RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If the tens digit of positive integer x is 3 and the tens digit of positive integer y is 3, how many possible values of the tens digit of 2(x+y) can there be?
A.2
B.3
C.4
D.5
Answer: C.4
Explanation: We only need to consider the tens and ones digits of x and y, and the last two digits can be represented as 30 + p and 30 + q respectively.
2(30+p+30+q)= 120 + 2(p + q)
2(p+q) can range from 0 up to a maximum value of 36 when p=q=9.
Then the tens and ones digits of 2(x+y) can range from 20 up to 56.
There can be 4 possibilities for the tens digit.
The answer is C.
Question: The editor of an anthology of short stories will select authors from a pool of 10 authors, of which 4 are female. If the anthology is to include the work of 6 authors of which at least 2 are female, in how many ways can the editor select the authors?
A.155
B.165
C.175
D.185
Answer: D.185
Explanation: 10C6 = 210
The number of ways to select 6 males is 6C6 = 1
The number of ways to select 5 males and 1 female is 6C5*4C1 = 24
210 - 1 - 24 = 185
The answer is D.
Question: Three partners A,B,C starts a business. Twice A's capital is equal to thrice B's capital and B's capital is four times C's capital. Out of a total profit of Rs.15000 at the end of the year, B's share is
A.Rs.4000
B.Rs.5400
C.Rs.7500
D.Rs.6600
Answer: B.Rs.5400
Explanation: Solution
Let C = x.
Then, B = 4x and 2A = 3x4x = 12x or A = 6x.
âˆ´ A : B : C = 6x : 4x : x	= 6 : 4 : 1.
So B's capital	= Rs(15000 x 4 / 11)
= Rs.5400.
Answer B
Question: I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
A.228
B.280
C.287
D.115
Answer: B.280
Explanation: Explanation:
x*(85/100) = (480 - x)119/100
x = 280
Answer:B
Question: 82
a7
+ 6b
____
190
If a and b represent positive single digits in the correctly worked computation above, what is the value of a + 2b ?
A.2
B.6
C.9
D.11
Answer: B.6
Explanation: Adding the digits in unit's place , 2+ 7 + b = 10 (Since a and b are positive single digits )
=> b = 1
Now adding the digits in ten's place , 8+a + 6 + 1= 19 (1 has been carried over from unit's place addition)
=> a= 4
a+2b = 4+2*1
=6
Answer B
Question: Two persons Raj and Ramu started working for a company in similar jobs on January 1, 1991. Raj's initial monthly salary was Rs 400, which increases by Rs 40 after every year. Ramu's initial monthly salary was Rs 500 which increases by Rs 20 after every six months. If these arrangements continue till December 31, 200. Find the total salary they received during that period.
A.Rs 108000
B.Rs 144000
C.Rs 132000
D.Rs 152400
Answer: D.Rs 152400
Explanation: Explanation :
Raj's salary as on 1 jan 1991 is Rs 400 per month.
His increment in his month salary is Rs 40 per annum
His total salary from 1 jan 1991 to 31st dec 2000
i.e. in ten years
=>12[2(400)+(10−1)40]×10/2.
=>Rs 69,600.
Ramu's salary as on Jan 1st 1991 is Rs 550 and his half yearly increment in his month salary is Rs 20.
His total salary from 1 jan 1991 to dec 31, 2000
=>6[2(500)+(20−1)20]×20/2.
=>Rs 82,000.
Total salary of Raj and Ramu in the ten year period:
=> Rs. 69600+ Rs. 82800.
=>Rs 1,52,400.
Answer : D
Question: A completes a work in 15 days and B complete the same work in 30 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: C.10 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 = 15 ×30/ 45 = 10 days.
Answer : C
Question: Which of the following numbers is between 1⁄2 and 1⁄4?
A..65
B..55
C..29
D..22
Answer: C..29
Explanation: Isn't it C?
1/2 = .50
1/4 = .25
The only answer between that is C, .29.
Question: if 2 pipes take an hour to fill a tank, then how long should 8 pipes take to fill the same tank?
A.20 min
B.10 min
C.15 min
D.25 min
Answer: C.15 min
Explanation: if 2 pipes take an hour to fill a tank, then
8 pipes will take 2*60/8 = 15 mins to dig a ditch of the same type.
ANSWER:C
Question: Find √? /19 = 4 ?
A.76
B.5776
C.304
D.1296
Answer: B.5776
Explanation: Answer
Let √N/19 = 4
Then √N = 19 x 4 = 76
∴ N = 76 x 76 = 5776.
Correct Option: B
Question: Mr. Thomas invested an amount of 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be 3508, what was the amount invested in Scheme B?
A.6200
B.6300
C.6400
D.6500
Answer: C.6400
Explanation: Let the sum invested in Scheme A be x and that in Scheme B be (13900 - x).
Then, (x x 14 x 2)/100 + ((13900 - x) x 11 x 2)/100 = 3508
28x - 22x = 350800 - (13900 x 22)
6x = 45000
x = 7500.
So, sum invested in Scheme B = (13900 - 7500) = 6400.
answer : C
Question: How many numbers between 200 and 400 begin or end with 2?
A.20
B.60
C.100
D.110
Answer: D.110
Explanation: How many numbers between 200 and 400 begin or end with 2?
Just think that those numbers are:
i) The ones ending in 2: 202, 212, 222, ... , 392 --> 20 numbers
ii) The ones beginning in 3: 200, 201, 202, 203, ... , 293, ... , 299 --> 100 numbers
BUT 10 out of the first 20 numbers are repeated in the second set.
THEREFORE, the solution is 110 numbers.
Answer: D
Question: A square and an equilateral triangle have the same perimeter. What is the ratio of the area of the circle circumscribing the square to the area of the circle inscribed in the triangle?
A.9:8
B.15:8
C.27/8
D.8:9
Answer: C.27/8
Explanation: let x be side of square
perimeter of square=4x=perimeter of triangle=3*side of triangle
so side of eq. triangle=(4/3)*x
diameter of circle circumscribing the square=sqrt(2)*x
area of circle circumscribing the square= pi*(sqrt(2)*x)^2/4=(pi/2)*x^2 ----(1)
to find radius of the circle inscribed in the triangle
area of triangle=r*s=sqrt(3)/4 * (4x/3)^2
now s=(4/3)*x+(4/3)*x+(4/3)*x/2=2x
so sqrt(3)/4 * (4x/3)^2=r*2x gives
r={2/3*(3^1/2)}*x
area of the circle inscribed in the triangle=pi*[{2/3*(3^1/2)}*x]^2
=pi*(4/27)*x^2 -------(2)
so reqd ratio= eqn(1)/eqn(2)
=[(pi/2)*x^2]/[pi*(4/27)*x^2]=27/8
so reqd ratio=27:8
ANSWER:C
Question: If 600y is a perfect square (the square of an integer) and y is a positive integer, then which of the following must also be an integer?
I y/6
II y/42
III y/30
A.I only
B.III only
C.I and II only
D.I and III only
Answer: A.I only
Explanation: 600∗y=2^3∗3^1∗5^2∗y
For an integer to be a perfect square means that all its prime factors must have even powers.
Min value of yy required fo that is 2^1∗3^1
Answer A
Question: If m times the mth series of an A.P. is equal to n times its nth series, what is the (m+n)th term of the A.P. ?
A.1
B.m
C.n
D.0
Answer: D.0
Explanation: mth term of an A.P.
Am = a + (m-1)d
nth term of an A.P.
An = a + (n+1)d
[here a= First term of an A.P
d= difference between two consecutive terms
Am= mth term of A.P.]
According to the question;
m*Am = n*An
m(a + (m-1)d)= n(a + (n-1)d)
m(a + md - d)= n(a + nd - d)
am + m^2d-md = an + n^2d - nd
a(m-n)+ (m^2-n^2)d -(m-n)d = 0
a(m-n)+ (m-n)(m+n)d -(m-n)d= 0
(m-n)[a + (m+n)d - d ]= 0
[a + (m+n)d - d ]= 0
[a + (m+n-1)d ]= 0
So Am+n = 0
so answer will be 0
ANSWER:D
Question: A fruit salad mixture consists of apples, peaches, and grapes. There are 2 times as many pounds of apples as grapes and 3 times as many pounds of peaches as grapes. If a mixture that has an average (arithmetic mean) of 24 pounds per fruit, how many more pounds of apples than grapes does the mixture have?
A.15
B.12
C.8
D.6
Answer: C.8
Explanation: A+P+G= 24*2
A=3G
P=2.5G
3G+2G+G= 24*2
G= 24*2/6= 8
A= 8*2=16
Difference = 16-8=8
'C' is the answer
Question: Kim finds a 5-meter tree branch and marks it off in thirds and fifths. She then breaks the branch along all the markings and removes one piece of every distinct length. What fraction of the original branch remains?
A.8/15
B.1/2
C.7/5
D.3/5
Answer: D.3/5
Explanation: 3 pieces of 1/5 length and two piece each of 1/15 and 2/15 lengths. removing one piece each from pieces of each kind of lengths the all that will remain will be
2 pieces of 1/5 i.e 2/5, 1 piece of 1/15, and 1 piece of 2/15
Which gives us 2/5 + 1/15 + 2/15 -----> 3/5
Answer is D
Question: A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
A.228
B.277
C.350
D.882
Answer: C.350
Explanation: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 39 = 50/3
3(x + 300) = 1950 è x = 350m.
Answer:C
Question: If log a/b + log b/a = log (a + b), then:
A.a = b
B.a - b = 1
C.a + b = 1
D.15
Answer: C.a + b = 1
Explanation: Explanation:
log a/b + log b/a = log (a + b)
log (a + b)=log(b/a*a/b)= log 1
So, a + b = 1.
answer C
Question: At Tea factory, each employee working the second shift produced 2/3 as many widgets as each employee working the first shift. If the first shift has 3/4 as many employees, what fraction of the total widgets did the second shift produce?
A.8/17
B.1/2
C.8/9
D.9/8
Answer: A.8/17
Explanation: At Tea factory,Let the first shift have 3 employee and each produce 3 widgets, so the total number of widgets produced by the first shift is 3*3=9;
Then the second shift would have 4 employees and each second shift employee would produce 3*2/3=2 widgets, so the total number of widgets produced by the second shift employees would be 4*2=8;
The ratio of the second shift production to the total is 8/(9+8)=8/17.
Answer: A.
Question: In a class, the average age of 40 boys is 18 years and the average of 30 girls is 15 years. what is the average age of the whole class?
A.12 Years
B.12.3 Years
C.12.6 Years
D.16.7 Years
Answer: D.16.7 Years
Explanation: Total age of 70 students
(40X 18+30 X 15) = 1170
Average = 1170/70 = 16.7 Years
D
Question: In a theater, the first row has 14 seats and each row has 2 more seats than previous row. If the last row has 56 seats, what is the total number of seats in the theater?
A.770
B.780
C.790
D.800
Answer: A.770
Explanation: The number of seats in the theater is
14 + (14+2) + ...+ (14+42)=
22(14) + 2(1+2+...+21)=
22(14) + 2(21)(22)/2=
22(14+21) = 22(35) = 770
The answer is A.
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.30
B.33 1/3
C.35
D.25
Answer: B.33 1/3
Explanation: 100---150
150----50
100-----? ==>33 1/3
ANSWER B
Question: A motorcycle importer is planning on increasing the price of a certain model by $1000. At this new price 5 fewer motorcycles will be sold per month, but the total revenues will increase by $26,000 to $594,000. What is the number of motorcycles the manufacturer will sell at this new price?
A.51
B.61
C.66
D.71
Answer: C.66
Explanation: 66 bikes.
Got two equations bikes*price = 568 units
(bikes - 5)*(price + 1 ) = 594 units.
factorise 568 = 71 * 8.
use n = 71 and p = 8 in the second , it works.
Hence 66.
ANSWER:C
Question: Which of the following lines is perpendicular to y = − 2x + 3 and has the same y-intercept as y = 2x − 4?
A.y = -1/2*x + 3
B.y = 1/2*x - 4
C.y = 1/2*x + 3
D.y = 2x + 3
Answer: B.y = 1/2*x - 4
Explanation: Since our line has to perpendicular to y = − 2x + 3
Slope of this line , m = -2
Slope will be required line L = 1/2 ( Product of slope of perpendicular lines = -1)
y-intercept of line L is same as y intercept of line y = 2x − 4
y - intercept of line L = -4
Required line = 1/2* x - 4
Answer B
Question: The average of first ten prime numbers which are odd is?
A.15.9
B.15.0
C.15.2
D.15.8
Answer: D.15.8
Explanation: Sum of first 10 prime no. which are odd = 158
Average = 158/10 = 15.8
Answer: D
Question: For positive integers s and t, which of the following can be written as t^2?
A.s^2+9
B.s^2+2
C.s^2+3
D.s^2-1
Answer: A.s^2+9
Explanation: Plug values: if s=4, then 4^2+9=25
The question asks which of the following CAN be written as t^2. If s=4, then s^2+9 CAN be written as 5^2.
Answer: A
Question: Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 3 ½ hours if they are walking in the same direction?
A.4 3/9 km
B.4 7/8 km
C.4 3/8 km
D.8 3/8 km
Answer: C.4 3/8 km
Explanation: Explanation:
RS = 5 ¾ - 4 ½ = 1 ¼
T = 3 ½ h.
D = 5/4 * 7/2 = 35/8
= 4 3/8 km
Answer:C
Question: Navjivan Express from Ahmedabad to Chennai leaves Ahmedabad at 6.30 a.m. and travels at 50 kmph towards Baroda situated 100 km away. At 7.00 a.m. Howrah-Ahmedabad Express leaves Baroda towards Ahmedabad and travels at 40 kmph. At 7.30 a.m. Mr Shah, the traffic controller at Baroda realizes that both the trains are running on the same track. How much time does he have to avert a head-on collision between the two trains?
A.15 min
B.20 min
C.25 min
D.30 min
Answer: B.20 min
Explanation: Explanation :
Let A be ahmedabad and B for baroda.
At 7:30 train from A to B would have covered 50km while train from B to A would have covered 20 km since it travels for only half an hour.
Distance remaining between the trains = 100-(50+20) i.e. 30km and the relative speed =90kmph. Therefore, time =30/90 hours = 20mins.
Answer : B
Question: A chemist mixes one liter of pure water with x liters of a 60% salt solution, and the resulting mixture is a 15% salt solution. What is the value of x?
A.1/4
B.1/3
C.1/2
D.1
Answer: B.1/3
Explanation: Concentration of salt in pure solution = 0
Concentration of salt in salt solution = 60%
Concentration of salt in the mixed solution = 15%
The pure solution and the salt solution is mixed in the ratio of --> (60 - 15)/(15 - 0) = 3/1
1/x = 3/1
x = 1/3
Answer: B
Question: A sum was put at simple interest at certain rate for 3 years. Had it been put at 1% higher rate it would have fetched Rs. 78 more. The sum is: A. Rs. 2,400 B. Rs. 2,100 C. Rs. 2,200 D.Rs. 2,480
A.2000
B.2600
C.2200
D.2300
Answer: B.2600
Explanation: 1 percent for 3 years= 78
1 percent for 1 year = 26
=> 100 percent = 2600
ANSWER:B
Question: Manoj borrowed Rs.3450 from Anwar at 6% p.a. simple interest for three years. He then added some more money to the borrowed sum and lent it to Ramu for the same time at 9% p.a. simple interest. If Manoj gains Rs.824.85 by way of interest on the borrowed sum as well as his own amount from the whole transaction, then what is the sum lent by him to Ramu?
A.22877
B.5355
C.2778
D.6787
Answer: B.5355
Explanation: Let the sum lent by Manoj to Ramu be Rs.P.
Amount gained by Manoj = P. 3.9 /100 = 3450.3.6/100 = Rs.824.85
27P = 62100 = 82485
P = (82485 + 62100)/27 = 3055 + 2300 = Rs.5355
Answer: B
Question: On a certain date, Pat invested $8,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 10 years will be $32,000, in how many years total will the total value of the investment plus interest increase to $64,000?
A.15
B.16
C.18
D.20
Answer: A.15
Explanation: 32,000 = 8,000(1 + x)^10
4 = (1+x)^10 = 2^2
(1+x)^10 = ((1+x)^5)^2 = 2^2
Therefore, (1+x)^5 = 2
64,000 = 8,000(1 + x)^n
(1+x)^n = 8
(1+x)^n = 2^3
(1+x)^n = ((1+x)^5)^3 = (1+x)^15
Therefore, n = 15.
The answer is A.
Question: 39x7 - 45x7 - 134x7 - 39x7 + 134x7 + 44x7 =
A.-x7
B.x7
C.2x7
D.3x7
Answer: A.-x7
Explanation: Solution:
39x7 - 45x7 - 134x7 - 39x7 + 134x7 + 44x7 =
39x7 - 39x7 - 45x7 + 44x7 - 134x7 + 134x7=
0 - x7 + 0= -x7
Answer A
Question: If a function f is defined by f(x)= -1/x for all non zero numbers x. If f(a) = -1/3 and f(ab) = 1/6 then b= ?
A.2
B.1/2
C.-1/2
D.-2
Answer: D.-2
Explanation: f(a) = -1/3 = -1/a, and thus a = 3
f(ab) = 1/6, and thus ab = -6
3b = -6
b = -2
The answer is D.
Question: 270 students appeared for an examination, of which 252 passed. What is the pass percentage?
A.93(1/3)%
B.93(2/3)%
C.92(2/3)%
D.92%
Answer: A.93(1/3)%
Explanation: Explanation :
Pass percentage = (252/270) × 100 = 2520/27 = 280/3 = 93(1/3)%
Answer : Option A
Question: Nicky and Cristina are running a 100 meter race. Since Cristina is faster than Nicky, she gives him a 12 second head start. If Cristina runs at a pace of 5 meters per second and Nicky runs at a pace of only 3 meters per second, how many seconds will Nicky have run before Cristina catches up to him?
A.30
B.35
C.40
D.25
Answer: A.30
Explanation: The distance traveled by both of them is the same at the time of overtaking.
3(t+12) = 5t
t=18.
Cristina will catch up Nicky in 18 seconds.
So in 18 seconds Cristina would cover = 18*5 = 90 meter.
Now Time taken my Nicky to cover 90 meter = 90/3 = 30 Seconds.
A
Question: Initially, the men and women in a room were in the ratio of 4 : 5. Then, 2 men entered the room and 3 women left the room. Then, the number of women doubled. Now there are 14 men in the room. How many W women are currently in the room?
A.12
B.14
C.15
D.24
Answer: D.24
Explanation: the number of women doubled means that they have become 24 from 12..
and we have to tell the current strength so 24 is the answer..
let the number be 4x and 5x..
given 4x+2=14.. so x=3..
women number=5*3-3=12, then doubled=24..
ans D
Question: The average weight of a 30 students increases by 2 kg when the weight of their teacher was added. If average weight of the group after including the weight of the teacher is 32 kg, what is the weight of their football coach?
A.31 kg
B.60 kg
C.61 kg
D.124 kg
Answer: D.124 kg
Explanation: let t=teacher's weight
original total weight=(30 students)(30 kg avge)=900kg
(900+t)/(30+2)=32 kg avge
t=124 kg
Answer D
Question: The number of timeshare condos available at Sunset Beach is 3/5 the number of timeshare condos available at Playa del Mar. If the total number of timeshare condos available at the two beaches combined is 320, what is the difference between the number of condos available at Sunset Beach and the number of condos available at Playa del Mar?
A.80
B.90
C.120
D.150
Answer: A.80
Explanation: Let x be the number of timeshare condos available at Playa del Mar.
Then number of timeshare condos available at Sunset Beach = 3/5x
We know, x + 3/5 x = 320
Hence, x = 200. So, number of timeshare condos available at Playa del Mar = 200
the difference between the number of condos available at Sunset Beach and the number of condos available at Playa del Mar = x - 3/5x = 2/5x = 2/5(200) = 80
The correct answer is A.
Question: Truck A is 25 miles ahead of Truck B, which is traveling the same direction along the same route as Truck A. If Truck A is traveling at an average speed of 49 miles per hour and Truck B is traveling at an average speed of 54 miles per hour, how long will it take Truck B to overtake and drive 15 miles ahead of Truck A?
A.2 hours 20 minutes
B.6 hours
C.8 hours
D.5 hours 45 minutes
Answer: C.8 hours
Explanation: Relative speed = 54-49 = 5 miles per hour
Dist required = 25+15 = 40 miles
Time taken to overtake = 40/5 = 8 hours. C is the answer.
Question: A shopkeeper sells two articles at Rs.1000 each, making a profit of 20% on the first article and a loss of 20% on the second article. Find the net profit or loss that he makes?
A.8
B.7
C.6
D.4
Answer: D.4
Explanation: SP of first article = 1000
Profit = 20%
CP = (SP)*[100/(100+P)] = 5000/6 = 2500/3
SP of second article = 1000
Loss = 20%
CP = (SP)*[100/(100-L)] = 5000/4 = 1250
Total SP = 2000
Total CP = 2500/3 + 1250 = 6250/3
CP is more than SP, he makes a loss.
Loss = CP-SP = (6250/3)- 2000 = 250/3
Loss Percent = [(250/3)/(6250/3)]*100 =
0.04 * 100 = 4%
Answer: D
Question: A 260-metre-long train crosses a 120-metre-long wall in 19 seconds. What is the speed of the train?
A.27 km/hr
B.49 km/hr
C.72 km/hr
D.70 km/hr
Answer: C.72 km/hr
Explanation: Speed of train = 260+120/19×18/5=72km/h
Answer C
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.140. How much was lent at 5%?
A.1666
B.2688
C.1198
D.1000
Answer: D.1000
Explanation: (x*5*1)/100 + [(2500 - x)*6*1]/100 = 140
X = 1000
Answer:D
Question: If x^2=x-2, then x^3=?
A.3x+2
B.3x-2
C.2x+1
D.-x-2
Answer: D.-x-2
Explanation: Given X^2 = X-2
X^3 = X*X^2 = x*(X-2)-- Substituted from above.
= X^2 - 2X = X-2-2X = -X-2.
Hence D.
Question: If 8 people can eat a gallon of ice cream in 10 days, how long would it take 5 people to eat a gallon of ice cream?
A.12 days
B.14 days
C.16 days
D.18 days
Answer: C.16 days
Explanation: 8 * 10 = 5 * x
x = 16
Answer: C
Question: Find the value of 3/11 × [(1 + 1/3) (1 + 1/4) …………. (1 + 1/120)] is
A.8
B.10
C.11
D.13
Answer: C.11
Explanation: 3/11 × [(1 + 1/3) (1 + 1/4) ....... (1 + 1/120)]
3/11 × [4/3 + 5/4 × ........ 121/120]
3/11 × 4/3 × 5/4 × .... 121/120
121/11 = 11.
C
Question: If -2<= x <= 2 and 3 <= y <= 4, which of the following represents the range of all possible values of y-x?
A. 1 <= y-x <= 6
B. 1 <= y-x <= 5
C. 1 <= y-x <= 6
D. 5 <= y-x <= 10
Answer: A. 1 <= y-x <= 6
Explanation: Maximum value of y-x= 4 - (-2)= 6
Minimum value of y-x= 3-2= 1
A mentions the correct range
Question: A chair is bought for Rs.600/- and sold at a loss of 50% find its selling price
A.s.300/-
B.s.550/-
C.s.560/-
D.s.590/-
Answer: A.s.300/-
Explanation: 100 % ------> 600 (100 * 6 = 600)
50 % ------> 540 (50 * 6 = 300)
Selling price = Rs.300/-
A)
Question: 16 children are to be divided into two groups A and B of 10 and 6 children. The average percent marks obtained by the children of group A is 75 and the average percent marks of all the 16 children is 76. What is the average percent marks of children of group B ?
A.233/3
B.733/3
C.533/3
D.293/3
Answer: A.233/3
Explanation: Explanation:
Required average = [(76 * 16) - (75 * 10)] / 6 = (1216 - 750)/6 = 466/3 = 233 /3.
Answer: A
Question: Three table runners have a combined area of 204 square inches. By overlapping the runners to cover 80% of a table of area 175 square inches, the area that is covered by exactly two layers of runner is 24 square inches. What is the area of the table that is covered with three layers of runner?
A. 18 square inches
B. 20 square inches
C. 24 square inches
D. 28 square inches
Answer: B. 20 square inches
Explanation: Total = a + b + c - (sum of EXACTLY 2-group overlaps) - 2*(all three) + Neither
80%*175 = 204 - 24 - 2*(all three) + 0
2*(all three) = 204 - 24 - 140
all three = 20
Answer: B
Question: What is the sum of all the prime numbers greater than 50 but less than 70?
A.249
B.248
C.246
D.240
Answer: D.240
Explanation: Required sum = (53 + 59 + 61 + 67 ) = 240
Note: 1 is not a prime number
Answer D
Question: If x = 6^36 and x^x = 6^k, what is k?
A.6^36
B.6^38
C.6^72
D.6^216
Answer: B.6^38
Explanation: Solution:
We know that x=6^36
which implies x^x = (6^36)^(6^36) = 6^(36 * 6^36) [because (x^y)^z = x^(y*z))]
so 6^(6^2 * 6^36) = 6^(6^(2+36)) [because x^a * x^b = x^(a+b)]
therefore x^x = 6^(6^38)
Given that x^x=6^k
so 6^(6^38) = 6^k
Since the base is same the exponent will also be same
therefore k = 6^38
Answer:B
Question: From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is?
A.1/26
B.1/27
C.1/24
D.1/21
Answer: A.1/26
Explanation: Let E1 be the event of drawing a red card.
Let E2 be the event of drawing a king .
P(E1 ∩ E2) = P(E1) . P(E2)
(As E1 and E2 are independent)
= 1/2 * 1/13 = 1/26
Answer: A
Question: Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 36?Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 4?
A.5x = y - 6
B.75x^2 = 3y^2 - 12
C.25x^2 = (y + 2)(y - 2)
D.5x = y - 2
Answer: A.5x = y - 6
Explanation: 1) Take the original equation and try to manipulate it so that it becomes 4 of the 5 answers
2) Take each answer choice and see if you can manipulate it to make it into the original equation.
With Answer D, we have...
5X = Y - 6
If we square both sides, we end up with....
(5X)^2 = (Y-6)^2
(5X)(5X) = (Y-6)(Y-6)
25X^2 = Y^2 - 12Y + 36
This is NOT a match for the original equation, so it's the answer that is NOT equivalent.A
Question: If m is an integer such that (-2)^2m=2^(6-m) then m=?
A.1
B.2
C.3
D.5
Answer: B.2
Explanation: (-2)^(2m) = 4^m
and
2^(6-m) = 4^((6-m)/2)
Therefore,
m = (6-m)/2
2m = 6 - m
m = 2
Answer B