RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If the day before yesterday was Thursday, when will Sunday be?
A.Day after tomorrow
B.Tomorow
C.Two days after today
D.Today
Answer: B.Tomorow
Explanation: Explanation :
Day before yesterday was Thursday
=>Yesterday was a Friday
=> Today is a Saturday
=> Tomorrow is a Sunday. Answer : Option B
Question: There are two batches A and B of a class. Batch A consists of 36 students and batch B consists of 44 students. Find the average weight of whole class, if average weight of batch A is 40 kg and that of batch B is 35 kg.
A.29.23 kg
B.32.56 kg
C.35.66 kg
D.37.25 kg
Answer: D.37.25 kg
Explanation: Given: Average weight of batch A = 40 kg , average weight of batch B = 35 kg
1) First find the total weight of all students
- Weight of batch A = (36 x 40) = 1440
- Weight of batch B = (44 x 35) = 1540
Total weight of all students = (1440 + 1540) = 2980 kg
2) Find average weight of whole class
(Batch A + Batch B) students = (36 + 44) = 80 students
Average Weight =	Total weight of all the students /	No. of Students
= 2980 / 80
= 37.25 kg
ANSWER IS D
Question: 30 men can do a work in 40 days. When should 20 men leave the work so that the entire work is completed in 40 days after they leave the work?
A.87 days
B.10 days
C.55 days
D.44 days
Answer: B.10 days
Explanation: Total work to be done = 30 * 40 = 1200
Let 20 men leave the work after 'P' days, so that the remaining work is completed in 40 days after they leave the work.
40P + (20 * 40) = 1200
40P = 400 => P = 10 days
Answer:B
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
A.38
B.2767
C.245
D.277
Answer: C.245
Explanation: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.
Answer:C
Question: In how many ways can live boys and three girls sit in a row such that all boys sit together?
A.2888
B.2827
C.2880
D.2827
Answer: C.2880
Explanation: Treat all boys as one unit. Now there are four students and they can be arranged in 4! ways. Again five boys can be arranged among themselves in 5! ways.
Required number of arrangements
= 4! * 5! = 24 * 120
= 2880.
Answer: C
Question: In year Y imported machine tools accounted for 25 percent of total machine-tools sales in the United States, and Japanese imports accounted for 35 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?
A.80x/7
B.13x/20
C.80/9x
D.20x/13
Answer: A.80x/7
Explanation: Sales of imported tools = 25% of the total sales = 0.25*{total} = {total}/4;
Sales of Japanese tools = 35% of the sales of imported tools = 0.35*{total}/4 = 7/20*{total}/4 = 7*{total}/80.
Since the sales of of Japanese tools was x, then 7*{total}/80 = x --> {total} = 80x/7.
Answer: A.
Question: Suppose two numbers are in the ratio 2:3. If 5 is subtracted from both of the numbers then the ratio becomes 1:2 then find the greatest number?
A.5
B.15
C.10
D.20
Answer: B.15
Explanation: Given Ratio -> 2:3
2x - 5 : 3x - 10 = 1 : 2
2[2x - 5] = 1[3x - 5]
4x - 10 = 3x - 5
4x - 3x = 10 - 5
x = 5
Then greatest number is = 3x
3x = 15
Ans - B
Question: A restaurant buys fruit in cans containing 3 1/2 cups of fruit each. If the restaurant uses 1/2 cup of the fruit in each serving of its fruit compote, what is the least number of cans needed to prepare 60 servings of the compote ?
A.7
B.8
C.9
D.10
Answer: C.9
Explanation: 7/2 cups = 1 can
1/2 cup of each serving. so 7 serving per 1 can.
Least number is 7*9=63 =60 approx
Answer -9
ANSWER:C
Question: The probability that it is Friday and that a student is absent is 0.03. Since there are 5 school days in a week, the probability that it is Friday is 0.2. What is the probability that a student is absent given that today is Friday?
A.10%
B.15%
C.12%
D.13%
Answer: B.15%
Explanation: P(Absent|Friday) = P(Friday and abscent)/P(Friday)
= 0.03/0.2
= 15%
ANSWER:B
Question: What was the day on 15th august 1947 ?
A.Friday
B.Sunday
C.Saturday
D.Thursday
Answer: A.Friday
Explanation: Explanation:
15 Aug, 1947 = (1946 years + Period from 1.1.1947 to 15.8.1947)
Odd days in 1600 years = 0
Odd days in 300 years = 1
46 years = (35 ordinary years + 11 leap years) = (35 x 1 + 11 x 2)= 57 (8 weeks + 1 day) = 1 odd day
Jan. Feb. Mar. Apr. May. Jun. Jul. Aug
( 31 + 28 + 31 + 30 + 31 + 30 + 31 + 15 ) = 227 days = (32 weeks + 3 days) = 3 odd days.
Total number of odd days = (0 + 1 + 1 + 3) = 5 odd days.
Hence, as the number of odd days = 5 , given day is Friday.
Answer: A
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?
A.3/1
B.3/2
C.3/9
D.3/5
Answer: B.3/2
Explanation: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23
==> 27 x + 17 y = 23 x + 23 y
==> 4 x = 6 y ==> x/y = 3/2.
Answer: B
Question: Sum of 19 odd numbers is?
A.341
B.351
C.361
D.371
Answer: C.361
Explanation: sum of 1st n odd no.s = 1+3+5+7+... = n^2
so, Sum of 1st 19 odd numbers = 19^2 = 361
ANSWER:C
Question: if 3rd ter, and 9th term is 8 in a.p,then find the 11th term
A.61
B.62
C.63
D.64
Answer: D.64
Explanation: a3=a1+(3-1)d
8=a1+2d.....(1)equ.
a9=a1+(9-1)d
8=a1+8d....(2)equ.
solve (1) and (2) then a1=4 and d=6.
a11=a1+(11-1)d
a11=4+10*6
a11=64.
ANSWER:D
Question: Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is?
A.Rs.8429
B.Rs.8420
C.Rs.8400
D.Rs.8420
Answer: C.Rs.8400
Explanation: Ratio of their shares = 22500 : 35000 = 9:14
Deepak's share = 13800 * 14/23
= Rs.8400.
Answer:C
Question: he average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
A.0
B.1
C.10
D.19
Answer: D.19
Explanation: Average of 20 numbers = 0.
Sum of 20 numbers (0 x 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a the 20th number is (-a).
Answer: Option D
Question: The difference between the place values of 6 and 5 in the number 826533 is
A.5500
B.4500
C.2500
D.6970
Answer: A.5500
Explanation: Sol.= (Place value of 6) – (place Value of 5)= (6000 - 500)= 5500 Answer A
Question: In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is:
A.2 Hours
B.3 Hours
C.4 Hours
D.1 Hour
Answer: D.1 Hour
Explanation: Let the duration of the flight be x hours.
Then, 600/X - 600/(X +1/2) = 200 ==> 600/X - 1200/(2X +1) = 200
==> X(2X + 1) = 3 ==> 2X sqr. + X - 3 = 0 ==> (2X +3)(X - 1) = 0.
by neglecting negative value of X we got X = 1 hr.
Answer D) 1 Hour.
Question: A tank is filled in FOUR hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?
A.56 hours
B.28 hours
C.55 hours
D.14 hours
Answer: D.14 hours
Explanation: 1/A + 1/B + 1/C = 1/4 (Given)
Also given that A = 2B and B = 2C
=> 1/2B + 1/B + 2/B = 1/4
=> (1 + 2 + 4)/2B = 1/4
=> 2B/7 = 4
=> B = 14 hours.
Answer: D
Question: What is the ratio whose term differ by 35 and the measure of which is 2/7?
A.A)32:23
B.B)14:49
C.C)71:85
D.D)32:39
Answer: B.B)14:49
Explanation: Let the ratio be x:(x+35)
Then, x/(x+35) = 2/7
x=14
required ratio = 14:49
Answer is B
Question: If X gets 25% more than Y and Y gets 20% more than Z, the share of Z out of Rs. 1110 will be:
A.Rs. 300
B.Rs. 200
C.Rs. 240
D.Rs. 350
Answer: A.Rs. 300
Explanation: Z share = Z,
Y = 1.2Z
X = 1.25Ã—1.2Z,
X+Y+Z =111
(1.25Ã— 1.2+1.2+1)Z=1110
3.7Z=1110, Z=300
Answer: . A
Question: One side of a triangle has length 7 and a second side has length 4. Which of the following could be the area of the triangle?
I. 15
II. 10
III. 5
A.I only
B.II only
C.III only
D.II and III only
Answer: D.II and III only
Explanation: The triangle will have a maximum area when it is a right angled triangle
The largest triangle will be formed when 7 and 4 are the base and height of triangle .
Area = 1/2 * 7 * 4 = 14
There is no lower limit on the area of any triangle whose only 2 sides are known.
Then 0 < Area <= 14
The answer is D.
Question: 2 no.'s, when divided by 17, leave remainders 13 and 11 respectively. If the sum of those 2 no.'s is divided by 17, the remainder will be
A.4
B.5
C.7
D.9
Answer: C.7
Explanation: (C)
Required remainder = remainder by (13 +11)/17 = 7
Question: What is the value of (P + Q)/(P - Q) if P/Q is 4?
A.5/3
B.2/3
C.2/6
D.7/8
Answer: A.5/3
Explanation: (P + Q)/(P - Q) = [(P/Q) + 1]/[(P/Q) - 1]
= (4 + 1)/(4 - 1)
= 5/3
= 5/3
ANSWER:A
Question: When a is divided by b, the quotient is c with remainder 4. What is a in terms of 4, b, and c?
A.b+c/4
B.bc+4
C.b+c
D.bc*4
Answer: B.bc+4
Explanation: a/b =c with remainder 4
i.e, a-4 = bc
a= bc+4
Answer : B
Question: If a and b are unique prime integers, which of the following must be even?
A.a−b
B.a−2b
C.2a−2b
D.2a−b
Answer: C.2a−2b
Explanation: Let's assume that a is an even prime integer and b is an odd prime integer, their subtraction results in an odd integer and an odd integer multiplied by an even integer yields an even integer.
Answer C
Question: Given that E and F are events such that P(E) = 0.16, P(F) = 0.4 and P(E n F) = 0.4,
find P (E|F) and P(F|E)?
A.1
B.1/4
C.2
D.2/5
Answer: B.1/4
Explanation: Here, E and F are events
P(E|F) = P(EnF)/P(F) = 0.4/0.4 = 1
P(F|E) = P(EnF)/P(E) = 0.4/0.16 = 1/4.
Option is B
Question: What amount does an investor receive if the investor invests $4000 at 10% p.a. compound interest for two years, compounding done annually?
A.$4720
B.$4840
C.$4920
D.$5080
Answer: B.$4840
Explanation: A = (1 + R/100)^n * P
(1.1)^2 * 5000 = 1.21 * 5000 = 4840
The answer is B.
Question: Which of the following is closest to the difference between sum W of all proper fractions (fractions less than 1) in the form 1/x , where x is a positive digit, and the product of all proper fractions in the form y/(y+1), where y is a positive digit?
A.2.82
B.2.72
C.1.82
D.1.72
Answer: D.1.72
Explanation: Sum W of all proper fractions (fractions less than 1) in the form 1/x, where x is a positive digit:
1/1 + 1/2 + 1/3 +.....+ 1/9
This is a harmonic progression. Harmonic progression is inverse of arithmetic progression.
Approximate sum of a harmonic progression with even number of terms = number of terms * (average of middle 2 terms)
Approximate sum of a harmonic progression with odd number of terms = number of terms * (middle term)
The actual sum will be slightly more than the approximation.
Here we have 9 terms (odd).
Sum = 9 * 1/5
= 9/5
Product of all proper fractions in the form y/(y+1), where y is a positive digit:
1/2 * 2/3 * 3/4 *.....*9/10
We will be left with 1/10.
Required = 9/5 - 1/10
= 1.8 - 0.1
= 1.7
Closest is 1.72
Answer (D).
Question: Antonio works in a bakery. He made cookies that cost $2 and made $420. How many customer did he have?
A.200 customers
B.210 customers
C.250 customers
D.230customers
Answer: B.210 customers
Explanation: A cookie costs $2 adding another one is $4. 420 divided by 4 is 105 x 2 is 210. He had 210 customers. The correct answer is B.
Question: Gold is 11 times as heavy as water and copper is 5 times as heavy as water. In what ratio should these be mixed to get an alloy 8 times as heavy as water?
A.3:2
B.1:1
C.3:1
D.5:2
Answer: B.1:1
Explanation: G = 11W
C = 5W
Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy
1gm gold + x gm copper = x+1 gm of alloy
11W+5Wx = x+1 * 8W
11+5x = 8(x+1)
x = 1/1
Ratio of gold with copper = 1:1 = 1:1
Answer is B
Question: A gardener wants to plant trees in his garden in rows in such a way that the number of trees in each row to be the same. If there are 24 rows the number of trees in each row is 42 if there are 12 more rows find the number of trees in each row?
A.A)63
B.B)28
C.C)48
D.D)32
Answer: B.B)28
Explanation: Required number of trees
= 24/36 * 42 = 28.
ANSWER:B
Question: A Orange costs Rs 11 each and a watermelon costs Rs. 7 each. If I spend Rs 40 on total what is the number of orange I purchased?
A.7
B.8
C.9
D.3
Answer: D.3
Explanation: 3*11 + 7 = 40
Answer : 3
Option : D
Question: Solve the following quadratic equation by factoring.
x2-5x-14=0
A.-2,7
B.2,-7
C.1,8
D.1,-8
Answer: A.-2,7
Explanation: We already have zero on one side of the equation, which we need to proceed with this problem. Therefore, all we need to do is actually factor the quadratic.
(x+2)(x-7)=0
x=-2 and x=7
ANSWER A
Question: A bus started its journey from Mumbai and reached Pune in 44min with its average speed of 50 km/hr. If the average speed of the bus is increased by 5km/hr, how much time will it take to cover the same distance?
A.10 min
B.20 min
C.30 min
D.40 min
Answer: D.40 min
Explanation: Sol. Distance between Ramgarh and Devgarh =(50*44)/60=110/3
Average speed of the bus is increased by 5 km/hr then the
speed of the bus = 55 km/hr
Required time = 110/3*60/55 = 40 min
D
Question: In how many ways can the letters {U, U, R, R} be arranged?
A.4
B.20
C.120
D.720
Answer: A.4
Explanation: My answer : A
There is 4! ways to arrange those letters in total, however letter U repeats 2! times and letter R repeats 2! times
=> the way to arrange without repeating = 4!/ [2!x2!] = 4
Question: Five pieces of wood have an average length of 128cm and a median length of 140cm. What is the maximum possible length, in cm, of the shortest piece of wood?
A.a) 90
B.b) 100
C.c) 110
D.d) 130
Answer: C.c) 110
Explanation: C. 110
sum of all lengths of all 5 pieces of wood = 128 * 5 = 640
3rd piece (sorted in increasing length) length = 140 (median)
for sum of first 2 wood length to become max, last two should be least.
let 4th, 5th wood also have length 140 each.
total of last 3 = 140 * 3 = 420
sum of first 2 = 640 - 420 = 220
each of these 2 will have length 220/2 = 110
Answer C
Question: If the price of gold increases by 50%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before?
A.27 2/23 %
B.33 1/3 %
C.30%
D.19%
Answer: B.33 1/3 %
Explanation: Explanation:
100
150
------
150-------50
100-------? => 331/3%
ANSWER IS B
Question: A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 18 kilometer long bridge, at the same speed?
A.14 min
B.20 min
C.18 min
D.19 min
Answer: B.20 min
Explanation: S = 600/40 = 15 mps
S = 18000/15 = 1200 sec = 20 min.Answer: B
Question: If x and y are integers such that x^2= y and xy = 343, then x – y = ?
A.-42
B.-20
C.-5
D.5
Answer: A.-42
Explanation: here x and y are integers .
x^2=y,xy =343.
substitute x^2=y in xy => x^3=343.
here x^3 is positive ,
x is also positive.
x=7 then y=49.
x-y=-42
so option A is correct
Question: What is the sum of all the composite numbers up to 18?
A.228
B.112
C.80
D.96
Answer: B.112
Explanation: Explanation:
4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 +18 = 112
Answer: B
Question: The average successfull Search time for sequential search on n items is
A.n/2
B.(n-1)/2
C.(n+1)/2
D.log(n)+1
Answer: C.(n+1)/2
Explanation: To understand this think as there is an array and now you are searching for an element which is a[0] element in that arrary...so for this you need to do 1 comparison.
Now similarly for sequential searching suppose your are looking for an element which is present at 2nd position i.e a[1] position of that array then you will get answer within 2 comparisons.
Now similarly if you have n elements and your desired element is the nth element then you will have to do n comparisons.
so we can write total search time will be: (1+2+3+........+n)
average search time will be (1+2+3+........+n)/n
NOW we know sum of n natural numbers i.e 1+2+3+.....n= {n(n+1)}/2
ANSWER: C
Question: A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Rs. 855, the total profit is:
A.Rs. 1425
B.Rs. 1500
C.Rs. 1537.50
D.Rs. 1576
Answer: B.Rs. 1500
Explanation: Let the total profit be Rs. 100.
After paying to charity, A's share = Rs. (95 x3/5) = Rs. 57.
If A's share is Rs. 57, total profit = Rs. 100.
If A's share Rs. 855, total profit = (100	x 855/57)	= 1500.
THE CORRECT ANSWER IS B
Question: Find the perimeter and area of a square of side 12 cm.
A.144
B.121
C.169
D.196
Answer: A.144
Explanation: We know that the perimeter of square = 4 Ã— side
Side= 12 cm
Therefore, perimeter = 4 Ã— 12 cm = 48 cm
Now, area of the square = (side Ã— side) sq. units
= 12 Ã— 12 cmÂ²
= 144 cmÂ²
ANSWER : A
Question: Find the simple interest on Rs. 71,200 at 16 2/3% per annum for 9 months.
A.s.8500
B.s.8900
C.s.7500
D.s.7000
Answer: B.s.8900
Explanation: P = Rs.71200,R = 50/3% p.a and T = 9/12 years = 3/4years.
S.I. = (P*R*T)/100 = Rs.(71,200*(50/3)*(3/4)*(1/100))
= Rs.8900
Answer is B.
Question: Find the unit's digit in the product (2467)^153 * (341)^72
A.0
B.1
C.2
D.7
Answer: D.7
Explanation: unit digit of 341^72 will be 1.
unit digit of (2467)^153 will be same as that of 7^1 (153 mod 4 = 1)
answer 7
ANSWER:D
Question: The average age of 39 students in a group is 10 years. When teacher’s age is included to it, the average increases by one. What is the teacher’s age in years?
A.50
B.55
C.60
D.cannot be determined
Answer: A.50
Explanation: Age of the teacher = (40 × 11 – 39 × 10) years
= 50 years.
Answer A
Question: Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.135. How much was lent at 5%?
A.2333
B.2777
C.2688
D.1500
Answer: D.1500
Explanation: (x*5*1)/100 + [(2500 - x)*6*1]/100 = 135
X = 1500
Answer: D
Question: A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?
A.12.8 kmph
B.12.7 kmph
C.12.6 kmph
D.12.5 kilometre per hour
Answer: D.12.5 kilometre per hour
Explanation: Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.
Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7
Solving the equation, the speed of man in still water is 12.5 kmph.
Answer:D
Question: In a party every person shakes hands with every other person. If there were a total of 136 handshakes in the party then what is the number of persons present in the party ?
A.15
B.16
C.17
D.18
Answer: C.17
Explanation: Explanation :
Let the number of persons be n
âˆ´ total handshakes = nC2 = 136
n(n-1)/2 = 136 âˆ´ n = 17
Answer : C
Question: If a, b, and c are consecutive even positive integers, which of the following could be equal to a + b + c ?
A.141
B.200
C.618
D.391
Answer: C.618
Explanation: The key to answering this question quickly is to realize that a+b+c is a multiple of BOTH 2 and 3. With that information, you can quickly eliminate answer choices. If you don't recognize those two Number Properties though, then you can still get to the correct answer (but it will require a bit more work).
We're told that a, b and c are CONSECUTIVE EVEN INTEGERS, so we could write them algebraically as...
A + (A+2) + (A+4) = 3A + 6
We know that 3A + 6 COULD equal one of those five answers; we just have to find it...
Could 3A + 6 = 141
3A = 135
A = 45
This is NOT an EVEN INTEGER, so 141 is NOT the answer
Could 3A + 6 = 200
3A = 194
A = 64.6666
This is NOT an EVEN INTEGER, so 200 is NOT the answer
Could 3A + 6 = 618
3A = 612
A = 204
This IS an EVEN INTEGER! The numbers would be 204, 206 and 208. This IS the answer
Final Answer:
C
Question: What is the remainder when you divide 2^200-2 by 7?
A.1
B.2
C.3
D.4
Answer: B.2
Explanation: answer is B. this is very similar to the 32^32^32-2 divided by 7 question.
Question: A certain list consists of 11 different numbers. If n is in the list and n is 5 times the average (arithmetic mean) of the other 10 numbers in the list, then n is what fraction of the sum of the 11 numbers in the list?
A.1/3
B.2/5
C.1/4
D.3/5
Answer: A.1/3
Explanation: series : a1, a2....a10,n
sum of a1+a2+...+a10 = 10*x (x = average)
so, n = 5*x
Hence, a1+a2+..+a10+n = 15x
So, the fraction asked = 5x/15x = 1/3
Answer is A
Question: A clock gains 5 minutes. in 24 hours. It was set right at 10 a.m. on Monday. What will be the true time when the clock indicates 10:30 a.m.on the next Sunday ?
A.10 a.m
B.11 a.m
C.25 minutes past 10 a.m.
D.5 minutes to 11 a.m.
Answer: A.10 a.m
Explanation: Time between 10 a.m. on Monday to 10:30 a.m. on Sunday = 144 1⁄2
24 1⁄2 hours of incorrect clock = 24 hours of correct time.
∴ 1441⁄2 hours of incorrect clock = x hours of correct time.
∴ 144 1/2×24 / 24 1/2=144hoursi.e,
The true time is 10 a.m. on Sunday.
Answer A
Question: If 893 × 78 = p, which of the following is equal to 893 × 79?
A. p + 1
B. p + 78
C. p + 79
D. p + 893
Answer: D. p + 893
Explanation: Since 893 × 78 = p and 79=78+1, we have 893 × 79 = 893 ×(78+1)=893×78 + 893 ×1 = p + 893.
The answer is (D).
Question: The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is:
A.74
B.94
C.184
D.364
Answer: D.364
Explanation: L.C.M. of 6, 9, 15 and 18 is 90. Let required number be 90k + 4, which is multiple of 7. Least value of k for which (90k + 4) is divisible by 7 is k = 4. Required number = (90 x 4) + 4 = 364. Answer :D
Question: Which of the following fractions is greater than 1/3?
A.1. 12/50
B.2. 3/11
C.3. 2/9
D.4. 4/17
Answer: A.1. 12/50
Explanation: 1. 12/50
12.5/50 = 1/4 thus 12/50 < 1/4
2. 3/11
3/12 = 1/4 thus 3/11 > 1/4
3. 2/9
2/8 = 1/4 thus 2/9 < 1/4
4. 4/17
4/16 = 1/4 thus 4/17 < 1/4
5. 6/24
6/24 = 1/4
A
Question: The music class consists of 3 girls and 7 boys. How many ways can a group of 3 be formed if it has to include at least one boy?
A.119
B.158
C.161
D.165
Answer: A.119
Explanation: Reverse combinatorics approach is preferred method on this one
Note that at least 1 boy gives clue to using this method
All combinations - three girls = answer
All combinations is 10C3 = 120
All girls 3C3 = 1
So our answer is 120-1= 119
Hence, answer is (A)
Question: Running at the same constant rate, 6 identical machines can produce a total of 420 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
A.648
B.1800
C.2800
D.10800
Answer: C.2800
Explanation: Let the required number of bottles be x.
More machines, More bottles (Direct Proportion)
More minutes, More bottles (Direct Proportion)
Machines	6	:	10	:: 420 : x
Time (in minutes)	1	:	4
6 x 1 x x = 10 x 4 x 420
x =	(10 x 4 x 420)/(6)
x = 2800.
ANSWER:C
Question: 90 is increased by 50%. Find the final number.
A.100
B.110
C.135
D.140
Answer: C.135
Explanation: Final number = Initial number + 50%(original number) = 90 + 50%(90) = 90 + 45 = 135.
Answer C
Question: A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:
A.130 kmph
B.110 kmph
C.150 kmph
D.120 kmph
Answer: D.120 kmph
Explanation: D
120 kmph
Let speed of the car be x kmph.
Then, speed of the train=(150/100)*x=(3/2)*x kmph
(75/x)-(75/(3/2x))=125/(10*60)
(75/x)-(50/x)=5/24
x = 25x24/5 = 120kmph.
Question: A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 51.84, the number of the member is the group is:
A.57
B.67
C.72
D.87
Answer: C.72
Explanation: Explanation:
Money collected = (51.84 x 100) paise = 5184 paise.
∴ Number of members = √(5184) = 72.
Answer: C
Question: Tickets numbered from 1 to 26 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bears a number which is a multiple of 3?
A.1/5
B.2/5
C.3/10
D.4/13
Answer: D.4/13
Explanation: Here, S = [1, 2, 3, 4, …., 19, 20, 21, 22, 23, 24, 25, 26]
Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18, 21, 24]
P (E) = n (E) / n (S) = 8 / 26 = 4/13
The answer is D.