RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Two pipes function simultaneously the reservoir will be filled in 12 hours. One pipe fills reservoir 10 hours faster than the other. How many hours does the faster pipe take to fill the reservoir?
A.39
B.23
C.20
D.27
Answer: C.20
Explanation: 1/x + 1/(x + 10)
= 1/12
x = 20
Answer:C
Question: A charity collected $3,199 from donors during the last month. If each donor gave at least $20, what is the greatest possible number of donors the charity could have?
A.145
B.150
C.155
D.159
Answer: D.159
Explanation: Min fund = 20
Total = 3199
The closest multiple of 20 to 3199 is : 159
Which implies 158 people gave 20 and 1 person gave 39
Ans. D
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 17, the how old is B?
A.	7
B.	8
C.	9
D.	10
Explanation:
A.6
B.7
C.9
D.10
Answer: A.6
Explanation: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 17
5x = 15
x = 3.
Hence, B's age = 2x = 6 years.
Answer: Option A
Question: A trader purchased two colour televisions for a total of Rs. 35000. He sold one colour television at 30% profit and the other 40% profit. Find the difference in the cost prices of the two televisions if he made an overall profit of 32%?
A.21000
B.22882
C.12112
D.27788
Answer: A.21000
Explanation: Let the cost prices of the colour television sold at 30% profit and 40% profit be Rs. x and Rs. (35000 - x) respectively.
Total selling price of televisions = x + 30/100 x + (35000 - x) + 40/100 (35000 - x)
=> 130/100 x + 140/100 (35000 - x) = 35000 + 32/100 (35000)
x = 28000
35000 - x = 7000
Difference in the cost prices of televisions = Rs. 21000
Answer: A
Question: A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
A.76
B.87
C.72
D.11
Answer: C.72
Explanation: Length = Speed * time
Speed = L/T
S = 400/20
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph
Answer: C
Question: What is the 101st digit after the decimal point in the decimal representation of 1/3 + 1/9 + 1/27 + 1/37?
A.0
B.1
C.5
D.7
Answer: A.0
Explanation: 1/3 + 1/9 + 1/27 = 13/27. = .481481…
1/37=.027027…
13/27 + 1/27 = .508508..
Hence 101st digit is 0.(3*33 +2=> hence the second digit of the recurring decimal which is 0)
Answer:A
Question: Pam and Stanley packed several boxes with reams of paper. While both packed, Pam packed 50% of the boxes. After Pam stopped, Stanley packed the same number of boxes that he had packed while working with Pam. What is the ratio of the number of boxes Pam packed to the number of boxes Stanley packed?
A.1 to 4
B.1 to 3
C.3 to 6
D.3 to 4
Answer: C.3 to 6
Explanation: Correct Answer: C
Solution: C. We know that when Pam and Stanley were both working, the ratio was 3 boxes by Pam to 3 boxes by Stanley. We also know that Stanley continued working after Pam stopped. He packed as many boxes alone as he had packed whlie working with Pam, effectively doubling his number of boxes. Thus, the ratio of Pam's boxes to Stanley's boxes is 3 to 6. Answer C is correct.
Question: The average of 10 numbers is 40.2. Later it is found that two numbers have been wrongly copied. The first is 15 greater than the actual number and the second number added is 13 instead of 31. Find the correct average.
A.40.2
B.40.4
C.40.5
D.40.8
Answer: C.40.5
Explanation: Sum of 10 numbers = 402
Corrected sum of 10 numbers
= 402 – 13 + 31 – 15 = 405
Hence, new average = 405⁄10 = 40.5
Answer C
Question: Solve the equation :
A) 7(3x – 6) + 5(x - 3) - 2(x - 7) = 5 ,
B) (x -3)(x + 4) - 2(3x - 2) = (x - 4)2,
C) (x + 1)3 – (x - 1)3 = 6(x2 + x + 1)
A.3, 8, -2/3
B.2, 8, -2/3
C.4, 8, -2/3
D.5, 8, -2/3
Answer: B.2, 8, -2/3
Explanation: Solution:
A) 21x - 42 + 5x - 15 - 2x + 14 = 5<=>
21x + 5x - 2x = 5 + 42 + 15 - 14<=>
24x = 48 <=> x = 2
B) x2 + 4x - 3x - 12 - 6x + 4 = x2 - 8x + 16 <=>
x2 - 5x – x2 + 8x = 16 + 12 – 4 <=>
3x = 24 <=> x = 8
C) x3 + 3x2 + 3x + 1 – (x3 - 3x2 + 3x - 1) = 6x2 + 6x + 6 <=>
x3 + 3x2 + 3x + 1 – x3 + 3x2 + 1 = 6x2 + 6x + 6 <=>
2 = 6x + 6 <=> 6x = -4 <=> x = -2/3
Answer B
Question: A single discount equivalent to the discount series of 20%, 10% and 5% is?
A.31.9
B.31.2
C.31.6
D.71.2
Answer: C.31.6
Explanation: 100*(80/100)*(90/100)*(95/100) = 68.4
100 - 68.4 = 31.6'
Answer: C
Question: The events A and B are independent, the probability that event A occurs is greater than 0, and the probability that event A occurs is twice the probability that event B occurs. The probability that at least one of events A and B occurs is 12 times the probability that both events A and B occur. What is the probability that event A occurs?
A.21/26
B.25/26
C.11/26
D.6/26
Answer: D.6/26
Explanation: Let us say probability of A occuring is a.
Let us say probability of B occuring is b.
a = 2b
Probability (either A or B or both) = 12 times Probability (A and B)
a*(1-b) + b*(1-a) + ab = 12*ab
Substituting a=2b in the second equation:
2b*(1-b) + b*(1-2b) + 2b*b = 12*2b*b
3b-2b^2 = 24b^2
3b = 26b^2
b = 3/26 = 3/26
So, a = 2b = 6/26
THE CORRECT ANSWER IS D.
Question: In a house a hall is 20 m long, 15m wide and 5m high. Its interior has to be covered with mat. What will be the total expenditure if it costs Rs. 60 per square m?
A.Rs. 50000
B.Rs. 52000
C.Rs. 57000
D.Rs. 60000
Answer: C.Rs. 57000
Explanation: Length (l) = 20 m, Breadth (b) = 15 m and Height (h) = 5 m
Total area of the hall to be covered with mat = 2(lb + bh + hl)
= 2(20 * 15 + 15 * 5 + 5 * 20)
=2(300 + 75 + 100)
= 2 * 475
= 950 sq. m
Total expenditure = 60 * 950
= Rs. 57000
C
Question: Three numbers are in the ratio of 2 : 3 : 4 and their L.C.M. is 288. What is their H.C.F.?
A.18
B.24
C.36
D.42
Answer: B.24
Explanation: Let the numbers be 2x, 3x, and 4x.
LCM of 2x, 3x and 4x is 12x.
12x = 288
x = 24
HCF of 2x, 3x and 4x = x = 24
The answer is B.
Question: The probability of having a girl is identical to the probability of having a boy. In a family with seven children, what is the probability that all the children are of the same gender?
A.1/64
B.1/9
C.1/16
D.1/25
Answer: A.1/64
Explanation: There are two cases. All boys and all girls
case 1. all boys.
1/2*1/2*1/2*1/2*1/2*1/2*1/2= 1/128
case 2 .all girls.
1/2*1/2*1/2*1/2*1/2*1/2*1/2=1/128
We will add the cases to get 1/64
Question: A rectangular block 10cm by 20cm by 30cm is cut into an exact number of equal cubes. Find the least possible number of cubes?
A.6
B.10
C.15
D.40
Answer: A.6
Explanation: Volume of the block = 10*20*30 = 6000 cm^3
Side of the largest cube = H.C.F of 10,20,30 = 10cm
Volume of the cube = 10*10*10 = 1000 cm^3
Number of cubes = 6000/1000 = 6
Answer is A
Question: There are 8 stores in town that had a total of 24 visitors on a particular day. However, only 12 people went shopping that day; some people visited more than one store. If 9 people visited exactly two stores each, and everyone visited at least one store, what is the largest number of stores anyone could have visited?
A.2
B.3
C.4
D.5
Answer: C.4
Explanation: 9 people visited 2 stores each for 18 visits.
To maximize the number of stores that one person visited, let's assume that 2 people visited 1 store each. The number of remaining visits is 24 - 18 - 2 = 4, which is the maximum that one person could have visited.
The answer is C.
Question: Which of the following is closest to (20!-19!)/(20!+19!)?
A.1.25
B.0.9
C.2.1
D.0.3
Answer: B.0.9
Explanation: (20!-19!)/(20!+19!)
19! (20-1)/19! (20+1)
19/21 = 0.9
B is the answer
Question: If we multiply the digits of a number until we get a single digit, then which is the only two digit number which require multiplication of digits more than 3 times?
A.77
B.67
C.87
D.97
Answer: A.77
Explanation: 77 =7*7 =49
49 =4*9 =36
36 =3*6 =18
18 =1*8 =8
ANSWER:A
Question: A man invests some money partly in 10% stock at 90 and partly in 5% stock at 90.To obtain equal dividends from both,he must invest the money in the ratio :
A.1 : 2
B.3 : 5
C.4 : 5
D.16 : 15
Answer: A.1 : 2
Explanation: Solution
For an income of Rs. 1 in 10% stock at 90, investment = Rs. (90/10)= Rs. 9 .
For an income of Rs. 1 in 5% stock at 90, investment = Rs.(90/5) = Rs. 18.
∴ Ratio of investments = 9 :18 =1:2
Answer A
Question: At a certain food stand, the price of each apple is 40¢ and the price of each orange is 60¢. Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 54¢. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 50¢?
A.1
B.2
C.3
D.4
Answer: D.4
Explanation: If the average price is 54, then Mary has 7 oranges and 3 apples (a ratio of 7:3).
For the average price to be 50, the ratio should be 1:1.
Mary must put back 4 oranges.
The answer is D.
Question: A FAIR AND LOVELY manufacturer produces 100 units of a certain model each month at a cost to the manufacturer of £10 per unit and all of the produced units are sold each month. What is the minimum selling price per unit that will ensure that the monthly profit (revenue from sales minus production costs) on the sales of these units will be at least £10,000?
A.90
B.60
C.110
D.30
Answer: C.110
Explanation: 100(x-10)≥10,000
x-10≥100
x≥110
Answer: Option C
Question: Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A?
A.7
B.5
C.4
D.2
Answer: B.5
Explanation: There are five letters in the given word.
Consider 5 blanks ....
The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways.
The number of words = 3! = 6.
Answer:B
Question: A train 100 m long passed a pole in 20 sec. How long will it take to pass a platform 500 m long?
A.90 sec
B.100 sec
C.110 sec
D.120 sec
Answer: D.120 sec
Explanation: Speed = 100/20 = 5 m/sec.
Required time = (100 + 500)/5 = 120 sec
Answer:D
Question: What least number must be added to 1056, so that the sum is completely divisible by 23 ?
A.1
B.2
C.3
D.4
Answer: B.2
Explanation: B
2
If the number 1056 is completely divisible by 23 means, remainder should come zero.
But if we divide 1056 by 23, the remainder is 2.
So if 2 is added to the 1056, we get remainder 0.
Therefore solution is 2
Question: A gym offers 11 levels of fitness classes, and in an attempt to reward those who progress toward higher levels of fitness it charges $50 less per course for each level of fitness. Jessica completed all 11 levels by taking one course at each level, and her total cost was $4675. What is the cost Z for a course at the gym's highest level?
A.$175
B.$245
C.$425
D.$675
Answer: A.$175
Explanation: Let the cost of a course in level 1 = x
=> Cost of level 2 = x-(50*1)... and so on
=> cost of level 11 = x-(50*10) = x-500
=> Total cost Z of 1 course in each of the 11 levels = x+(x-50)+(x-100)+.....+(x-500)
= 11x -50 (1+2+....+10)
= 11x - (50*55)
=> 11x-2750 = 4675
11x = 7425
x= 675
x-500=175
Answer A
Question: 39! is divided by 41. Then what is the remainder?
A.1
B.2
C.3
D.5
Answer: A.1
Explanation: Substituting p = 41 in the wilson's theorem, we get
40!+141=0
40×39!+141=0
−1×39!41=−1
Cancelling -1 on both sides,
39!41=1
A
Question: What percent of a day is 5 hours?
A.12%
B.12.5%
C.13%
D.20.8%
Answer: D.20.8%
Explanation: Explanation :
Solution: required percentage = (5/100 * 24) = 20.8%
Answer : D
Question: Find the highest common factor of 36 and 84.
A.12
B.10
C.16
D.19
Answer: A.12
Explanation: 36 = 2^2 x 3^2
84 = 2^2 x 3 x 7
H.C.F. = 2^2 x 3 = 12.
Answer: Option A
Question: A passenger train takes two hours less for a journey of 300km if its speed is increased by 5 kmph from its normal speed. The normal speed is
A.35 kmph
B.50 kmph
C.25kmph
D.30 kmph
Answer: C.25kmph
Explanation: let normal speed = x
Increased speed = x + 5
Initial => x = 300/t1
=> t1 = 300/x
After => (x + 5) = 300/(t1 - 2)
=> (x + 5) = 300 / [ (300/x) - 2]
=> x = 25kmph
ANSWER:C
Question: Mangala completes a piece of work in 10 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is?
A.8 days
B.9 days
C.12 days
D.14 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.
That is, the required No. of days = 10 × 40/50 = 8 days.
A)
Question: A card board of 34 * 14 has to be attached to a wooden box and a total of 35 pins are to be used on the each side of the cardbox. Find the total number of pins used .
A.135
B.136
C.137
D.138
Answer: B.136
Explanation: (35*4)-4=136
ANSWER:B
Question: Rajan got married 8 years ago. His present age is 6/5 times his age at the time of his marriage. Rajan's sister was 10 years younger to him at the time of his marriage. The age of Rajan's sister is?
A.11 years
B.88 years
C.38 years
D.17 years
Answer: C.38 years
Explanation: Let Rajan's present age be x years.
Then, his age at the time of marriage = (x - 8) years.
x = 6/5 (x - 8)
5x = 6x - 48 => x = 48
Rajan's sister's age at the time of his marriage = (x - 8) - 10 = 30 years.
Rajan's sister's present age = (30 + 8) = 38 years.
Answer: C
Question: An inspector rejects 10% of the meters as defective. How many will he examine to reject 15?
A.A)100
B.B)150
C.C)250
D.D)200
Answer: B.B)150
Explanation: Then, 10% of x= 15
(10/100)x = 15
x = (15*100*)/10= 150
Answer is B
Question: A pupil's marks were wrongly entered as 83 instead of 63. Due to the average marks for the class got increased by half. The number of pupils in the class is?
A.13
B.18
C.40
D.82
Answer: C.40
Explanation: Let there be x pupils in the class.
Total increase in marks
= (x * 1/2) = x/2
x/2 = (83 - 63)
=> x/2 = 20
=> x = 40
Answer:C
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
A.7
B.9
C.8
D.6
Answer: C.8
Explanation: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer: C
Question: In a function they are distributing noble prize. In how many ways can 4 prizes be distributed among 6 boys when a boy gets any no. of prizes?
A.1296
B.1678
C.1456
D.1200
Answer: A.1296
Explanation: Ans.(A)
Sol. In this case, repetitions are allowed, so all the 4 prizes can be given in 6 ways, i.e. (6 x 6 x 6 x 6) ways = 64 ways = 1296 ways Or nr ways = 64 ways = 1296 ways
Question: A train running at the speed of 60 km/hr crosses a pole in 3 sec. What is the length of the train?
A.50
B.75
C.100
D.120
Answer: A.50
Explanation: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 3 = 50 m
Answer: A
Question: From a nine-member dance group, six will be chosen at random to volunteer at a youth dance event. If Kori and Jason are three of the nine members, what is the probability that three will be chosen to volunteer?
A.a) 1/21
B.b) 100/7
C.c) 4/21
D.d) 2/7
Answer: B.b) 100/7
Explanation: Total number of ways to choose 6 out of 9 = 9C6 = 21/5.
Number of ways to choose 3 (any but Kori and Jason) out of 6 (excluding Kori and Jason) = 6C3 = 60.
P = favorable/total = 60/(21/5) = 100/7.
Answer: B.
Question: 400 + 5 × 4 = ?
A.820
B.202
C.420
D.209
Answer: C.420
Explanation: 400 + 5 × 4 = ?
or, ? = 400 + 20 = 420
Answer C
Question: If the ratio of the sum of the first 6 terms of a G.P. to the sum of the first 3 terms of the G.P. is 28, what is the common ratio of the G.P?
A.3
B.1/3
C.2
D.9
Answer: A.3
Explanation: 28=(a1+a2+a3+a4+a5+a6)/(a1+a2+a3)
Factorize the same terms
28=1+(a4+a5+a6)/(a1+a2+a3)
Write every term with respect to r
a1=a1
a2=a1*r^1
a3=a1*r^2
.........
28=1+(a1(r^3+r^4+r^5))/(a1(1+r^1+r^2))
27=(r^3 (1+r^1+r^2))/((1+r^1+r^2))
27=r^3
r=3
A
Question: How many natural numbers are there between 43 and 200 which are exactly divisible by 6?
A.28
B.26
C.24
D.22
Answer: B.26
Explanation: Explanation :
43/6 = 7, remainder = 1. Hence 5 more should be added to 43 to get the minimum
number divisible by 6 between 43 and 200.
=> Minimum number divisible by 6 between 43 and 200 = 43 + 5 = 48
200/6 = 33, remainder = 2. Hence 2 should be decreased from 200 to get the maximum
number divisible by 6 between 43 and 200.
=> Maximum number divisible by 6 between 43 and 200 = 200 - 2 = 198
Hence, natural numbers numbers divisible by 6 between 43 and 200 are 48, 54, 60,...198
This is Arithmetic Progression with a = 48, d = 6, l=198
Number of terms = (l − a)/d + 1 = (198 − 48)/6 + 1 = 150/6 + 1 = 25 + 1 = 26. Answer : Option B
Question: Jack and Christina are standing 360 feet apart on a level surface. Their dog, Lindy, is standing next to Christina. At the same time, they all begin moving toward each other. Jack walks in a straight line toward Christina at a constant speed of 5 feet per second and Christina walks in a straight line toward Jack at a constant speed of 7 feet per second. Lindy runs at a constant speed of 12 feet per second from Christina to Jack, back to Christina, back to Jack, and so forth. What is the total distance, in feet, that Lindy has traveled when the three meet at one place?
A.270
B.300
C.330
D.360
Answer: D.360
Explanation: The relative speed of Jack and Christina is 5+ 7 = 12 feet per second.
The distance between them is 210 feet, hence they will meet in (time) = (distance)/(relative speed) = 360/12 = 30 seconds.
For all this time Lindy was running back and forth, so it covered (distance) = (speed)*(time) = 12*30 = 360 feet.
Answer: D.
Question: The product of x and y is a constant. If the value of x is increased by 40%, by what percentage must the value of y be decreased?
A.34%
B.36%
C.28.57%
D.30%
Answer: C.28.57%
Explanation: x*y = constt.
Let x = y = 100 in beginning
i.e. x*y = 100*100 = 10000
x (100) ---becomes---> 1.4x (140)
i.e. 140*New 'y' = 10000
i.e. New 'y' = 10000/140 = 71.43
i.e. y decreases from 100 to 71.43 i.e. Decrease of 28.57%
C
Question: Bill purchases an item and receives no change. Before the purchase, he has only a five dollar bill, two 10 dollar bill, and a twenty dollar bill. How many distinct possibilities are there for the total amount of his purchase?
A.3
B.4
C.6
D.9
Answer: D.9
Explanation: We have 5, 10, 10 and 20 to work with
From least to greatest, we have...
5 (the least)
10
15
20
25
30
35
40
45 (the greatest)
Total options = 9
Final Answer:D
Question: If â€œ*â€ is called â€œ+â€, â€œ/â€ is called â€œ*â€, â€œ-â€ is called â€œ/â€, â€œ+â€ is called â€œ-â€. 240*80 / 60 + 40 / 10 = ?
A.-2305
B.-2407
C.2509
D.-2101
Answer: B.-2407
Explanation: Explanation:
Given : 240*80 / 60 + 40 / 10 = ?
Substituting the coded symbols for mathematical operations, we get,
240 / 80 - 60 * 40 - 10 = ?
3 - 2400 - 10 = -2407
ANSWER : B
Question: The average height of 35 boys in a class was calculated as 180cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places)?
A.178.88
B.178.29
C.188.29
D.178.2
Answer: B.178.29
Explanation: Calculated average height of 35 boys = 180 cm.
Wrong total height of 35 boys = 180 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 180 * 35 cm - 166 cm + 106 cm
= 180 * 35 cm - 166 cm + 106 cm/35
= 180 cm - 60 /35 cm
= 180 cm - 1.71 cm
= 178.29 cm.
Answer:B
Question: A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2460?
A.Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.750
B.Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.759
C.Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.758
D.Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.752
Answer: A.Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.750
Explanation: 1/2:1/3:1/4 = 6:4:3
Ram = 6/13 * 3250 = 1500
Shyam = 4/13 * 3250 = 1000
Mohan = 3/13 * 3250 = 750
Answer: A
Question: A lady who lived in a shoe had to buy Christmas gifts for her big family. She selected the cheapest stocking stuffers. The bill was still high. There was an addition of 15 percent of the sales tax and an addition of the 5 percent of the luxury tax to the actual amount. She paid $100.
Find out the original price of the stuffers without the taxes ?
A.$55.26
B.$83.33
C.$45.87
D.$90.12
Answer: B.$83.33
Explanation: B
The original price is $83.33.
(20 percent of the taxes are added to the selling price.)
Question: A number when divided by 133 leaves 16 as a remainder. What will be the remainder if the number is divided by 50?
A.51
B.56
C.49
D.17
Answer: C.49
Explanation: 133+16=149
Dividing 149 evenly into whole numbers is 2 and leaves 49 remaining.
The correct answer is C.
Question: Two-third of a positive number and 25/216 of its reciprocal are equal. The number is:
A.5/12
B.12/5
C.25/144
D.144/25
Answer: A.5/12
Explanation: Let the number be x. Then,
2/3 x = 25/216 * 1/x
x2 = 25/216 * 3/2 = 25/144
x = 5/12
ANSWER:A
Question: If x^2 = y^3 , where x and y are non negative and non zero integers, what is the greatest possible value of x / y from options below?
A.1
B.3
C.2
D.4
Answer: B.3
Explanation: B. x=27, y=9
27^2=729
9^3=729
x / y=27 / 9=3
My Answer is (B) 3
Question: 39! is divided by 41 then find the remainder?
A.1
B.3
C.5
D.6
Answer: A.1
Explanation: Substituting p = 41 in the wilson's theorem, we get
40!+141=0
40×39!+141=0
−1×39!41=−1
Cancelling -1 on both sides,
39!41=1
A
Question: Two cubes each with side b are joined to form a cuboids. What is the surface area of this cuboids?
A.12b^2
B.10b^2
C.6b^2
D.4b^2
Answer: B.10b^2
Explanation: l=2b; b=b; h=b;
surface area=2*(lb+bh+hl)
=2*(2b^2+b^2+2b^2)
=10 b^2
ANSWER:B
Question: Two trains travelling in the same direction at 40 and 22 kmph completely pass off another in 1 minute. If the length of the first train is 125 m, what is the length of the second train?
A.195 m
B.145 m
C.175 m
D.179 m
Answer: C.175 m
Explanation: Explanation:
RS = 40 – 22 = 18 * 5/18 = 5 mps
T = 60 sec
D = 5 * 60 = 300 m
125
--------
175 m
Answer: Option C
Question: At an examination in which full marks were 500. A got 10% less than B, B got 25% more than C and C got 20% less than D. If A got 360marks, what percentage of full marks was obtained by D?
A.40%
B.60%
C.80%
D.20%
Answer: C.80%
Explanation: A B C D
90 100 80 100
A D
90 ---------100
360 ------ ? = 400
500 ------ 400
100 ------- ? => 80%
Answer:C
Question: A dog breeder currently has 9 breeding dogs. 6 of the dogs have exactly 1 littermate, and 3 of the dogs have exactly 2 littermates. If 2 dogs are selected at random, what is the probability R that both selected dogs are NOT littermates?
A.1/6
B.2/9
C.5/6
D.7/9
Answer: C.5/6
Explanation: We have three pairs of dogs for the 6 with exactly one littermate, and one triplet, with each having exactly two littermates.
So, in fact there are two types of dogs: those with one littermate - say A, and the others with two littermates - B.
Work with probabilities:
Choosing two dogs, we can have either one dog of type B or none (we cannot have two dogs both of type B).
The probability of choosing one dog of type B and one of type A is 3/9 * 6/8 * 2 = 1/2 (the factor of 2 for the two possibilities BA and AB).
The probability R of choosing two dogs of type A which are not littermates is 6/9 * 4/8 = 1/3 (choose one A, then another A which isn't the previous one's littermate).
The required probability is 1/2 + 1/3 = 5/6.
Find the probability for the complementary event: choose AA or BB.
Probability of choosing two dogs of type A who are littermates is 6/9 * 1/8 = 1/12.
Probability of choosing two dogs of type B (who necessarily are littermates) is 3/9 * 2/8 = 1/12.
Again, we obtain 1 - (1/12 + 1/12) = 5/6.
Answer: C
Question: When 24 is divided by the positive integer a, the remainder is 4. Which of the following statements about a must be true?
I. a is even
II. a is a multiple of 5
III. a is a factor of 20
A.III only
B.I and II only
C.I and III only
D.II and III only
Answer: D.II and III only
Explanation: 24= m*a + 4
m*a=20
put values of m
m=1 a=20
m=2 a=10
m=4 a=5
I. not true
II. true
III. true
D. correct