RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Arun makes a popular brand of ice cream in a rectangular shaped bar 6cm long, 5cm wide and 2cm thick. To cut costs, the company had decided to reduce the volume of the bar by 19%. The thickness will remain same, but the length and width will be decreased by some percentage. The new width will be,
A.33
B.87
C.99
D.367
Answer: A.33
Explanation: Answer:A
Question: The average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 26. Which of the following integers is the higher of the remaining two integers?
A.32
B.85
C.44
D.22
Answer: B.85
Explanation: Let the four integers be A, B, C and D where A > B > C > D.
(A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1)
A = 93, D = 39 and B - C = 26
(1) => B + C = 276 - (A + D) = 276 - 132 = 144.
B + B -26 = 144
B = (144 + 26)/2 = 85
Answer:Option B
Question: Abel can complete a work in 10 days, Ben in 12 days and Carla in 15 days. All of them began the work together, but Abel had to leave after 2 days and Ben 5 days before the completion of the work. How long did the work last?
A.6
B.7
C.8
D.8 1/9
Answer: D.8 1/9
Explanation: Abel in the 2 days that he worked completed 1/5 of the job = 4/5 remains
Then if Ben had to leave 5 days before the completion, this means that Carla had to work alone for these 5 days in which she completed 1/3 of the job.
Now together, Ben and Carla completed the job in (1/12 + 1/15)(t) = 7/15
3/20 (t) = 7/15 ---> t = 3 1/9
Therefore, these 3 1/9 days worked plus the 5 days that Carla had to work by herself add to 8 1/9 days
Answer: D
Question: Robert ate 13 chocolates, Nickel ate 4 chocolates. How many more chocolates did Robert ate than nickel?
A.A)4
B.B)7
C.C)9
D.D)5
Answer: C.C)9
Explanation: 13-4=9. Answer is C
Question: The average age of 21 students of a class is 21 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years, The age of the 21th student is
A.164
B.152
C.100
D.182
Answer: A.164
Explanation: Explanation:
Age of the 21th student = [21 * 21 - (14 * 5 + 16 * 9)] = (378-214) = 164 years.
Answer: A
Question: The average (arithmetic mean) of 20, 40, and 60 is 9 more than the average of 10, 70, and what number?
A.15
B.25
C.35
D.13
Answer: D.13
Explanation: a1 = 120/3 = 40
a2 = a1 -9 = 31
sum of second list = 31*3 = 93
therefore the number = 93 -80 = 13
ANSWER:D
Question: What is the unit digit in(7^95 - 3^58)?
A.6
B.4
C.7
D.9
Answer: B.4
Explanation: Explanation:
Unit digit in 7^95 = Unit digit in [(7^4)23 x 73]
= Unit digit in [(Unit digit in(2401))23 x (343)]
= Unit digit in (123 x 343)
= Unit digit in (343)
= 3
Unit digit in 3^58 = Unit digit in [(3^4)14 x 32]
= Unit digit in [Unit digit in (81)14 x 32]
= Unit digit in [(1)14 x 32]
= Unit digit in (1 x 9)
= Unit digit in (9)
= 9
Unit digit in (795 - 358) = Unit digit in (343 - 9) = Unit digit in (334) = 4.
B
Question: Ben and Shari have invited three other couples to their apartment for a game of charades. Everyone is to be split into two equal teams, but each team must consist of either two couples or no couples. How many different pairs of teams are possible?
A.11
B.14
C.22
D.35
Answer: A.11
Explanation: Ben and Shari can be paired with any of the other three couples, leaving the remaining two for the other team. So, the number of ways to split 4 couples into two teams is 3:
{1, 2} - {3, 4}
{1, 3} - {2, 4}
{1, 4} - {2, 3}
The number of teams where there are no couples:
{Ben, any from couple 2, any from couple 3, any from couple 4} and the remaining 4 people form team #2. The number of team for Ben = 2*2*2 = 8.
Total = 3 + 8 = 11.
Answer: A
Question: If xx is chosen at random from the set {1,2,3,4} and yy is to be chosen at random from the set {5,6,7}, what is the probability that xy will be even?
A.24
B.29
C.28
D.23
Answer: D.23
Explanation: SS ={(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)}
Total element n(S)=12
xy will be even when even xx or yy or both will be even.
Events of x,y being even is E.
E ={(1,6),(2,5),(2,6),(2,7),(3,6),(4,5),(4,6),(4,7)}
n(E)=8
So, Probability,
P=n(E)n(S)
P=812
P=23
D
Question: 7^b + 7^b + 7^b + 7^b + 7^b + 7^b + 7^b =
A.7^b
B.7^(b + 1)
C.7^(7b)
D.8^b
Answer: B.7^(b + 1)
Explanation: Easy one.
7*7^b = 7^(b+1)
Ans. B
Question: Calculate the circumference of a circular field whose radius is 5 centimeters.
A.5 π cm
B.6 π cm
C.7 π cm
D.8 π cm
Answer: B.6 π cm
Explanation: Circumference C is given by
C = 2πr = 2π*5 = 10 π cm
correct answer B
Question: Find the odd man out. 9, 12, 15, 18, 21, 25
A.9
B.25
C.12
D.15
Answer: B.25
Explanation: All numbers except 25 are multiples of 3
Answer is B
Question: Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's salary?
A.Rs.5000
B.Rs. 38,000
C.Rs.6300
D.Rs.9000
Answer: B.Rs. 38,000
Explanation: Explanation:
Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.
Then, 2x+4000/3x+4000=40/57
57(2x + 4000) = 40(3x + 4000)
6x = 68,000
3x = 34,000
Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000.
Answer:B
Question: There are 9 women and 8 men in a certain club. If the club is to select a committee of 2 women and 2 men, how many different such committees are possible?
A.836
B.942
C.1008
D.1224
Answer: C.1008
Explanation: 9C2 * 8C2 = 36*28 = 1008
The answer is C.
Question: A completes a work in 12 days and B complete the same work in 24 days. If both of them work together, then the number of days required to complete the work will be
A.8 days
B.9 days
C.10 days
D.12 days
Answer: A.8 days
Explanation: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 12 × 24/ 36 = 8 days.
A
Question: A train 225 m long running at 90 kmph crosses a platform in 25 sec. What is the length of the platform?
A.271
B.266
C.400
D.277
Answer: C.400
Explanation: Length of the platform= 90 * 5/18 * 25 = 625 – 225
= 400
Answer:C
Question: The parameter of a square is equal to the perimeter of a rectangle of length 20 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)
A.77.14 cm
B.47.14 cm
C.26.71 cm
D.94.94 cm
Answer: C.26.71 cm
Explanation: Let the side of the square be a cm.
Parameter of the rectangle = 2(20 + 14) = 68 cm Parameter of the square = 68 cm
i.e. 4a = 68
A = 17
Diameter of the semicircle = 17 cm
Circimference of the semicircle
= 1/2(∏)(17)
= 1/2(22/7)(17) = 374/14 = 26.71 cm to two decimal places
ANSWER:C
Question: 9 engines consume 24 metric tonnes of coal, when each is working 8 hours day. How much coal is required for 8 engines, each running 13 hours a day, if 3 engines of former type consume as much as 4 engines of latter type?
A.20 metric tonnes
B.22 metric tonnes
C.24 metric tonnes
D.26 metric tonnes
Answer: D.26 metric tonnes
Explanation: Explanation :
Let required amount of coal be x metric tonnes
More engines, more amount of coal (direct proportion)
If 3 engines of first type consume 1 unit, then 1 engine will consume 1/3 unit which is its the rate of consumption.
If 4 engines of second type consume 1 unit, then 1 engine will consume 1/4 unit which is its the rate of consumption
More rate of consumption, more amount of coal (direct proportion)
More hours, more amount of coal(direct proportion)
⇒ 9 × (1/3) × 8 × x = 8 × (1/4) × 13 × 24
⇒ 3 × 8 × x = 8 × 6 × 13
⇒ 3 × x = 6 × 13
⇒ x = 2 × 13 = 26. Answer : Option D
Question: Kamal obtained 66, 65, 77, 62 and 75 marks(out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
A.65
B.69
C.72
D.75
Answer: B.69
Explanation: Sol.
Average
= 66 + 65 + 77 + 62 + 75 / 5)
= (345 / 5)
= 69.
Answer B
Question: Louie takes out a three-month loan of $1000. The lender charges him 10% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louis have to pay each month?
A.333
B.383
C.402
D.433
Answer: C.402
Explanation: After 1st month: (1000)(1.1)-X = 1100-X
After 2nd month: (1100-X)(1.1)-X = 1210-2.21X
After 3rd month: (1210-2.21X)(1.1)-X = 1331-3.31X
Now, the amount after the last payment in 3rd month must bring the total to 0. Hence:
1331-3.31X = 0
X = 1331/3.31 = 402.11
The answer is C
Question: If 2 (A's capital) = 4 (B's capital) = 6 (C's capital). Then the ratio of their capitals is?
A.6:3:2
B.5:3:2
C.6:3:5
D.6:4:2
Answer: A.6:3:2
Explanation: 2A = 4B = 6 C
A:B:C = 1/2:1/4:1/6
= 6:3:2
Answer: A
Question: In how many ways can 7 different objects be dived among 3 persons so that either one or two of them do not get any object?
A.381
B.180
C.36
D.84
Answer: A.381
Explanation: case 1: for all obj are given to one person 3
case 2: choose two out of 3 3c2=3
naw no of ways to distribute 7 obj to two person=2^7
sub two way when no obj is given to both
so no of ways=3+3c2(2^7-2)=381
ANSWER:A
Question: A bowl was filled with 10 ounces of water, and 0.014 ounce of the water evaporated each day during a 50-day period. What percent of the original amount of water evaporated during this period?
A.0.004%
B.0.04%
C.0.40%
D.7%
Answer: D.7%
Explanation: Total amount of water evaporated each day during a 50-day period = .014 * 50
=.014 * 100/2
= 1.4/2
= .7
percent of the original amount of water evaporated during this period = (.7/10) * 100%
= 7 %
Answer D
Question: Oranges are bought at 7 for Rs.4.50. At what rate per hundred must they be sold to gain 33%?
A.57.5
B.85.5
C.89.5
D.94.5
Answer: B.85.5
Explanation: 7 oranges bought for rs 4.5
1 orange cost =4.5/7
therefore for 100 oranges =100*(4.5/7)
gain =33%
450/7+(33/100)*450/7=rate per hundred he want to sell
ans :85.50
ANSWER:B
Question: If 4 persons can do 4 times of a particular work in 4 days, then, 7 persons can do 7 times of that work in?
A.3 days
B.4 days
C.6 days
D.7 days
Answer: B.4 days
Explanation: That is, 1 person can do one time of the work in 4 days.
Therefore, 7 persons can do 7 times work in the same 4 days itself
B)
Question: An alloy of copper and zinc contains copper and zinc in the ratio 9 : 6. Another alloy of copper and zinc contains copper and zinc in the ratio 6 : 9. In what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc?
A.1 : 5
B.1 : 4
C.1 : 3
D.1 : 1
Answer: D.1 : 1
Explanation: Let Alloy_1 be x units, and let Alloy_2 be y units.
So, fraction of copper in Alloy_1 = 9x/15, and fraction of zinc in Alloy_1 = 6x/15
Similarly, fraction of copper in Alloy_2 = 6y/15, and fraction of zinc in Alloy_2 = 9y/15.
Mixing them, we get
copper = 9x/15 +6y/15; zinc = 6x/15 + 9y/15
So, 9x+6y = 6x+9y
-> 3x = 3y
-> x/y =3/3 = 1/1
So, they must be mixed in the ratio 1 : 1
Answer : D
Question: In how many ways can the letters D, I, G, I, K be arranged so that the two I's are not next to each other?
A.36
B.48
C.72
D.96
Answer: A.36
Explanation: 1 D
2 I
1 G
1 K
Number of ways these letters can be arranged = 5!/2! (2! to account 2 same Is) = 60
Consider 2 Is as 1 entity and thus the number of arrangements for (II)DGK = 4! = 24
Total allowed cases = 60-24 =36
A is the correct answer.
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B =6:3 and B:C = 6:5. If the total runs scored by all of them are 118, the runs scored by B are?
A.24
B.20.13
C.30.93
D.20.93
Answer: A.24
Explanation: A:B = 6:3
B:C = 6:5
A:B:C = 36:18:15
12/59 * 118 = 24
ANSWER:A
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
A.2.5 sec
B.4.25 sec
C.5 sec
D.12.5 sec
Answer: A.2.5 sec
Explanation: Speed = 144 * 5/18 = 40 m/sec
Time taken = 100/40 = 2.5 sec.
ANSWER:A
Question: A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is?
A.3.34 sq m
B.3.97 sq m
C.1.17 sq m
D.2.98 sq m
Answer: A.3.34 sq m
Explanation: Area of the path = Area of the outer circle - Area of the inner circle
= ∏{4/2 + 25/100}2 - ∏[4/2]2
= ∏[2.252 - 22] = ∏(0.25)(4.25) { (a2 - b2 = (a - b)(a + b) }
= (3.14)(1/4)(17/4)
= 53.38/16 = 3.34 sq m
Answer: A
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions.
A.704 m
B.300 m
C.350 m
D.450 m
Answer: A.704 m
Explanation: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 500 * 2 * 22/7 * 22.4 = 70400 cm = 704 m
ANSWER A
Question: If a and b are positive numbers, and a^3 + b^3 = 30, then the greatest possible value of a is between:
A.0 and 3
B.3 and 4
C.4 and 5
D.5 and 7
Answer: B.3 and 4
Explanation: If a = 3.1 and b is very small, then a^3 + b^3 can equal 30.
If a > 4, then a^3 + b^3 > 30.
The answer is B.
Question: A shop owners pays an average salary of $400 to his 10 employees and $100 to the 2 accountants. What is the average salary for the shop owner?
A.$350
B.$500
C.$460
D.$120
Answer: A.$350
Explanation: Number of employees in the shop is 10
Their average salary is $400
Number of accountants in the shop is 2
Their average salary is $100
Total salary of the employees is 10*400=$4,000
Total salary of the accountants is 2*100=$200
Total salary for the shop owner is $4,200
Average salary for the shop owner is 4,200/12=$350
Answer is A
Question: What is the difference between the local value of 6 and 9 in the number 2694?
A.510
B.377
C.288
D.277
Answer: A.510
Explanation: Explanation:
600 â€“ 90 = 510
Answer: A
Question: An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 12-meter platform and caught it after it had traveled 35.65 meters. How many times did the ball bounce?
A.5
B.6
C.7
D.8
Answer: B.6
Explanation: Ans: 6
Division of total diatance travelled will be 12+12+6+3+1.5+.75+0.4 ANS B
Question: An woman sitting in a train which is travelling at 20 kmph observes that a goods train travelling in a opposite direction, takes 15 seconds to pass him. If the goods train is 300 m long, find its speed.
A.52
B.54
C.56
D.58
Answer: A.52
Explanation: Relative speed = (300/15)m/s = (300/15)*(18/5) = 72 kmph
speed of goods train = 72-20 = 52 kmph
Answer is A
Question: A train 600 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
A.277 m
B.700m
C.500 m
D.187 m
Answer: B.700m
Explanation: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (600 + x)/60 = 65/3
x = 700 m.
Answer:B
Question: By investing Rs. 1620 in 8% stock, Michael earns Rs. 135. The stock is then quoted at:
A.25
B.96
C.22
D.76
Answer: B.96
Explanation: Explanation:
To earn Rs. 135, investment = Rs. 1620.
To earn Rs. 8, investment == Rs. 96.
Market value of Rs. 100 stock = Rs. 96.
Answer: B) 96
Question: The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?
A.349
B.349
C.342
D.346
Answer: C.342
Explanation: 400*(90/100)*(95/100) = 342
Answer:C
Question: If the selling price of 7 articles is same as the cost price of 10 articles. Find the gain or loss percentage?
A.93%
B.23%
C.33%
D.43%
Answer: D.43%
Explanation: Let the C.P of each article be Re 1. Then,
S.P of 7 articles = C.P of 10 articles = Rs. 10
Now, C.P of 7 articles = Rs. 7, S.p of 7 articles = Rs 10
Gain = Rs ( 10 - 7 ) = Rs 3.
Gain% = ( 3/7 × 100 ) % = 43%
Answer : D
Question: How many 4 letter words can we make from the letters in an alphabet?
A.358800
B.358802
C.358801
D.358809
Answer: A.358800
Explanation: There are 26 letters in an alphabet
to choose 4 from these 26 would mean
26P4 = 26!/(26-4)!
We take Permutation and not Combination since the arrangement of letters matter in forming a word. Like MAPS and PAMS both are different words.
Therefore the answer is 26!/ 22! = 26*25*24*23 = 358800
Answer:A
Question: A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68% of the distribution lies one standard deviation f of the mean, what percent of the distribution is less than m+f?
A. 16%
B. 32%
C. 48%
D. 84%
Answer: D. 84%
Explanation: 16%
________________________________________________ m+f
34%
________________________________________________ m
34%
________________________________________________ m-f
16%
since 68% lies one standard deviation from mean m, => 50% of 68% lies on either side as it is symmetric about m.
thus 16% lie below m-f and 16% lie above m+f
now below m+f = 16+34+34 = 84%
hence D
Question: one pipe can fill a tank in 15 hour.but because of hole in a tank,this tank fill in 20 hour.so in how much time this hole will empty the full tank?
A.30
B.40
C.50
D.60
Answer: D.60
Explanation: in 1 hour hole empty=[1/15-1/20]=1/60
so total time taken to empty the full tank through hole=60 hour.
answer D
Question: Mr. John used to purchase certain number of mangoes for $360 Since the price of mangoes is reduced by 10% he got 12 more mangoes today. Find the original price of 115 mangoes.
A.360
B.383
C.400
D.406
Answer: B.383
Explanation: Mr. John used to purchase certain number of mangoes for $360 Since the price of mangoes is reduced by 10% he got 12 more mangoes today. Find the original price of 120 mangoes.
Method 1:
Let price per mango = x. Let number of mangoes be n. Then, nx = 360.
Now price = 0.9x; number of mangoes = n + 12. Total amount = 0.9x*(n+12) = 360.
nx = 0.9nx + 10.8x => 0.1nx = 10.8x => n = 108 => x = 360/108 = 3.33
Original price of 115 mangoes = 115*3.33 = 383.
Answer B
Question: A meal cost $ 33.50 and there was no tax. If the tip was more than 10 pc but less than 15pc of the price, then the total amount paid should be:
A.40-42
B.39-41
C.38-40
D.37-39
Answer: D.37-39
Explanation: 10%(33.5) = 3.35
15%(33.5) = 5.025
total amount could have been 33.5+3.35 and 33.5+5.025
=> could have been between 36.85 and 38.525
=> approximately between 37 and 39
Answer is D.
Question: A line with slope 2 intersects a line with slope 6 at the point (40, 30).
What is the distance between the x-intercepts of these lines?
A.4
B.6
C.8
D.10
Answer: D.10
Explanation: The line with slope 2 passing through (40, 30) has x-intercept 40−(30/2). The line with slope
6 passing through (40, 30) has x-intercept 40 − (30/6). So the difference in the x-intercepts is
(30/2) − (30/6) = 10.
correct 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.20 kmph
B.40 kmph
C.30 kmph
D.55 kmph
Answer: C.30 kmph
Explanation: US = 25
DS = 35
M = (35 + 25)/2 = 30
Answer:C
Question: In what ratio must rice at Rs.9.30 per Kg be mixed with rice at Rs.10.80 per Kg so that the mixture be worth Rs.10 per Kg?
A.8 : 7
B.7 : 8
C.8 : 9
D.9 : 8
Answer: A.8 : 7
Explanation: Solution
Required ratio = 80 : 70 = 8 : 7.
Answer A
Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 hours to fill the tank. The leak can drain all the water of the tank in:
A.14 hrs
B.15 hrs
C.10 hrs
D.8 hrs
Answer: A.14 hrs
Explanation: work done by leak in 1 hr = (1/2-3/7)=1/4
=>14 hrs
ANSWER A
Question: A shopkeeper loses 15%,if an article is sold for Rs. 102. What should be the selling price of the article to gain 20%?
A.Rs.167
B.Rs.144
C.Rs.148
D.Rs.179
Answer: B.Rs.144
Explanation: Given that SP = Rs. 102 and loss = 15%
CP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6
= Rs. 120.
To get 20% profit, New SP
= [(100 + p%)CP]/100
= (120 * 120)/100 = Rs.144
Answer: B
Question: Two numbers are in the ratio 1:2, if 7 is added to both, their ratio changes to 3:5. The greatest number is
A.24
B.26
C.28
D.32
Answer: C.28
Explanation: Let the numbers be x and 2x
Then, (x+7)/(2x+7)=3/5
X=14
There fore answer is 28
ANSWER C 28
Question: one disk of 20cm radius, out of that 4 disk of 5cm are cut , find diffrence of leftout and cut out area?
A.200pi
B.300pi
C.100pi
D.400pi
Answer: B.300pi
Explanation: Radius r=20cm
Total areal of big disc = pi* r^2 = pi * 20 * 20 = 400 pi
Total cut out area = 4 * pi * 5 * 5 = 100 pi
Difference between them = 400 - 100 = 300pi
ANSWER:B
Question: A certain sum amounts to Rs.1725 in 3 years and Rs.1875 in 5 years. Find the rate % per annum?
A.8%
B.5%
C.6%
D.4%
Answer: B.5%
Explanation: 3 --- 1725
5 --- 1875
--------------
2 --- 150
N = 1 I = 75 R = ?
P = 1725 - 225 = 1500
75 = (1500*1*R)/100
R = 5%
Answer:B
Question: If the Average (mean ) of 11 positive temperatures is x degrees fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
A.6x
B.9x
C.5x/3
D.3x/2
Answer: B.9x
Explanation: Let the 5 numbers be 1,2,3,4,5,...,11 (since no restrictions are given). There mean is 6 (x).
Now the sum of greatest three would be 9+10+11= 30
so the answer has to be 9x....that is option B
Question: The average expenditure of a labourer for 6 months was 75 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income i
A.70
B.72
C.75
D.78
Answer: B.72
Explanation: Income of 6 months = (6 × 75) – debt
= 450 – debt
Income of the man for next 4 months
= 4 × 60 + debt + 30
= 270 + debt
∴ Income of 10 months = 720
Average monthly income = 720 ÷ 10 = 72
Answer B
Question: Sum of the squares of 3 no. is 156 and the sum of their products taken two at a time is 50. Find the sum?
A.18
B.16
C.19
D.21
Answer: B.16
Explanation: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 156 + 2* 50
a + b + c = âˆš256 = 16
Answer B
Question: log xy3 = a; log x2y = b then then value of log y /log x
A.23
B.277
C.997
D.1781
Answer: B.277
Explanation: log xy3 = logx + 3logy = a - - - (1)
log x2y = 2logx + logy = b - - - (2)
Multiplying (1) by 2 and subtracting (2) from it
5logy = 2a-b
logy = 2a−b52a−b5
Put the value of log y in equation (2),
2logx + 2a−b52a−b5 = b
logx = 3b−a53b−a5
logylogx=2a−b53b−a5log⁡ylog⁡x=2a−b53b−a5 = 2a−b3b−a
Answer:B
Question: A bag of potatoes weighs 16 kg divided by a quarter of its weight. How much does the bag weigh?
A.4 kg
B.8 kg
C.7 kg
D.3 kg
Answer: B.8 kg
Explanation: B
8 kg
8 kg : 16/2
Question: Two boats are heading towards each other at constant speeds of 5 miles/hr and 21 miles/hr respectively. They begin at a distance 20 miles from each other. How far are they (in miles) one minute before they collide ?
A.1/12
B.5/12
C.1/6
D.13/30
Answer: D.13/30
Explanation: The question asks: how far apart will they be 1 minute=1/60 hours before they collide?
Since the combined rate of the boats is 5+21=26 mph then 1/60 hours before they collide they'll be rate*time=distance --> 26*1/60=13/30 miles apart.
Answer: D.
Question: Using all the letters of the word "THURSDAY", how many different words can be formed?
A.7
B.8!
C.9
D.3
Answer: B.8!
Explanation: Total number of letters = 8
Using these letters the number of 8 letters words formed is ⁸P₈ = 8!.
Answer:B
Question: The distance between Delhi and Mathura is 130 kms. A starts from Delhi with a speed of 25 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 30 kmph at 9 p.m. from Delhi. When will they meet?
A.11
B.77
C.16
D.10
Answer: A.11
Explanation: D = 130 – 25 = 105
RS = 30 + 25 = 55
T = 105/55 = 2 hours
8 a.m. + 2 = 11 a.m..Answer: A
Question: In the following sequence: [x, y, z, 5, 7, 16, 28] each number is equal to the sum of the three numbers preceding it. What is x+y?
A.-5
B.-1
C.1
D.5
Answer: C.1
Explanation: lets start from z, as per the question stem
z + 5 + 7 = 16
-->> z= 4
similarly, y + 4 + 5 = 7
--> y = -2
similarly,, x + -2 + 4 = 5
--> x = 3
hence , x+y = 3-2 = 1
ANSWER:C
Question: If x and y are positive integers, then xy + x is
A.Always even
B.Always odd
C.Even whenever x is even
D.Even whenever x + y is odd
Answer: C.Even whenever x is even
Explanation: xy + x can be factorized as x(y + 1) by taking out x common.
Now, anything multiplied by even is always even.
Answer (C).
Question: What is the product of all the possible values of x if x^2+4x+7=|x+2|+3
A.-6
B.–12
C.12
D.29
Answer: A.-6
Explanation: x^2+4x+4=|x+2|
(X+2)^2 = |x+2|
Only 3 values possible,
x = -3, x = -2, x =-1
So multiplication = -6
answer option -6
ANSWER:A