RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The average salary of workers in an industry is Rs.200 the average salary of technicians being Rs.400 and that of non-technicians being Rs.125. What is the total number of workers?
A.399
B.665
C.998
D.2771
Answer: B.665
Explanation: 8 * 84 = 672 – 7
= 665
Answer:B
Question: In a friendship gang Andrew has 8 gang, in how many ways can he invite one or more of the gang to his house?
A.234
B.255
C.278
D.289
Answer: B.255
Explanation: Andrew can select one or more than one of his 8 gang.
=> Required number of ways = 28 – 1= 255.
B
Question: 11 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be :
A.84 m
B.88 m
C.14 m
D.137 m
Answer: C.14 m
Explanation: Sol.
Let the length of the wire b h.
Radius = 1/2 mm = 1/20 cm. Then,
22/7 * 1/20 * 1/20 * h = 11 ⇔ = [11 * 20 * 20 * 7 / 22] = 1400cm = 14 m.
Answer C
Question: A man rows down stream 40 km and upstream 21 km taking 4 hrs each time. what is the velocity of current?
A.2.735 Kmph
B.2.375 kmph
C.2. 573 kmph
D.2 kmph
Answer: B.2.375 kmph
Explanation: Explanation:
Man's rate downstream = 40/4 = 10 Kmph
Man's rate upstream = 21/4 = 5.25 Kmph
Velocity of current = 1/2( 10 - 5.25)
= 2.375 Kmph
Answer: Option B
Question: Due to construction, the speed limit along an 10-mile section of highway is reduced from 55 miles per hour to 20 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
A.A) 6.24
B.B) 8
C.C) 10
D.D) 19.1
Answer: D.D) 19.1
Explanation: Old time in minutes to cross 10 miles stretch = 10*60/55 = 10*12/11 = 10.9
New time in minutes to cross 10 miles stretch = 10*60/20 = 10*3 = 30
Time difference = 19.1
Ans:D
Question: A and B can do a piece of work in 50 days and 50 days respectively. They work together for 10 days and B leaves. In how many days the whole work is completed?
A.30days
B.35days
C.40days
D.44days
Answer: A.30days
Explanation: Explanation:
(A+B)’s 10 days work = 10[1/50+1/50]=10[1+1/50]= 2/5
A complete remaining work in 2/5*50 = 20
Total work = 10+20= 30days
Answer: Option A
Question: Three boys, two girls, and two women are to be seated on a bench. If one specific boy must be seated on one of the end seats, and one specific girl must me seated exactly in the middle, find the number of possible arrangements E.
A.a) E=48
B.b) E=144
C.c) E=240
D.d) 288
Answer: C.c) E=240
Explanation: One specific boy is seated to either of end seat, lets call him b1
One specific girl is seated in the middle, lets call her g1
Note the question says *specific girl* and *specific boy*, so we do not consider for example the other girl , g2, being seated on seat #4. Same goes with the specific boy, b1.
b1 can be seated 2 different seats : 2!
g1 is seated on the seat #4, fixed (no other alternative) : 1
the remaining 5 seats can be filled with the remaining people b2,b3,g2,w1,w2: 5!
2! x 1 x 5! = 240
Answer C
Question: An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of?
A.600km/hr
B.720km/hr
C.710km/hr
D.510km/hr
Answer: B.720km/hr
Explanation: Distance = 240*5 = 1200 km
Required speed = 1200 * 3/5 = 720km/hr
Answer is B
Question: 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 8 women and 12 children take to complete the work?
A.4
B.5
C.7
D.8
Answer: B.5
Explanation: 1 women's 1 day work = 1/70
1 child's 1 day work = 1/140
(8 women + 12 children)'s 1 day work
= (8/70 + 12/140) = 1/5
8 women and 4 children will complete the work in 5 days.
B
Question: If d is the standard deviation x, y, and z, what is the standard deviation of x +3, y + 3, z + 3 ?
A.3d
B.3d+3
C.d
D.3d+9
Answer: C.d
Explanation: CONCEPT: Standard Deviation is Defined as Average Deviation of Terms in the set from the Mean value of the set. i.e.
1) It depends on the separation between the successive terms of the set
2) If a Constant Value is Added/Subtracted in every terms of set then the Separation between successive terms does NOT change Hence S.D. remains Constant
e.g.{1, 2, 3, 4, 5} will have same standard Deviation as {1+10, 2+10, 3+10, 4+10, 5+10}
3) If a Constant Value is Multiplied in every terms then the Separation between succesive terms gets multiplied by the constant Hence S.D. remains gets multiplied by same Number
e.g. {0.7, 1.4, 2.1, 2.8, 3.5} will have Standard Deviation = 0.7* Standard deviation of set {1, 2, 3, 4, 5}
When 3 is added in each term of set {x, y, z} then the new set {x+3, y+3, z+3} will remain same as the previous standard deviation i.e. d
Answer: C
Question: Right now, the ratio between the ages of Sandy and Molly is 4:3. After 6 years, Sandy’s age will be 30 years. What is Molly's age right now?
A.12
B.14
C.16
D.18
Answer: D.18
Explanation: Now, Sandy is 30 - 6 = 24
Molly's age is (3/4) * 24 = 18
The answer is D.
Question: A person lent a certain sum of money at 6% per annum at simple interest and in 8 years the interest amounted to $572 less than the sum lent. What was the sum lent?
A.1000
B.1100
C.1200
D.1300
Answer: B.1100
Explanation: P - 572 = (P*6*8)/100
P = 1100
The answer is B.
Question: The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, What is the the speed of the first train?
A.87.0
B.87.5
C.87.2
D.87.1
Answer: B.87.5
Explanation: Speed and time are inversely proportional (when distance is constant) ⇒Speed ∝ 1Time (when distance is constant)
Here distance is constant and hence speed and time are inversely proportionalSpeed ∝ 1Time⇒Speed1Speed2=Time2Time1⇒78=4Time1⇒Time1 = 4×87 hr⇒Speed of the first train = DistanceTime1=400(4×87)=100×78=12.5×7=87.5 km/hr
Answer :B
Question: The diameter of the driving wheel of a bus in 140 cm. How many revolutions per minute must the wheel make in order to keep a speed of 20 kmph?
A.21.21
B.20.25
C.32.25
D.75.75
Answer: D.75.75
Explanation: distance covered in 1 min=(20*1000)/60=333.33m
circumference of the wheel=(2*(22/7)*.70)=4.4m
no of revolution per min=333.33/4.4=75.75
ANSWER:D
Question: 6, 11, 21, 36, 56, ?
A.51
B.71
C.81
D.61
Answer: C.81
Explanation: The pattern is + 5, + 10, + 15, + 20,....
Answer : C.
Question: Salaries of A, B and C were in the ratio 3 : 5 : 7 respectively. If their salaries were increased by 50 per cent, 60 per cent and 50 per cent respectively, what will be the new ratio of their respective salaries?
A.4 : 5 : 7
B.3 : 6 : 7
C.4 : 15 : 18
D.9 : 16 : 21
Answer: D.9 : 16 : 21
Explanation: New ratio will be 3 x (150/100) : 5 x (160/100) : 7 x (150/100) = (9/2) : 8 : (21/2)
= 9 : 16 : 21
ANSWER:D
Question: How many terms are there in 2, 4, 8, 16,..., 2048?
A.14
B.11
C.12
D.10
Answer: B.11
Explanation: 2, 4, 8, 16, ...,2048 is a G.P with a =2
and r =4/2 =2
Let the number of terms be n. Then
2 x 2 ^n-1 = 2048
or 2^n-1 = 1024= 2^10
Thus n - 1 =10
n= 11
ANSWER:B
Question: Which of the following is the product of two integers whose sum is 12?
A. -42
B. -28
C. 12
D. 26
Answer: B. -28
Explanation: I solved this Question like this,
Let the two integers are x,y
x+y=12 (Given)
xy=? (Needed)
instead of solving this algebraically, Test the Answer choices
B. -28
Do the factorization : (-1,28)----> There sum is not 12--eliminate
(-2,14)---->There sum is 12 Bingo!!!!
So, my answer is B...
As the answer is in B, it took me very less time to answer the question. but i think this method is be simple and efficient.
Question: In the formula V = 1/(2r)^2, if r is halved, then V is multiplied by?
A.4
B.8
C.1
D.1/8
Answer: A.4
Explanation: Say r=2 => V1 = 1/16
when r=1; V2 = 1/4
V2 = 4*V1.
Answer : A
Question: Mrs. Napier has 38 stickers to give to 5 students for a reward. How many
stickers will each student get? Will there be any stickers left over?
A.2-5
B.2-4
C.7-6
D.2-3
Answer: C.7-6
Explanation: 38/5 = 7 R 6 Mrs. Napier will give each student 7 stickers and there
will be 6 left over.
correct answer C
Question: If 3<x<6<y<8, then what is the greatest possible positive integer difference of x and y?
A.3
B.4
C.5
D.6
Answer: B.4
Explanation: 3 < x < 6 < y < 8;
3 < x
y < 8
3 + y < x + 8
y - x < 5.
Positive integer difference is 4 (for example y = 7.5 and x = 3.5)
Answer: B.
Question: Two Copiers are being used to produce 2400 copies of a 1-page document. One Copier runs at 150% of the speed of the other. How many copies should be made on the faster copier so that both copiers will finish the same time?
A.1240
B.1440
C.1340
D.1540
Answer: B.1440
Explanation: Let the speed of one copier be x
Speed of other copier 150x/100
Ratio of speed = 1:150/100 = 2:3
copies made on faster copier = 3/5 *2400
= 1440
ANSWER:B
Question: Two students appeared at an examination. One of them secured 9 marks more than the other and his
marks was 56% of the sum of their marks. The marks obtained by them are
A.42,30
B.42,31
C.42,32
D.42,33
Answer: D.42,33
Explanation: Explanation:
Let their marks be (x+9) and x.
Then, x+9 = 56/100(x + 9 +x)
=> 25(x+9)
=> 14 (2x + 9)
=> 3x = 99
=> x = 33.
So, their marks are 42 and 33
Answer: Option D
Question: 12 men and 18 boys working 7.5 minutes an hour complete a particular piece of work in 60 hours. If a boy’s work is half as efficient as a man’s work, how many boys will be needed to help 21 men to achieve twice the work in 50 hours working 9 minutes in an hour.
A.28
B.77
C.42.
D.99
Answer: C.42.
Explanation: Explanation:
1 man is equivalent to 2 boys in work capacity. 12 men + 18 boys = 12 x 2 + 18 = 42 boys.
Let the required number of boys be x. So Total number of people doing work = 21 men x 2 (according to work capacity) + x boys.
Taking respective ratios as required:
Given:
=> Hours 50:60
=> Minutes per hour 9: 15/2
=> Work 1:2
=> People: 42: 42 + x
=> 50 x 9 x 1 x (42+x) = 60 x 15/2 x 2 x 42
=> 42 +x = 84
x = 42
ANSWER:C
Question: Find a sum for first 5 prime number's?
A.24
B.28
C.30
D.32
Answer: B.28
Explanation: Required sum = (2 + 3 + 5 + 7 + 11) = 28
Note: 1 is not a prime number
Option B
Question: The number of new words that can be formed by rearranging the letters of the word 'OF' is
A.5
B.8
C.1
D.3
Answer: C.1
Explanation: Explanation:
Number of words which can be formed = 2! - 1 = 2- 1 = 1.
Answer: C
Question: A student travels from his house to school at 10 km/hr and reaches school 2 hours late. The next day he travels 15 km/hr and reaches school 1 hour early. What is the distance between his house and the school?
A.60
B.70
C.80
D.90
Answer: D.90
Explanation: Let x be the distance from his house to the school.
x/10 = x/15 + 3
6x = 4x + 180
2x = 180
x = 90 km
The answer is D.
Question: How many positive integers less than 7,000 are there in which the sum of the digits equals 5?
A.52
B.54
C.56
D.58
Answer: C.56
Explanation: Basically, the question asks how many 4 digit numbers (including those in the form 0XXX, 00XX, and 000X) have digits which add up to 5. Think about the question this way: we know that there is a total of 5 to be spread among the 4 digits, we just have to determine the number of ways it can be spread.
Let X represent a sum of 1, and | represent a seperator between two digits. As a result, we will have 5 X's (digits add up to the 5), and 3 |'s (3 digit seperators).
So, for example:
XX|X|X|X = 2111
||XXX|XX = 0032
etc.
There are 8C3 ways to determine where to place the separators. Hence, the answer is 8C3 = 56.
C
Question: The value of a scooter depreciates in such a way that its value of the end of each year is 3/4 of its value of the beginning of the same year. If the initial value of the scooter is Rs.40,000, what is the value at the end of 1 year?
A.3277
B.2977
C.30000
D.6077
Answer: C.30000
Explanation: Explanation: 40,000*(3/4)^1
Answer:C
Question: For integers x, y, and z, if (3^x) (4^y) (5^z) = 13,107,200,000 and x + y + z = 16, what is the value of xy/z?
A.undefined
B.0
C.3
D.5
Answer: B.0
Explanation: The number 13,107,200,000 is not divisible by 3. (We can verify this by adding the digits of the number to see that the sum is not a multiple of 3.)
Thus x = 0 and xy/z = 0.
The answer is B.
Question: A does a work in 20 days and B does the same work in 30 days. In how many days they together will do the same work ?
A.5 days
B.6 days
C.9 days
D.12 days
Answer: D.12 days
Explanation: Explanation:
Firstly we will find 1 day work of both A and B, then by adding we can get collective days for them,
So,
A's 1 day work = 1/20
B's 1 day work = 1/30
(A+B)'s 1 day work =
(1/20+1/30)=1/12
So together they can complete work in 12 days.
Answer: D
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
A.246
B.240
C.88
D.76
Answer: B.240
Explanation: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.
Answer:B
Question: If 4 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is?
A.10:5:5
B.10:5:8
C.10:5:2
D.10:5:4
Answer: D.10:5:4
Explanation: 4A = 8B = 10 C
A:B:C = 1/4:1/8:1/10
= 10:5:4
Answer: D
Question: Frank the Fencemaker needs to fence in a rectangular yard. He fences in the entire yard, except for one full side of the yard, which equals 40 feet. The yard has an area of 200 square feet. How many feet offence does Frank use?
A.14
B.47
C.50
D.180
Answer: C.50
Explanation: Area = Length x Breadth
200 = 40 x Breadth
So, Breadth = 5 Units
Fencing required is -
Breadth + Breadth + Length
5 + 5 + 40 => 50 feet
Answer must be (C) 50
Question: If n is an even negative integer, which of the following must then be an odd positive integer?
A.2n
B.-2n + 1
C.-(n^2)
D.2n - 1
Answer: B.-2n + 1
Explanation: Answer: B
A: 2n = even negative
B: -2n + 1 = odd positive
C: -(n^2) = even negative
D: 2n - 1 = odd negative
E: n^3 = odd negative
Answer: B
Question: A store purchased a pair of pants for $210 and was selling it at a price that equaled the purchase price of the pants plus a markup that was 25 percent of the selling price. After some time a store owner decided to decrease the selling price by 20 percent. What was the store's gross profit on this sale?
A.$14
B.$2
C.$10
D.$6
Answer: A.$14
Explanation: Sale Price(SP) = 210 + Markup(MP)
--> Mp = SP-210
and given MP=SP/4 ( 25% is 1/4th)
so SP/4= SP-210
3SP/4= 210
SP=280
Now a discount of 20% is given so NEW SP is .8 *280 =224
Profit=224-210 =14
Answer is A
Question: There were two clock one is getting slow by two minutes/hr and another one is gaining 1 minute every hour and exactly after how many hours there two clock has a 1hr difference.
A.10 Hours
B.15 Hours
C.20 Hours
D.25 Hours
Answer: C.20 Hours
Explanation: Assume x as the current time.
After an hour:
Time in Clock1=x+58mins
Time in Clock2=x+61 mins
Time difference between both the clocks after an hour=61-58=3 mins
3 mins of time difference happens in 1 hour
therefore 60 min (i.e. 1 hour) of time diffrence will happen in= 1/3 *60 =20 Hours
ANSWER:C
Question: Jerry left a job paying $75,000 per year to accept a sales job paying $45,000 per year plus 15 percent commission. If each of his sales is for $750, what is the least number of sales he must make per year if he is not to lose money because of the change?
A.40
B.200
C.266
D.267
Answer: D.267
Explanation: In order not to lose money because of the change Jerry's total commission must beat least$75,000-$45,000=$30,000, so total sales must beat least$30,000/0.15=$200,000. Which means that he must makeat least$200,000/750=800/3=266.6 sales, so 267 sales.
Answer: D.
Question: Mathematics, physics, and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many mathematics books as physics books and the number of physics books is 4 greater than that of the chemistry books. Ricardo selects 1 book at random from the shelf, reads it in the library, and then returns it to the shelf. Then he again chooses 1 book at random from the shelf and checks it out in order to read at home. What is the probability Ricardo reads 1 book on mathematics and 1 on chemistry?
A.3%
B.6%
C.12%
D.20%
Answer: C.12%
Explanation: Shelf can accommodate 25 books but 20% of it is empty so there are in all 20 books.
If no of Chem books = x, number of Physics book = x+4, number of Math books = 2(x+4)
x + x+4 + 2(x+4) = 4x + 12 = 20
x = 2
Chem books = 2, Phy books = 6, Math books = 12
Probability of picking a Math book = 12/20
Probability of picking a Chem book = 2/20
Total Probability = Pick Math first and then Chem + Pick Chem first and then Math
= (12/20) * (2/20) + (2/20) * (12/20) = 12/100 = 12%
Answer:C
Question: A number increased by 20% gives 600. The number is
A.250
B.400
C.450
D.500
Answer: D.500
Explanation: Formula = TOTAL=100% ,INCRESE = "+" DECREASE= "-"
A number means = 100 %
That same number increased by 20 % = 120 %
120 % -------> 600 (120 × 5 = 600)
100 % -------> 500 (100 × 5= 500)
D)
Question: .
On dividing a number by 357, we get 38 as remainder. On dividing the same number 17, what will be the remainder ?
A.0
B.3
C.4
D.8
Answer: C.4
Explanation: Let x be the number and y be the quotient. Then,
x = 357 x y + 38
= (17 x 21 x y) + (17 x 2) + 4
= 17 x (21y + 2) + 4)
Required remainder = 4.
Answer: Option C
Question: The average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 18 years(the child was born during the interval). What is the present age of the child?
A.13 years
B.9 years
C.6 years
D.4 years
Answer: A.13 years
Explanation: 28 * 2 = 56
23 * 3 = 69
-----------
13 years
Answer: A
Question: There are 8 digit mobile numbers. From that how many 8 digit mobile numbers can be formed if any digit can be repeated and 0 can also start the mobile number?
A.9^2
B.7^3
C.10^8
D.11^9
Answer: C.10^8
Explanation: Here the digits(0,1,2,3,4,5,6,7,8,9) can be repeated and 0 can also be used to start the mobile number. Hence, any of the 10 digits can be placed at each place of the 8 digit number.
10	10	10	10	10	10	10	10
Hence, required number of 8 digit mobile numbers
=10^8
C
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
A.4
B.5
C.6
D.7
Answer: A.4
Explanation: M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9 = 4
Answer: A
Question: Find two numbers whose sum is 26 and whose product is 165.
A.11 and 12
B.11 and 13
C.11 and 15
D.11 and 16
Answer: C.11 and 15
Explanation: Let the two numbers be a and b and use the sum and product to write two equations with two unknowns
a + b = 26 and a b = 165
Solve the first equation for b
b = 26 - a
Substitute b in the equation a b = 165 by 26 - a
a (26 - a) = 165
Write the above equation in standard form
- a 2 + 26 a - 165 = 0
Solve the above equation for a
a = 11 and a = 15.
Use b = 26 - a to find b
when a = 11 , b = 15 and when a = 15 , b = 11.
The two numbers are 11 and 15.
Answer C
Question: Pure milk costs 3.60 per litre. A milkman adds water to 25 litres of pure milk and sells the mixture at 3 per litre. How many litres of water does he add?
A.2 litres
B.5 litres
C.7 litres
D.11 litres
Answer: B.5 litres
Explanation: In mixture,
Quantity of pure milk /Quantity of water=3−0/3.6−3=3/0.6=5/1
Since in every 5 litres of milk, he adds 1 litre of water.
∴ In every 25 litres of milk, he adds 5 litres of water.
Answer B
Question: If y = x^2 + mx + n, y is minimum when x is:
A.m/n
B.-m/n
C.-m/2
D.-n/2
Answer: C.-m/2
Explanation: We're given the equation Y = X^2 + mX + n.
IF.. we use a simple Classic Quadratic....
m = 2
n = 1
Y = X^2 + 2X + 1
We can then go about finding the answer that yields the MINIMUM result when X = ...
Answer A: m/n = 2/1 = 2 --> 4+4+1 = +9
Answer B: -m/n = -2/1 = -2 --> 4-4+1 = +1
Answer C: -m/2 = -2/2 = -1 --> 1-2+1 = 0
Answer D: -n/2 = -1/2 -->(1/4)-1+1 = +1/4
Answer E: n/m = 1/2 --> (1/4)+1+1 = +2 1/4
From these results, we can see the minimum result:
C
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 850 grams per kg, what is his percent?
A.2%
B.25%
C.22%
D.17.65%
Answer: D.17.65%
Explanation: 850 --- 150
100 --- ? => 17.65%
Answer:D
Question: The sale price sarees listed for Rs.340 after successive discount is 20% and 15% is?
A.298
B.231
C.342
D.876
Answer: B.231
Explanation: 340*(80/100)*(85/100)
= 231
Answer: B
Question: If 2|2 –w| = 5, what is the sum of all the possible values for w ?
A.1/2
B.2
C.5/2
D.4
Answer: D.4
Explanation: if w<2, then 2-w=5/2; w=-1/2
if w>2 , then w-2=5/2; w=9/2
9/2-1/2=8/2=4=D
Question: Factor: 16w3 – u4w3
A.w3(4 + u2)(2 + u)(2 + u)
B.w3(4 + u2)(2 - u)(2 + u)
C.w3(4 + u2)(2 + u)(2 - u)
D.w3(4 - u2)(2 + u)(2 - u)
Answer: C.w3(4 + u2)(2 + u)(2 - u)
Explanation: 16w3 – u4w3.
= w3(16 – u4).
= w3(42 - ((u2)2).
= w3(4 + u2)(4 - u2).
= w3(4 + u2)(22 - u2).
= w3(4 + u2)(2 + u)(2 - u).
Answer: (C)w3(4 + u2)(2 + u)(2 - u).
Question: Let the polynomials be:
P1(x)=3x2−7x+5,
P2(x)=−5x2−4x+2,
P1(x)+P2(x)=
A.2x2 + 11x - 7
B.-2x2 - 11x + 7
C.-2x2 - 11x + 6
D.2x2 - 9x + 7
Answer: B.-2x2 - 11x + 7
Explanation: Solution:
P1(x)+P2(x)=(3x2−7x+5)+(−5x2−4x+2)=P1(x)+P2(x)=(3x2−7x+5)+(−5x2−4x+2)=
3x2−7x+5−5x2−4x+2=3x2−7x+5−5x2−4x+2=
−2x2−11x+7
Answer B
Question: A problem is given to three students whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved?
A.3/0
B.3/1
C.3/4
D.3/8
Answer: C.3/4
Explanation: Let A, B, C be the respective events of solving the problem and be the respective events of not solving the problem. Then A, B, C are independent events
are independent events
Now, P(A) = 1/2 , P(B) = 1/3 and P(C)=1/4
P( none solves the problem) = P(not A) and (not B) and (not C)
=
= =
=
Hence, P(the problem will be solved) = 1 - P(none solves the problem)
Answer: C) 3/4
Question: If x is real, find the maximum value of the expression -2x^2 + 11x + 13.
A.16.125
B.20.125
C.24.125
D.28.125
Answer: D.28.125
Explanation: This is an equation of a downward facing parabola.
The maximum value is the top point of the parabola.
-2x^2+11x+13 = (-2x+13)(x+1)
The roots are 13/2 and -1.
The maximum value must be when x is halfway between these two points.
x = 2.75
The maximum value is -2(2.75)^2+11(2.75)+13 = 28.125
The answer is D.
Question: A family of 7 queue to get ice cream from a an ice cream van. What is the probability that the father will be standing right in front of the mother in the queue?
A. 5%
B. 10%
C. 15%
D. 21%
Answer: D. 21%
Explanation: Possible Sitting position is 7! = 120
Father standing next to mother is 7 Combination 2
=7!/2!(7-2)!
=5040/2(120)
=5040/240
= 21
Answer = D
Question: Find the area of trapezium whose parallel sides are 24 cm and 18 cm long, and the distance between them is 15 cm.
A.227
B.299
C.315
D.161
Answer: C.315
Explanation: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (24 + 18) * (15)
= 315 cm2
Answer: C
Question: In a group of 800 people, 3/5 play at least one instrument, 96 play two or more. What is the probability that one student play exactly one instrument?
A.2/125
B.12/25
C.C)2/25
D.3/25
Answer: B.12/25
Explanation: P(playing 2 or more instruments) = 96/800 = 3/25.
Then, the probability of playing exactly one instrument is given by:
P(playing 1 or more instruments) - P(playing 2 or more instruments) = 3/5 - 3/25 = 12/25.
Answer B.
Question: The amount of principal Rs.8000 at compound interest at the ratio of 5% p.a. for 5 years is
A.s.9621
B.s.6921
C.s.10210
D.s.6261
Answer: C.s.10210
Explanation: c.i=p(1+r/100)^n
=8000(1+5/100)^5
=Rs10210
ANSWER:C
Question: If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
A.1
B.8
C.2
D.7
Answer: B.8
Explanation: 96% ---- 12
144% ---- ?
96/144 * 12 = 8
Answer: B
Question: A store sells seven different kinds of shirts. If we want to buy two different kinds of shirts, how many possible combinations of two shirts can we buy?
A.21
B.22
C.23
D.24
Answer: A.21
Explanation: 7C2=21.
The answer is A.