RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Simran started a software business by investing Rs.50,000. After six months, Nanda joined her with a capital of Rs.80,000. After 3 years , they earned a profit of Rs.24,500. What was Simran's share in the profit?
A.Rs.9423
B.Rs.10,250
C.Rs.10,500
D.Rs.14,000
Answer: C.Rs.10,500
Explanation: Solution
Simran : Nanda	=(5000x36):(80000x30)
= 3 : 4.
Simran's share	= Rs.(24500x3/7)
= Rs.10,500.
Answer C
Question: Danny drove his old car 100 kilometers, from his home to a friend. To prevent the engine from overheating, he stopped his car for 9 minutes every time he completed 40 kilometers of continuous driving. When the car was moving, Danny drove it at an average speed of 60 kilometers per hour. What was Danny's average speed on that trip?
A.37.5 kilometers per hour
B.48 kilometers per hour
C.50.8 kilometers per hour
D.75 kilometers per hour
Answer: C.50.8 kilometers per hour
Explanation: Time taken to reach first 40 km is 40/60 = 2/3 hr
Time taken to reach next 40 km is 40/60 = 2/3 hr
Time taken to reach next 20 km is 20/60 = 1/3 hr
Danny stopped twice on his way at 40 km from starting point and at 80km from the starting point...
Each stop was of 9 min , so two 9 min break = 2*3/20 => 3/10 hr
Total time taken to reach 100 km is (2/3 + 2/3 + 1/3+3/10 ) = 59/30 hrs
So, Average speed is 100/(59/30) = 50.8km/hour
Answer will be (C)
Question: If 12 men and 16 boys can do a piece of work in 5 days and 13 men together will 24 boys can do it in 4 days. Compare the daily work done by a man with that of a boy.
A.2:7
B.2:1
C.2:4
D.2:2
Answer: B.2:1
Explanation: 12M + 16B ----- 5 days
13M + 24B ------- 4 days
60M + 80B = 52M + 96B
8M = 16B => 1M = 2B
M: B = 2:1
Answer:B
Question: Three business people who wish to invest in a new company. Each person is willing to pay one third of the total investment. . After careful calculation, they realize that each of them would pay $ 7500 less if they could find two more equal investors. How much is the total investment in the new business.
A.a)	$ 64,000
B.b)	$ 56,250
C.c)	$ 21,000
D.d)	$ 5,400
Answer: B.b)	$ 56,250
Explanation: Initially each invest in x. Hence total investment is 3x.
Total investment is also 5(x-7500).
3x = 5(x-7500)
x= 5*7500/2 = 18750
3x = 56250 and the answer is B.
Question: A certain sum becomes Rs. 20720 in four years and 24080 in six years at simple interest. Find sum and rate of interest?
A.Rs. 12000; 12% p.a.
B.Rs. 22000; 12% p.a.
C.Rs. 12000; 22% p.a.
D.Rs. 12000; 14% p.a.
Answer: A.Rs. 12000; 12% p.a.
Explanation: Let the interest for one year be x.
As amount = Principal + Interest, we have
P + 4x = 20720 --- (1) ; P + 6x = 24080 --- (2)
Solving the equations (1) and (2), we can get
P = Rs. 14000 and x = Rs. 1680
Interest for one year on Rs. 14000 is Rs. 1680
So, R = (100 * 1680)/(14000 * 1) = 12% p.a.
ANSWER:A
Question: Oil cans x and y are right circular cylinders and the height and radius of y are each 5 times those of x. If the oil in can x filled to capacity sells for $1, how much does the oil in y sell for if y is only 1/5th filled?
A.$25
B.$26
C.$27
D.$28
Answer: A.$25
Explanation: formula for vol of a cyl is PI*r^2*h
so Vy = 125*Vy
y when half filled will cost 25 times x so ans is A
Question: If a and b are integers and (2^a)(3^b) is a factor of 300^40, what is the largest possible value of ab?
A.a
B.5a
C.20a
D.40a
Answer: A.a
Explanation: (2^a)(3^b) is a factor of 300^40
We need to find the largest possible value of ab.
We know that 300 = 2^2*5^2*3
Therefore 300^40 will have only one power of 3 in it.
Hence in (2^a)(3^b), b has to be 1
Therefore value of ab = a
Correct Option: A
Question: A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.3 per sq m?
A.675, Rs.2025
B.575, Rs.1350
C.1350, Rs.675
D.1450, Rs.775
Answer: A.675, Rs.2025
Explanation: Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 3 = Rs.2025
ANSWER:A
Question: The triplicate ratio of 1:2 is?
A.1:0
B.1:8
C.1:7
D.1:2
Answer: B.1:8
Explanation: 13: 23 = 1:8
Answer: B
Question: What two-digit number is less than the sum of the square of its digits by 11 and exceeds their doubled product by 4?
A. 95
B. 99
C. 26
D. 73
Answer: C. 26
Explanation: Let the digits be x and y. The number would be 10x + y.
We are given that 2xy + 4 = 10x +y = x^2 y^2 -11
Thus 2xy +4 = x^2 + y^2 - 11
x^2 + y^2 -2xy = 16
(x-y)^2 = 16
(x-y) = 4 or -4
Substituting the values of (x-y) in the equation 2xy +5 = 10x + y
x comes out to be 1 or 9... thus the two numbers can be 26 or 98
Thus the answer is C
Question: Jolene entered an 16-month investment contract that guarantees to pay 2 percent interest at the end of 6 months, another 3 percent interest at the end of 12 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract?
A.$506.00
B.$726.24
C.$900.00
D.$920.24
Answer: D.$920.24
Explanation: If interest were not compounded in every six months (so if interest were not earned on interest) then we would have (2+3+4)=9% simple interest earned on $10,000, which is $900. So, you can rule out A, B and C right away.
Interest earned after the first time interval: $10,000*2%=$200;
Interest earned after the second time interval: ($10,000+$200)*3%=$300+$6=$306;
Interest earned after the third time interval: ($10,000+$200+$306)*4%=$400+$8+(~$12)=~$420;
Total: 200+306+(~420)=~$920.24
Answer: D.
Question: The probability that a brand A widget is defective is x, the probability that a brand B widget is defective is 0.05, and the probability that a brand C widget is defective is 0.08. There are 40 brand A widgets, 35 brand B widgets, 25 brand C widgets, and nothing else in a container. If a widget is selected at random from the container, the probability that the widget selected is defective is 0.053. What is the value of x?
A.0.03875
B.0.04
C.0.05
D.0.6
Answer: A.0.03875
Explanation: Given probability of defective items in each brand,
So, the number of items defective in brand A=x*40, in brand B=0.05*35 and brand C=0.08*25
Total number of widgets=40+35+25=100
the probability that the widget selected is defective is 0.053=(x*40+0.05*35+0.08*25)/100
=> 40x+1.75+2=5.3
=>40x=1.55
>x=1.55/40=0.03875
Ans A.
Question: The present worth of Rs. 242 due in 2 years at 10% per annum compound interest is:
A.Rs. 200
B.Rs. 250
C.Rs. 240
D.Rs. 220
Answer: A.Rs. 200
Explanation: Explanation:
Present worth of Rs. x due T years hence is given by
Present Worth (PW) = x/(1+R/100)T
Present Worth (PW) = 242/(1+10/100)2 = 242/(11/10)2 = Rs. 200
Answer: Option A
Question: A and B together can do a piece of work in 20days. A having worked for 10days, B finishes the remaining work alone in 30days. In how many days shall B finish the whole work?
A.25
B.40
C.50
D.30
Answer: B.40
Explanation: Let A's 1day work = x
B's 1day work = y
x+y = 1/20
10x+30y = 1
x = 1/40
y = 1/40
B's 1 day work = 1/40
B alone can finish the job in 40 days
Answer is B
Question: One out of every 500 light bulbs are defected. If 4 out of every 10 defected light bulbs have a broken glass and there are 20 broken glass light bulbs in the shipment, how many light bulbs total are there in the shipment?
A.2,000
B.5,000
C.10,000
D.25,000
Answer: D.25,000
Explanation: out of 500 only 1 bulb is defective.So for 10 defective bulbs, we must have 5000 bulbs
Now out of these 10 bulbs, 4 bulbs, have broken glass
i.e 4 broken glass out of 5000 bulbs
20 broken glass will be from 25000 bulbs
Answer is D
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
A.277
B.266
C.288
D.150
Answer: D.150
Explanation: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9) m
= 150 m
.
Answer: D
Question: If the cost price of 24 articles is equal to the selling price of 16 articles, What is the percentage of profit or loss that the merchant makes?
A.20% loss
B.50% profit
C.33.33 % loss
D.30.33% loss
Answer: B.50% profit
Explanation: Explanation :
Let Cost price of 1 article be Re.1.
Therefore, Cost price of 24 articles = Rs. 24.
Selling price of 16 articles = Rs. 24
Therefore, Selling price of 24 articles is :-
=>24/16Ã—24
=>36.
Therefore, Profit = Selling price - Cost price.
=>36âˆ’24=12.
Hence, the percentage of profit = profit x 100/C.P.
=>12/24Ã—100.
=>50% Profit.
Answer : B
Question: The sum of two whole no. is 64.from the following which can not be the ratio of these no.
A.5:3
B.7:1
C.3:4
D.3:5
Answer: C.3:4
Explanation: Answer:	the addition of ratio no. should be factor of 64.so,3:4 can't be the ratio
answer C
Question: A credit card company has a cash back option for their customers which is based on the annual amount that they charge on their credit cards. The customer receives 1.5% cash on their first $5000 of purchase, 2.5% on the next $5000 of purchase and a 3% on cash back on portion that exceeds $10,000. If a customer receives a cash back of 2.8% on their total annual charges made on the credit card, then what was the customer's annual charge?
A.$40,000
B.$45,000
C.$50,000
D.$55,000
Answer: C.$50,000
Explanation: The customer receives $75 for the first $5000.
The customer receives $125 for the next $5000.
Let x be the total amount of the customer's annual charge.
$200 + 0.03(x-10,000)=0.028x
0.002x=100
x=50,000
The answer is C.
Question: ((-1.9)(0.6) – (2.6)(1.2))/3.0 = ?
A.0.71
B.1.0
C.1.07
D.-1.42
Answer: D.-1.42
Explanation: Dove straight into calculation but quickly realized that the sum of two negatives is a negative so there is only one option.
-1.42
Answer D
Question: Find the odd man out. 12, 24, 34, 48, 64, 84
A.48
B.34
C.24
D.12
Answer: B.34
Explanation: Explanation :
All numbers except 34 are multiples of 4
Answer : Option B
Question: There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
A.20
B.80
C.100
D.200
Answer: C.100
Explanation: Let the number of students in rooms A and B be x and y respectively.
Then, x - 10 = y + 10 x - y = 20 .... (i)
and x + 20 = 2(y - 20) x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
The required answer A = 100.
Answer = C
Question: A train travels from Albany to Syracuse, a distance of 120 miles, at the average rate of 30 miles per hour. The train then travels back to Albany from Syracuse. The total travelling time of the train is 6 hours . What was the average rate of speed of the train on the return trip to Albany?
A.31
B.38
C.60
D.50
Answer: C.60
Explanation: 30*T =120 THEREFORE T = 120/30 =4
ON RETURN SPEED * ( 6 -4) =120 THEREFORE T = 120/2 =60
C
Question: Andrew travelling to 7 cities. Gasoline prices varied from city to city. $1.75, $1.61, $1.79, $2.11, $1.96, $2.09, $1.86. What is the median gasoline price?
A.$1
B.$1.86
C.$1.92
D.$2.13
Answer: B.$1.86
Explanation: Ordering the data from least to greatest, we get:
$1.61, $1.75, $1.79, $1.86, $1.96, $2.09, $2.11
The median gasoline price is $1.86. (There were 3 states with higher gasoline prices and 3 with lower prices.)
B
Question: Julie wants to play chess with her friends. She have 6 friends. What are the possible ways to select friends to play with her?
A.10
B.3
C.6
D.2
Answer: C.6
Explanation: Julie want to play chess. So she need only one friend but there 6 friends.
That is she have to select 1 out of 6
6C1=6
6 possible ways to select her friends to play with julie(herself)
Answer is option C
Question: Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the game remainder in each case. Then sum of the digits in N is :
A.4
B.5
C.6
D.8
Answer: A.4
Explanation: Solution
N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)
= H.C.F. of 3360, 2240 and 5600 = 1120.
Sum of digits in N = (1 + 1 + 2 + 0) = 4. Answer A
Question: How many seconds will a 600 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
A.22
B.36
C.99
D.77
Answer: B.36
Explanation: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 600 * 3/50 = 36 sec.
Answer: B
Question: If Jake loses 33 pounds, he will weigh twice as much as his sister. Together they now weigh 153 pounds. What is Jake's present weight, in pounds?
A. 131
B. 135
C. 113
D. 147
Answer: C. 113
Explanation: J = Jake’s current weight, in pounds
S = Sister’s current weight, in pounds
We are told that “If Jake loses 8 pounds, he will weigh twice as much as his sister.We put this into an equation:
J – 33 = 2S
J = 2S + 33 (Equation 1)
Next, we are told that “Together they now weigh 153 pounds.” We can also put this into an equation.
J + S = 153 (Equation 2)
To solve this equation, we can substitute 2S + 8 from Equation 1 for the variable J in Equation 2:
2S + 33 = 153-S
3S = 120
S = 40
J + 40 = 153
J = 113
Answer: C
Question: In a division sum, the divisor is 5 times the quotient and two times the remainder. If the remainder is 40, then the dividend is
A.1320
B.1380
C.1395
D.1367
Answer: A.1320
Explanation: Explanation:
Dividend = (Divisor x Quotient) + Remainder
Remainder = 40
Divisor = 5Q = 2R = 2 x 40 = 80
=> Q = (80/5) = 16
Now, Dividend = (80 x 16) + 40 = 1320
Answer: Option A
Question: If x^2+(1/x^2)=5, x^4+(1/x^4)=?
A.10
B.11
C.23
D.14
Answer: C.23
Explanation: -> x^4+(1/x^4)=(x^2)^2+(1/x^2)^2=(x^2+1/x^2)^2-2x^2(1/x^2)=5^2-2=23.
Thus, the answer is C.
Question: At 12:00 a.m., Tom begins traveling on a certain bike path from Riverdale at a constant rate of 10 mph. If, at 4:00 p.m., Jim begins traveling from Riverdale on the same path at a constant rate of 20 mph, at what time will he catch up to Peter?
A.5:00 p.m.
B.6:00 p.m.
C.7:00 p.m.
D.8:00 p.m.
Answer: D.8:00 p.m.
Explanation: By the time Jim starts, Tom has already covered = 4 hr * 10 mph = 40 miles
Relative speed = 20- 10 = 10mph
To catch up, Jim needs to cover 40 miles which can be covered in = 40/10= 4 hours
If Jim leaves at 4 pm, he will catch Tom at 8 pm
Answer: D
Question: When 8% of a number is added to the number itself the result is 810. What is the number?
A.750
B.758
C.288
D.270
Answer: A.750
Explanation: Explanation:
No explanation is available for this question!
ANSWER: A
Question: John bought 2 shares and sold them for $95 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares John had
A. a profit of $10
B. a profit of $8
C. a loss of $8
D. a loss of $10
Answer: D. a loss of $10
Explanation: $ Profit of the share sold at 20% profit =
120-95
20-?
$15 profit on the sale of 1 share.
$ Loss of the share sold at 20% loss=
80-95
20-?
$25 loss on the sale of 1 share.
15-25=Loss of $10
Answer: D
Question: The salary of Mr. X is 30% more than that of Mr. Y . Find what percent of Mr. Y’s salary is less than Mr. X’s?
A.23 1/6%
B.23 9/3%
C.23 1/3%
D.28 1/3%
Answer: C.23 1/3%
Explanation: y=100	x=130
130---------30
100---------? => 23 1/3%
Answer: C
Question: A fair coin is to be tossed twice and an integer is to be selected at random from one of the integers 3, 8, and 10. What is the probability that at least one head is tossed and an even integer is selected?
A.1/6
B.1/4
C.1/3
D.1/2
Answer: D.1/2
Explanation: 1) Let us simply state the possibilities. This method works for this problem due to the limited number of possibilities
Ways of getting at least a head and an even number =6
HT8
TH8
HT10
TH10
HH8
HH10
Ways of not getting at least one head and an even number=6
TT8
TT10
HT3
TH3
HH3
TT3
Total probability=6/12=1/2
Answer:D
Question: Elizabeth bought a dress with a 35% off coupon. If the dress cost her $87.61, what is the original selling price of the dress?
A.$134.78
B.$250.31
C.$118.27
D.$87.61
Answer: A.$134.78
Explanation: Explanation:CP of Elizabeth is 35% of the Original SP.:. Original SP = $87.61x100/65 = $134.78.Answer: Option A.
Question: In a set of numbers from 100 to 400 inclusive, how many integers are odd and do not contain the digit 5?
A.180
B.196
C.286
D.288
Answer: A.180
Explanation: We have to find the total number of 3-digit odd numbers not having 5 as a digit.
Units digits will be among 1,3,5,7,9
Tenth digits will be among 0,1,2,3,4,6,7,8,9
Hundredth digits will be among 1,2,3,4
So total numbers = 5*9*4 =180
Answer : A
Question: How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?
A.22 sec
B.77 sec
C.25 sec
D.18 sec
Answer: C.25 sec
Explanation: D = 100 + 150 = 250
S = 36 * 5/18 = 10 mps
T = 250/10 = 25 sec
Answer:C
Question: A discount of 20 percent on an order of goods followed by a discount of 30 percent amounts to
A.the same as one 44 percent discount
B.the same as one 40 percent discount
C.the same as one 36 percent discount
D.the same as one 30 percent discount
Answer: A.the same as one 44 percent discount
Explanation: 0.8*0.7*x=0.56x from initial value, meaning 0.44 or 44% discount
A
Question: Car A runs at the speed of 60 km/hr and reaches its destination in 8 hours. Car B runs at the speed of 70 km/h and reaches its destination in 4 hours. What is the ratio of distances covered by Car A and Car B?
A.3 : 7
B.4 : 9
C.12 : 7
D.5 : 7
Answer: C.12 : 7
Explanation: Car A travels 60 × 8 = 480 km
Car B travels 70 × 4 = 280 km
The ratio is 480 : 280 = 48 : 28 = 12 : 7
The answer is C.
Question: A person distributed 20% of his income to his 3 children each. He deposited 30% of his income to his wife's account. He donated 5% of remaining amount to an orphan house.Finally he has $40000. Find his total income?
A.452000
B.562000
C.800000
D.500000
Answer: C.800000
Explanation: 3 children got = 3*20% = 60%
wife got = 30%
orphan house = 5%
total = 60+30+5 = 95%
remaining = 100-95 = 5%
5% = 40000
100% = 40000*100/5 = $800000
Answer is C
Question: A man rows his boat 95 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
A.6
B.7
C.10
D.8
Answer: C.10
Explanation: Speed downstream = d/t = 95/(2 1/2) = 38 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (38 - 18)/2
= 10 kmph
Answer: C
Question: How many 3 digit numbers can be formed from the digits 2,3,5,6,7 and 9 which are divisible by 5 and none of the digits is repeated?
A.30
B.20
C.10
D.45
Answer: B.20
Explanation: Since each desired number is divisible by 5,
so we much have 5 at the unit place.
The hundreds place
can now be filled by any of the remaining 4 digits .
so, there4 ways of filling it.
Required number of numbers = (1 * 5 * 4)
= 20
Ans: B
Question: A Jar contains a mixture of AB in the ratio 4:1. When 30 L of Mixture is replaced with liquid B, ratio becomes 2:3. How many liters of liquid A was present in mixture initially.
A.12
B.48
C.16
D.20
Answer: B.48
Explanation: 30 litres of mixture that is replaced will contain 24 litres of A and 6 litres of B (as A:B = 4:1)
Let the initial volume of the mixture be 4K + 1K = 5K
So by condition ,
[ 4K-24]/ [ K-6+30 ] = 2/3 = > 12K-72 = 2K-12+60 => 10K = 120
Solve for K which is K = 12
So initial volume of liquid A = 4K = 48 litres
Answer : B
Question: The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 20000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is:
A.23
B.49
C.22
D.20
Answer: B.49
Explanation: Let the total number of workers be x. Then,
8000x = (20000 * 7) + 6000(x - 7)
= 2000x = 98000
= x = 49.
ANSWER:B
Question: In the faculty of Reverse-Engineering, 500 second year students study numeric methods, 300 second year students study automatic control of airborne vehicles and 300 second year students study them both. How many students are there in the faculty if the second year students are approximately 50% of the total?
A.1100
B.1200
C.1150
D.1000
Answer: D.1000
Explanation: Total number of students studying both are 500 + 300 - 300 = 500 (Subtracting the 300 since they were included in the both the other numbers already).
So 50% of total is 500, so 100% is 1000
Answer is D
Question: Look at this series: 36, 34, 30, 28, 24, ... What number should come next?
A.20
B.22
C.23
D.26
Answer: B.22
Explanation: Explanation: This is an alternating number subtraction series. First, 2 is subtracted, then 4, then 2, and so on.
Answer: Option B
Question: If a rectangular room measures 10 meters by 5 meters by 4 meters, what is the volume of the room in cubic centimeters? (1 meter=100 centimeters)
A.24,000
B.240,000
C.2,400,000
D.200,000,000
Answer: D.200,000,000
Explanation: D. 200,000,000
10*100*5*100*4*100 = 200,000,000
Question: One room length is 16 m and breadth 12m.outside this room there is corridor 3.5 m wide.in this corridor how much stone will be used of size 7 decimeter× 5 decimeter?
A.600
B.700
C.800
D.900
Answer: B.700
Explanation: Area of room = (16*12) sq.m= 192 sq.m
Area of room along with corridor=[(16+2*3.5)×(12+2*3.5)] sq.m=(23×19)=437 sq.m.
Area of corridor=[437-192]=245 sq.m
Area of one stone=[7/10*5/10]=7/20sq.m
No. of stone=245×20/7=700
Answer B
Question: The length of each side of square A is increased by 100 percent to make square B. If the length of the side of square B is increased by 75 percent to make square C, by what percent is the area of square C greater than the sum of the areas of squares A and B?
A.75%
B.80%
C.145%
D.150%
Answer: C.145%
Explanation: Let length of each side of square A be 10
Area of A = 10^2 = 100
Since , length of each side of square A is increased by 100 percent to make square B
length of each side of square B = 2*10 = 20
Area of B = 20^2 = 400
Since , length of the side of square B is increased by 75 percent to make square C
length of each side of square C= 1.75*20 = 35
Area of C= 35^2 = 1225
Difference in areas of C and cummulative areas of A and B = 1225 -(400+100) = 725
percent is the area of square C greater than the sum of the areas of squares A and B = (725/500) * 100 % = 145%
Answer C
Question: A certain deck of cards contains 2 blue cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both be not Yellow?
A.15/28
B.1/4
C.9/16
D.1/32
Answer: A.15/28
Explanation: The question asks they will both be not Yellow. Considering that these are draws without replacement there are following possibilities :
draw 1, draw 2
===== =====
1) Not Yellow, Yellow;
2) Yellow, Not Yellow;
3) Yellow, Yellow;
4) Not Yellow, not Yellow;
The answer has to be either P(4) OR all exclusion of the 3 previous conditions i.e. 1- [P(1) + P(2) + P(3)] => neither of the draws are Yellow
P(4) = 6/8*5/7=15/28
1- [P(1) + P(2) + P(3)] = 1 - [ (6/8 * 2/7) + (2/8*6/7) + (2/8*1/7)] = 1 - [26/8*7] = 1 - [13/28] = 15/28
A
Question: A set of numbers has an average of 30. If the largest element is 4 greater than 3 times the smallest element, which of the following values cannot be in the set?
A. 85
B. 95
C. 23
D. 50
Answer: B. 95
Explanation: Ans: B
Solution: we are given the relation between smallest and the largest term. so let the smallest a and largest be 3a+4
so the avg = 50
which tells us that any value of a must be less than 30
so a<50 means, largest value 3a+4 <(3*30)+4
=largest value must be <94
so 95 can not be the value in the set.
Question: John had a stock of 1400 books in his bookshop. He sold 75 on Monday, 50 on Tuesday, 64 on Wednesday, 78 on Thursday and 135 on Friday. What percentage of the books were not sold?
A.50.4%
B.71.3%
C.66.5%
D.34.9%
Answer: B.71.3%
Explanation: Let N be the total number of books sold. Hence
N = 75 + 50 + 64 + 78 + 135 = 402
Let M be the books NOT sold
M = 1400 - N = 1400 - 402 = 998
Percentage
Books not sold / total number of books = 998/1400 = 0.713 = 71.3%
correct answer B