share = Rs.[(5/21) × 3780] = Rs. 900
Answer: Option D
Question: If two pipes function simultaneously, the reservoir will be filled in 12 days.One pipe fills the reservoir 10 hours faster than the other. How many hours does it take the second pipe to fill the reservoir.
A.53 hours
B.13 hours
C.30 hours
D.43 hours
Answer: C.30 hours
Explanation: If two pipes function simultaneously, the reservoir will be filled in 12 hours ( not days).One pipe fills the reservoir 10 hours faster than the other. How many hours does it take the second pipe to fill the reservoir.
Then one pipe will fill tank in 20 hrs and second in 30 hrs when opened alone.
ANSWER:C
Question: Megala bought an electric drill at 85% of the regular price.
She paid $850 for the drill. What was the regular price?
A.$1000
B.$1869
C.$3869
D.$5869
Answer: A.$1000
Explanation: Regular price = 850/85*100 = 1000
Answer : A
Question: A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:
A.34299
B.28789
C.15000
D.28999
Answer: C.15000
Explanation: Answer: C) Rs.15000
Question: What is the Compound Interest on Rs.8500 at 7.5% p.a. compounded half-yearly for 2 1/2 years.
A.1409.85
B.1717.85
C.1427.85
D.2717.85
Answer: B.1717.85
Explanation: Compound interest : A = P(1 + r/n)nt
A = 10,217.85
C.I. >> 10,217.85 - 8500 >> Rs. 1717.85
Answer:B
Question: Find the odd man out
3,12, 24,48, 56, 96
A.48
B.8
C.16
D.56
Answer: D.56
Explanation: 3*2 = 6
6*2 =12
12*2=24
24*2=48
48*2=96
ANSWER:D
Question: Two bullet train s 140 m and 210 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:
A.15.8 sec.
B.12.6 sec.
C.11.8 sec.
D.10.8 sec.
Answer: B.12.6 sec.
Explanation: Relative speed = (60 + 40) km/hr = 100x5/18 = 250/9 m/ sec.
Distance covered in crossing each other = (140 + 210) m = 350 m.
Required time = 350x9/250 = 54/5 = 12.6 sec.
ANSWER B
Question: A computer system uses alphanumeric case sensitive characters for its passwords. When the system was created it required users to create passwords having 4 characters in length. This year, it added the option of creating passwords having 5 characters in length. Which of the following gives the expression for the total number of passwords the new computer system can accept?
Assume there are 65 unique alphanumeric case sensitive characters.
A.63^4
B.62^5
C.62(62^4)
D.66(65^4)
Answer: D.66(65^4)
Explanation: Total number of passwords = number of 4 character password +number of 5 character password
= 65^4 + 65^5 (Since there is no limitation on repetition , each character can be chosen in 62 ways )
=65^4(1+ 65)
=65^4 * 66
Answer D
Question: 155 liters of a mixture of milk and water contains in the ratio 3:2. How much water should now be added so that the ratio of milk and water becomes 3:4?
A.12 liters
B.62 liters
C.41 liters
D.50 liters
Answer: B.62 liters
Explanation: Milk = 3/5 * 155 = 93 liters
Water = 62 liters
93 : (62+P) = 3:4
186 + 3P = 372 => P = 62
62 liters of water are to be added for the ratio become 3:4.
Answer:B
Question: A small, experimental plane has three engines, one of which is redundant. That is, as long as two of the engines are working, the plane will stay in the air. Over the course of a typical flight, there is a 1/3 chance that engine one will fail. There is a 55% probability that engine two will work. The third engine works only half the time. What is the probability that the plane will crash in any given flight?
A. 7/12
B. 1/4
C. 1/2
D. 7/24
Answer: C. 1/2
Explanation: In probability questions the trap answer is just the multiple of the numbers in the question.
i.e. if you multiply 1/3 * 1/4 * 1/2 = 1/24 is trap answer
The other trap answer could be 2/3 * 3/4 * 1/2 = 6/24 is trap answer
So lets say you have30 secsand you want to guess the answer then B, C are ruled out because they can be traps. You best guess is A, D, E. So you have 33% chances of being correct.
C
Question: A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is
A.2 mph
B.2.5 mph
C.3 mph
D.4 mph
Answer: A.2 mph
Explanation: Solution
Speed downstreams	=(10 + x)mph.
Speed upstreams	=(10 - x)mph.
= 18 kmph.
36/(10-x) - 36/(10+x)	= 90/60
= 72x ×60
= 90(100 - x²)
x²+48x+100= 0.
x= 2mph.
Answer A
Question: A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?
A.22 1/9 kmph
B.22 8/2 kmph
C.22 1/8 kmph
D.22 1/2 kmph
Answer: D.22 1/2 kmph
Explanation: 100 --- 10 DS = 10
? ---- 1
75 ---- 15 US = 5
? ----- 1 S = (10 - 5)/2
= 2 21/2 kmph
Answer:D
Question: Find the value of 10 + 2 â€¢ (8 â€“ 3)
A.25
B.13
C.17
D.20
Answer: D.20
Explanation: 10 + 2 â€¢ (8 â€“ 3)
= 10 + 2 (5)
= 10 + 2 *5
= 10 + 10
= 20
correct answer D
Question: A person crosses a 300 m long street in 4 minutes. What is his speed in km per hour?
A.1.6
B.4.5
C.8.2
D.6.5
Answer: B.4.5
Explanation: distance = 300 meter
time = 4 minutes = 4 x 60 seconds = 240 seconds
Speed = distance/time=300/240=1.25 m/s=1.25Ã—18/5 km/hr=4.5 km/hr
Answer :B
Question: At a certain high school, a student’s popularity is determined by his or her locker number. Whoever has the locker number with the greatest number of distinct prime factors is the most popular student in the school. If Raja,Kamal, Baskar, and Dinesh get lockers with the numbers 100, 400, 150, and 420, respectively, who is the most popular student?
A.Baskar
B.They have equal popularity
C.Dinesh
D.Raja
Answer: C.Dinesh
Explanation: Distinct prime factors of 100 (Raja) : 2,5
Distinct prime factors of 400 (Kamal): 2 and 5.
Distinct prime factors of 150 (Baskar): 2,3, and 5
Distinct prime factors of 420 (Dinesh): 2,3,5 and 7.
So most popular student - Dinesh
Answer C
Question: The radius of a wheel is 25.4 cm. What is the distance covered by the wheel in making 500 resolutions?
A.724 m
B.798.3 m
C.287 m
D.278 m
Answer: B.798.3 m
Explanation: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 500 * 2 * 22/7 * 25.4 = 79829 cm
= 798.3 m
Answer:B
Question: 5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.90 only. Men’s wages are?
A.6Rs
B.2Rs
C.4Rs
D.9Rs
Answer: A.6Rs
Explanation: 5M = xW = 8B
5M + xW + 8B ----- 90 Rs.
5M + 5M + 5M ----- 90 Rs.
15M ------ 90 Rs. => 1M = 6Rs.
Answer: A
Question: Two brothers took the exam, the higher score is X and the lower one is Y. If the difference between the two scores is equal to their average, what is the value of Y/X ?
A.3
B.2.
C.1/2.
D.1/3.
Answer: D.1/3.
Explanation: X-Y = (X+Y)/2
2 X - 2 Y = X + Y
X = 3 Y
Y/X = 1/3
D is the answer.
Question: The numbers in which of the following pairs do NOT have a pair of distinct prime divisors in common?
A.10 and 50
B.12 and 18
C.24 and 64
D.21 and 63
Answer: C.24 and 64
Explanation: 64 has only the prime 2 (64=2^6) in its prime factorization, so it can not have a PAIR of distinct prime divisors in common with ANY of the numbers.
The answer is C.
Question: Rahul went to a shop and bought things worth Rs. 28, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
A.Rs 15
B.Rs 12.10
C.Rs 22.70
D.Rs 26.80
Answer: C.Rs 22.70
Explanation: Explanation :
Let the cost of the tax items = x
Given that tax rate = 6%
Cost of tax items, x*(6/100) = 30/100
x = 5 rs
Now non taxable item = total cost - cost for taxable item - tax
= 28 - 5 - 0.30
=22.70
Answer : C
Question: Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
A.16 : 5
B.14 : 5
C.16 : 7
D.19 : 5
Answer: D.19 : 5
Explanation: Quantity of alcohol in vessel P = 62.5/100 * 2 = 5/4 litres
Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres
Quantity of alcohol in the mixture formed = 5/4 + 7/2 = 19/4 = 4.75 litres
As 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed = 4.75 : 1.25 = 19 : 5.
ANSWER:D
Question: What is the least number of digits (including repetitions) needed to express 10^300 in decimal notation?
A.a) 4
B.b) 100
C.c) 301
D.d) 1000
Answer: C.c) 301
Explanation: 10^n is a decimal number with a 1 followed by n zeros.
So 10^300 will include 300 0's + 1 digit for 1 = 301
So the answer is C.
Question: A train 120 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train. Find the speed of the train.
A.67 kmph
B.50 kmph
C.55 kmph
D.60 kmph
Answer: A.67 kmph
Explanation: Explanation:
Let the speed of the train be x kmph.
Speed of the train relative to man = (x + 5) kmph = (x + 5) ×5/18 m/sec.
Therefore 120/((x+5)×5/18)=6 <=> 30 (x + 5) = 2160 <=> x = 67
Speed of the train is 67 kmph.
Answer: Option A
Question: A boat can move upstream at 25 kmph and downstream at 31 kmph, then the speed of the current is?
A.3
B.6
C.7
D.54
Answer: A.3
Explanation: US = 25
DS = 31
M = (31 - 25)/2 = 3.Answer:A
Question: 9 - 3 ÷ 1/3 + 1 = ?
A.1
B.3
C.6
D.9
Answer: A.1
Explanation: 9 - 3 1/3 + 1
=9-3÷1/3+1
=9-(3X3) +1
=9-9+1
=1
CORRECT ANSWER : A
Question: In the last set of tests, a student scored marks in each of 5 subjects in the ratio 4:5:6:7:8 and got an overall average score of 72%. If a mark of 50% in a subject is a pass and the maximum marks of each subject is the same, how many subjects did the student pass?
A.1
B.2
C.3
D.4
Answer: D.4
Explanation: The tests scores are 4k, 5k, 6k, 7k, and 8k.
The sum of the test scores is 30k.
The average test score is 30k/5 = 66. Then k = 11.
The test scores are 44, 55, 66, 77, and 88.
The student passed 4 subjects.
The answer is D.
Question: A basket contains 7 apples, of which 1 is spoiled and the rest are good. If we select 2 apples from the basket simultaneously and at random, what is the probability that the 2 apples selected will include the spoiled apple?
A.1/5
B.2/7
C.2/9
D.3/5
Answer: B.2/7
Explanation: The total number of ways to choose 2 apples is 7C2 = 21
The number of ways that include the spoiled apple is 6C1 = 6
P(the spoiled apple is included) = 6/21 = 2/7
The answer is B.
Question: Find the number of elements in the power set of {1,2}
A.4
B.0
C.2
D.3
Answer: A.4
Explanation: Power set is the set of subsets of {1,2}
That is { {1,2}, {1}, {2}, f}
ANSWER:A
Question: A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 8 is
A.189
B.197
C.221
D.227
Answer: A.189
Explanation: In that case, the Sophie prime numbers greater than 8 are 11,23,47,59, .. which yields units digit as 1,3,7 and 9
Product would be 1 x 3 x 7x9 =189 Answer should be A.
Question: A newly-wed couple is using a website to design an eBook Wedding Album to distribute to their friends and families. The template they have chosen has places for 3 large photos and 19 smaller photos. The couple has 5 large photos they could use for those three slots, and 21 smaller photos they could use for those 19 slots. Given these choices, how many different possible albums could they create?
A.2,100
B.4,200
C.5,040
D.20,520
Answer: A.2,100
Explanation: MAGOOSHOFFICIAL SOLUTION:
For the large photos, we need 5C3, which we calculated in the article:
5C3 = 10
For the smaller photos, we need 21C19, which by symmetry must equal 21C2, and we have a formula for that. In fact, in the article above, we already calculated that 21C2 = 210.
Now, by the FCP, we just multiply these: total number of possible albums = 10*210 = 2100.
Answer = A
Question: Two cars start from the same places in opposite directions. One is going towards north at 60 kmph and the other is going towards south 40kmph. What time will they take to be 100km apart?
A.1hr
B.2hrs
C.3hrs
D.4hrs
Answer: A.1hr
Explanation: To be (60+40) km apart, they take 1 hour
To be 100 km apart, they take 1/100 *100 = 1 hr
Answer is A
Question: Two teams are distributing information booklets. Team A distributes 60% more boxes of booklets than Team Z, but each box of Team A’s has 60% fewer booklets than each box of Team Z’s. Which of the following could be the total number of booklets distributed by the two groups?
A.2,000
B.3,200
C.4,100
D.4,800
Answer: C.4,100
Explanation: Let x be the no of booklets in each box that team distributes. So, Team A has 60% fewer - 0.4x.
Let y be the no. of boxes distributed by team Z. So, Team A distributes 60% more - 1.6y
Total booklets distributed by team A = xy
Total booklets distributed by team Z=0.64xy
Total booklets distributed = xy+0.64xy=1.64xy
As no. of booklets can only be integer, plugging the answer choice equal to 1.64xy should give an integer.
Choice A - 1.64xy=2000; xy=2000/1.64 = doesn't provide an integer value.
Similarly all answer choices, except choice C, fail to provide an integer value.
Choice C = 4100/1.64= 2500 and is the correct answer.
Question: The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 40 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is
A.87
B.95
C.99
D.100
Answer: C.99
Explanation: If the value of all other except the largest is 55..
Largest will be 60*10-55*9=600-495=105..
However the top 5 are distinct and the smallest of these can be 55, so remaining THREE will be 1,2,&3 more so total combined value will be 1+2+3 or 6 more..
Therefore the largest will be 6 less than max possible..... 105-6=99
ANSWER:C