RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: In what time will a train 100 m long cross an electric pole, it its speed be 90 km/hr?
A.2.5
B.2.9
C.4 sec
D.2.8
Answer: C.4 sec
Explanation: Speed = 90 * 5/18 = 25 m/sec
Time taken = 100/25
= 4 sec.
Answer:C
Question: The total circumference of two circles is 80. If the first circle has a circumference that is exactly twice the circumference of the second circle, then what is the approximate sum of their two radii?
A.5.7
B.6.0
C.10.6
D.9.7
Answer: C.10.6
Explanation: Let r= Radius of smaller circle. Let R = Radius of larger circle
Therefore:
2πr + 2πR = 80
where 2r = R
Thus:
2πr + 4πr = 80
6πr = 80
r = approx 4.2
πR + 2Rπ = 80
3πR = 80
R = approx 8.4
r + R = approx 10.6
Answer is C
Question: Which of the following equations has a root in common with x^2−3x+2=0 ?
A.x^2-2x+1=0
B.x^2-2x-1=0
C.x^2-x+1=0
D.x^2-3x+3=0
Answer: A.x^2-2x+1=0
Explanation: If we carefully look at the given equation we can arrange it in the following manner:
(x-1)(x-2)= 0
so the two roots are 1 and 2.
Now put 1 and 2 in given equations. The equation in which one of them gives value 0, that will be our answer.
(A) putting 1: we get 0. This is the equation.
We are lucky. No need to check other options.
A is the answer.
Question: Three different containers contain 496 litres, 403 litres and 713 litres of mixtures of milk and water respectively. What biggest measure can measure all the different quantities exactly ?
A.30 litres
B.31 litres
C.32 litres
D.33 litres
Answer: B.31 litres
Explanation: 403)713(1
403
---------
310)403(1
310
----------
93)310(3
279
--------
31)93(3
93
-------
X
so answer is 31 litres......
ANSWER:B
Question: Find the missing number. 1, 4, 9, 16, 25, 36, 49, (....)
A.64
B.54
C.56
D.81
Answer: A.64
Explanation: Explanation :
The series is 1^2, 2^2, 3^2, 4^2, 5^2, 6^2, 7^2,
Hence, next term = 8^2 = 64
Answer : Option A
Question: When positive integer m is divided by positive integer x, the reminder is 7 and when positive integer n is divided by positive integer y, the reminder is 11. Which of the following E is a possible value for x + y?
I. 18
II. 19
III. 20
A.I only
B.II only
C.E=III only
D.II and III only
Answer: C.E=III only
Explanation: TIP FOR SUCH QUESTIONS:Make Algebraic Equation in the beginning to understand how to proceed further. Then Start thinking the possible values of variables asked about
i.e.When positive integer m is divided by positive integer x, the reminder is 7can be understood as
m = ax +7which means thevalue of x must be greater than 7as the remainder 7 is possible only when the Divisor is bigger than the Remainder 7
i.e. Min Value of x = 8
AND
i.e.When positive integer n is divided by positive integer y, the reminder is 11can be understood as
n = by +11which means thevalue of y must be greater than 11as the remainder 11 is possible only when the Divisor is bigger than the Remainder 11
i.e. Min Value of y = 12
i.e. Minimum Value of x+y = 8+12 = 20
Hence III only can be True
Answer: Option
C
Question: 96% of the population of a village is 23040. The total population of the village is?
A.29992
B.24000
C.26892
D.29991
Answer: B.24000
Explanation: X * (96/100) = 23040
X = 240 * 100
X = 24000
Answer: B
Question: A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?
A.100 m
B.200 m
C.600 m
D.800 m
Answer: A.100 m
Explanation: Explanation:
Relative speed of the thief and policeman = (11 â€“ 10) km/hr = 1 km/hr
Distance covered in 6 minutes = {\color{Blue} \left ( \frac{1}{60}\times 6 \right )} km = {\color{Blue} \frac{1}{10}} km = 100 m
{\color{Blue} \therefore } Distance between the thief and policeman = (200 â€“ 100) m = 100 m.
Answer: A
Question: P is a prime number. If 6p is between 15 and 95, which of the following W can be a value of 7p + 2?
A.W=15
B.W=79
C.121
D.65
Answer: B.W=79
Explanation: [3,5,7,11,13] are prime numbers that fits this equation 15< 6X <95. Afterwards subtract 2 from all the answer n see if it's divisible by 7. Therefore A and E are out. Leaves out with B C D.
B =11
C =17
D = 9
Only 11 is the set of prime numbers that fit between 15 and 95. Therefore 79 is the answer.B
Question: David has s pairs of shoes, which is 1/4 as many as Mary and twice as many as Jones. In terms of s, how many pairs of shoes do the three of them have combined?
A.9/2*s
B.7/2*s
C.3s
D.11/2*s
Answer: D.11/2*s
Explanation: == s +4s + s/2 ==> 5s + 1/2 s = 11/2*s
Ans .D
Question: 2224 × 9997 = ?
A.22244428
B.22255538
C.22233328
D.22266628
Answer: C.22233328
Explanation: C
22233328
2224 × 9997 = 2224 × (10000-3)
= 2224 × 10000 - 2224 × 3
= 22240000 - 6672
= 22233328
Question: If Finn was 15 months old one year ago, how old was he, in months, x months ago?
A.x − 30
B.x − 12
C.18 − x
D.27 − x
Answer: D.27 − x
Explanation: Age Today = 15 months + 12 months (1year) = 27 months
X months ago- Today's Age - X = 27 - X
Ans- D
Question: A, B and C can do a work in 6 days, 8 days and 12 days respectively. In how many days can all three of them working together, complete the work?
A.6 2/3 days.
B.2 2/3 days.
C.7 2/3 days.
D.1 2/3 days.
Answer: B.2 2/3 days.
Explanation: B
2 2/3 days.
Work done by all three of them in one day = 1/6 + 1/8 + 1/12 = 3/8.
The number of days required = 8/3 = 2 2/3 days.
Question: (A% of 4B + B% of A) is equal to ?
A.A% of B
B.B% of A
C.5% of AB
D.AB% of 3
Answer: C.5% of AB
Explanation: Answer
A% of 4B + B% of A =4AB/100 + AB/100
= 5AB/100 = 5% of AB
Correct Option: C
Question: Pipes A and B can fill a tank in 4 and 7 hours. Pipe C can empty it in 12 hours. If all pipes are opened together, then the tank will be filled in?
A.60/17 hr
B.13/12 hr
C.42/13 hr
D.13/42hr
Answer: C.42/13 hr
Explanation: Net part filled in 1 hour = 1/4 + 1/7 - 1/12 = 13/42
The tank will be full in 42/13 hr
Answer is C
Question: After decreasing 24% in the price of an article costs Rs.912. Find the actual cost of an article?
A.1400
B.1300
C.1200
D.1100
Answer: C.1200
Explanation: Explanation:
CP* (76/100) = 912
CP= 12 * 100 => CP = 1200
Answer is C
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
A.187
B.190
C.177
D.188
Answer: B.190
Explanation: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1900 m
T = D/S
T = 1900/10
T = 190 Sec
Answer: B
Question: The price of a certain product increased by the same percent from 1960 to 1970 as from 1970 to 1980. If its price of $1.20 in 1970 was 150 percent of its price in 1960, what was its price in 1980?
A.$ 1.80
B.$ 2.00
C.$ 2.40
D.$ 2.70
Answer: A.$ 1.80
Explanation: The price in 1970 was 150 percent of its price in 1960, means that the percent increase was 50% from 1960 to 1970 (and from 1970 to 1980).
Therefore the price in 1980 = $1.2*1.5 = $1.8.
Answer: A.
Question: Solve for x and check: x + 5 = 3
A.2
B.3
C.1
D.-2
Answer: D.-2
Explanation: Solution :
x+5-5=3-5
x=-2
Check :
x+5=3
-2+5=3
3=3
ANSWER : D
Question: A number has exactly 32 factors out of which 4 are not composite. Product of these 4 factors (which are not composite) is 30. How many such numbers G are possible?
A.2
B.4
C.6
D.3
Answer: C.6
Explanation: Firstly , we should note that 1 is NEITHER a prime nor a composite number.The first composite number is 4.Thus, when the problem states that there are 4 factors that are not composite, these nos are 1,2,3,5. Thus, the given number = 2^a*3^b*5^c. Also, (a+1)*(b+1)*(c+1) = 32. We can break down 32 into 3 integers as : 2*2*8 or 4*4*2
Also, the only possible combinations for a,b,c are : 3,3,1 OR 1,1,7. Thus, each combination has 3 possible orders and we have a total G of 6 possibilities.
C.
Question: 19 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played?
A.286
B.342
C.422
D.540
Answer: B.342
Explanation: 2*19C2 = 2*171 = 342
The answer is B.
Question: The sector of a circle has radius of 21 cm and central angle 130o. Find its perimeter?
A.89.7
B.91.4
C.91.7
D.91.3
Answer: A.89.7
Explanation: Perimeter of the sector = length of the arc + 2(radius)
= (130/360 * 2 * 22/7 * 21) + 2(21)
= 47.7 + 42 = 89.7 cm
Answer:A
Question: Twenty one identical machines, running continuously at the same constant rate, take 9 days to complete a shipment. How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by two days?
A.2
B.3
C.4
D.6
Answer: D.6
Explanation: From the question you know that 21R = 1/9. The question asks you (partially) to make the rate from 1/9 to 1/7 (drop from 9 day to 7). So the only thing that you need to do is to find the magic number than can convert 1/9 to 1/7.
So 1/9 * x = 1/7 (1 equation with one unknown). So by solving this you get x = 9/7 . Thats it then! Take the magic number 9/7 and multiply BOTH sides of the original equation and you have:
21*(9/7)*R = (9/7) * 1/9
27* R = 1/7, Hence 27R = 1/7, therefore 6 more machines!
D
Question: 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
A.7
B.8
C.9
D.10
Answer: A.7
Explanation: 1 woman's 1 day's work =	1
70
1 child's 1 day's work =	1
140
(5 women + 10 children)'s day's work = 5	+	10 = 1	+	1 =	1
70	140	14	14	7
5 women and 10 children will complete the work in 7 days.
Option A
Question: A man borrows Rs. 1200.00 from a bank for a period of 3 months. He finds that he has to repay Rs.1236.00. The bank rate of interest is:
A.3%
B.12%
C.6%
D.22%
Answer: B.12%
Explanation: amount returnd s 1236 , so interst Rs.36, borrowd 1200, n=3/12, so 36=(1200*3*r)/12*100, thus r=12%
ANSWER:B
Question: In a camp, there is a meal for 90 men or 160 children. If 110 children have taken the meal, how many men will be catered to with remaining meal?
A.20
B.30
C.50
D.28
Answer: D.28
Explanation: There is a meal for 160 children. 110 children have taken the meal.
Remaining meal is to be catered to 50 children.
Now, 160 children 90 men.
50 children (90/160)	* 50 = 28 men
Answer is D.
Question: If y > 0, (2y)/10 + (3y)/10 is what percent of y?
A.40%
B.50%
C.60%
D.70%
Answer: B.50%
Explanation: can be reduced to y/5+3y/10 =2y/5=50%
B
Question: If x = y+4.5x and y = x+18, what is the value of x/y ?
A.-6/5.
B.-7/20.
C.1/4.
D.-2/7.
Answer: D.-2/7.
Explanation: (1) x = y + 4.5x
Substitute y for y = x + 18 (Eq. we are given)
x = x + 18 + 4.5x
Combine like terms
x = 5.5x + 18 --> -4.5x =18 --> x = -4
(2) y = x + 18
Substitute x for x = -4
y = (-4) + 18 = 14
(3) x/y = ?
Substitute x and y we found above
x/y = (-4) / (14) =-2/7
My answer: D
Question: Jill works as a waitress at the local diner where she earns an hourly wage of $7.00 per hour and a standard tip rate of 5% of the cost of the orders she serves. If she worked four 12-hour shifts this week and averaged $40 in orders per hour, how much did Jill earn this week?
A.280
B.300
C.320
D.432
Answer: D.432
Explanation: Jill earns 7 dollars/hour and the hourly tip is (1/20)*40.
Jill thus earns 7*12+12*2 per day(or 7(12)+2(12)=9(12)=108).
Jill has worked for 4 days -> 108*4=432.
This matches answer choice D.
Question: Ramesh, Kiran and Ram started a business with capitals of Rs. 2000, Rs. 8000 and Rs. 6000 respectively. At the end of the year, the profit share of Kiran is Rs. 400. The difference between the profit shares of Ramesh and Ram is?
A.694
B.369
C.200
D.2356
Answer: C.200
Explanation: Ratio of investments of Ramesh, Kiran and Ram is 2000 : 8000 : 6000 = 1 : 4 : 3
And also given that, profit share of Kiran is Rs. 400
=> 4 parts out of 8 parts is Rs. 400
Now, required difference is 3 - 1 = 2 parts
Required difference = 2/4 (400) = Rs. 200.Answer: C
Question: Right now, Al and Eliot have bank accounts, and Al has more money than Eliot. The difference between their two accounts is 1/12 of the sum of their two accounts. If Al’s account were to increase by 10% and Eliot’s account were to increase by 20%, then Al would have exactly $20 more than Eliot in his account. How much money does Eliot have in his account right now?
A.$110
B.$120
C.$180
D.$200
Answer: D.$200
Explanation: Lets assume Al have amount A in his bank account and Eliot's bank account got E amount. We can form an equation from the first condition.
A-E = 1/12*(A+E) ==> 11A = 13E ------------ (1)
Second condition gives two different amounts, Al's amount = 1.1A and Eliot's amount = 1.2E
1.1A = 20 + 1.2E ==> 11A =200 +12E -------(2)
Substituting (1) in (2):
13E = 200+12E ==>E = 200
D
Question: Carol is Five times Alice’s age but only twice as old as Betty. Alice is twelve years younger than Carol. How old is Betty?
A.6
B.9
C.12
D.18
Answer: A.6
Explanation: given that C=5A=2B..AND A=C-12=5A-12-->4A=12-->A=3
substituting the values A=3,C=15 AND B=6..
ans A=6..
Question: In a certain random experiment, exactly one of the outcomes A, B, and J will occur. In each random experiment, the probability that outcome A will occur is 1/3 , and the probability that outcome B will occur is 1/3. What is the probability that when the random experiment is conducted 6 independent times, each of outcomes A, B, and J will occur twice?
A.5/243
B.1/12
C.10/81
D.1/6
Answer: C.10/81
Explanation: Number of ways in which a group of 2A,2B,2J can be formed in any order = 6!/(2!*2!*2!) [ formula for total of 6 items with 2 each of similar kind)
Total number of ways in which the die can be thrown independently = _ _ _ _ _ _ ; there are 6 places .First can be filled in 3 different ways A/B/J; Second in 3 diff ways again and so on.
So total number of ways = 3X3X3X3X3X3 = 3^6
There fore probability = 6!/(2!x2!x2!) by 3^6 = 90/3^6 = 10/81 Answer C
Question: A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 4000. With the help of C, they completed the work in 3 days. How much is to be paid to C?
A.s. 375
B.s. 400
C.s. 500
D.s. 800
Answer: C.s. 500
Explanation: C's 1 day's work = 1/3 - (1/6 + 1/8) = 1/3 - 7/24 = 1/24
A's wages : B's wages : C's wages = 1/6 : 1/8 : 1/24 = 4: 3 : 1
C's share (for 3 days) = Rs.	(3 * 1/24 * 4000) =Rs.500
Answer = C
Question: The smallest value of n, for which n+1 is not a prime number, is
A.5
B.6
C.8
D.3
Answer: D.3
Explanation: (1 + 1) = 2.
(2 + 1) = 3.
(3 + 1) = 4.
(4 + 1) = 5.
which is not prime , n=3.
ANSWER:D
Question: The value of a machine depreiates at the rate of 10% per annum. If its present is Rs.1,62,000 what will be its worth after 2 years ? What was the value of the machine 2 years ago ?
A.Rs.200000
B.Rs.100000
C.Rs.500000
D.Rs.300000
Answer: A.Rs.200000
Explanation: Value of the machine after 2 years
=Rs.[162000*(1-(10/100))^2] = Rs.[162000*(9/10)*(9/10)]
=Rs. 131220
Value of the machine 2 years ago
= Rs.[162000/(1-(10/100)^2)]=Rs.[162000*(10/9)*(10/9)]=Rs.200000
Answer is A.
Question: a man prpare the technical document it takes 2 hours for half an hour presentation and technical preparation. its screening takes 30 more minuts to prepare with the other guy.for to present a 7 half an hours how much time it will take
A.37 hours
B.35 hours
C.37 1/2 hours
D.33 hours
Answer: C.37 1/2 hours
Explanation: here first 2 hours to prepare a technical document and half-an-hour to screen it ..so total 2 1/2 hour work is need to 1/2 hour presentation....
For 7 1/2 hours presentation...
1/2 hour presentation-------------->>2 1/2 hour work done
7 1/2 hr presentation --------------> x hours work done
just do cross multiplication u will get x value i.e. required amount of time
since 7 1/2 hours contains 15 half-an-hours ...15* 2 1/2===== 30+7.5===total 37 1/2 hours
ANSWER:C
Question: A certain team has 8 members, including Joey. A three-member relay team will be selected as follows: one of the 8 members is to be chosen at random to run first, one of the remaining 7 members is to be chosen at random to run second, and one of the remaining 6 members is to be chosen at random to run third. What is the probability that Joey will be chosen to run second or third?
A.2/3
B.1/4
C.2/5
D.3/8
Answer: B.1/4
Explanation: Each member has an equal probability to run second (1/8) or third (1/8).
The probability that Joey runs second or third is 1/8 + 1/8 = 1/4
The answer is B.
Question: There exists exactly one positive value of k such that the line y = kx intersects the parabola
y = x2 + x + 4 at exactly one point. Compute the intersection point.
A.(2,10)
B.(5,10)
C.(7,10)
D.(3,10)
Answer: A.(2,10)
Explanation: If the line is tangent, then we must have that x2 + x + 4 = kx has a unique solution
in x, or x2 + (1 - k)x + 4 = 0 has a unique solution. Thus, (1 - k)2- 16 = 0, or (1- k) = 4.
Therefore, k = -3 or k = 5.
Taking k = 5, we have that y = 5x intersects y = x2 + x + 4 when x = 2, and the intersection
point is (2, 10) .
correct answer A
Question: Three friends sakthi, samy and Charlie divide $1010 amongs them in such a way that if $6, $8 and $10 are removed from the sums that sakthi, samy and Charlie received respectively, then the share of the sums that they got will be in the ratio of 4 : 8 : 6. How much did Charlie receive?
A.$316
B.$326
C.$331
D.$336
Answer: D.$336
Explanation: Explanatory Answer
Let the sums of money received by A, B and C be x, y and z respectively.
Then x - 6 : y - 8 : z -10 is 4a : 8a : 6a
When $6, $8 and $10 are removed, we are removing a total of $24 from $1010.
Therefore, 4a + 8a + 6a = 1010 - 24 = 986
i.e., 18a = 986
or a =55 .
We know that z - 6 = 6a =6 * 55 = 330
Therefore, z = 330 + 6 = $336
The correct choice is (D)
Question: How many positive even integers less than 100 contain digits 5 or 9?
A.16
B.10
C.18
D.19
Answer: B.10
Explanation: Two digit numbers:
5 at tens place: 50,52,54,56,58
9 at tens place: 90,92,94,96,98
If 5 and 9 is at units place, the number cant be even
Total:5+5= 10
Answer B
Question: A particular store purchased a stock of turtleneck sweaters and marked up its cost by 20%. During the New Year season, it further marked up its prices by 25% of the original retail price. In February, the store then offered a discount of 9%. What was its profit on the items sold in February?
A.27.5%
B.30%
C.35%
D.36.5%
Answer: D.36.5%
Explanation: Assume the total price = 100x
Price after 20% markup = 120x
Price after 25%further markup = 1.25*120x = 150x
Price after the discount = 0.91*150x = 136.5x
Hence total profit = 36.5%
Option D
Question: In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.20 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
A.160
B.185
C.190
D.200
Answer: B.185
Explanation: Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
160 x 2.20 + X x 3.20 = 432
X = 25.
Hence, total hours of work = (160 + 25) = 185.
answer :B
Question: The sector of a circle has perimeter of 144 cm and central angle 180o. Find its radius?
A.25 cm
B.32 cm
C.14 cm
D.28 cm
Answer: D.28 cm
Explanation: Let the radius is x cm
Perimeter of the sector = length of the arc + 2(radius)
144= (180/360 * 2 * 22/7 * x) + 2(x)
144= 22x/7 + 2x
144= 36x/7
36x= 1008
x = 28
Answer: D
Question: 78654 * 9999
A.784598562
B.765858254
C.784569825
D.786461346
Answer: D.786461346
Explanation: Explanation:
78654 * (10000 - 1)
= 786540000 - 78654
= 786461346
Option D
Question: 6 workers should finish a job in 8 days. After 3 days came 4 workers join them. How many days C do they need to finish the same job?
A.3
B.4
C.5
D.6
Answer: A.3
Explanation: Let Rate of one worker be R
=> (6*R)*8 = 1 (Rate * Time = work)
=> R = 1/48
=> Work remaining after 3 days
1 - (3*6)/48 = 30/48
After 4 ppl joined in
((6+4)*Time)/48 = 30/48
Time C= 3 days to finish the task
IMO A
Question: A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
A.2 3/2
B.2 2/3
C.2.5
D.3
Answer: C.2.5
Explanation: 100*(20/100) = 20 --- 10
? --- 1 => Rs.2
100 --- 80
? --- 2 => Rs.2.5
ANSWER:C
Question: If a train, travelling at a speed of 90 kmph, crosses a pole in 5 sec, then the length of train is?
A.125 m
B.104 m
C.140 m
D.152 m
Answer: A.125 m
Explanation: D = 90 * 5/18 * 5 = 125 m
ANSWER A
Question: Out of 9 persons, 8 persons spent Rs. 30 each for their meals. The ninth one spent Rs. 20 more than the average expenditure of all the nine. The total money spent by all of them was
A.Rs. 292.50
B.Rs. 297.50
C.Rs. 298
D.Rs. 298.50
Answer: A.Rs. 292.50
Explanation: Explanation:
Let the average expenditure be Rs. x Then,
9x = [8× 30 + (x + 20)] ⇔9x = x + 260 ⇔ x = 32.50
Total money spent = 9x = Rs. (9 x 32.5O) = Rs 292. 50 Answer: A
Question: Find the average of first 3 multiples of 5?
A.10
B.15
C.12.5
D.13
Answer: A.10
Explanation: average = (5+10+15)/3 = 10
Answer is A
Question: The amounts of time that three secretaries worked on a special project are in the ratio of 2 to 3 to 5. If they worked a combined total of 110 hours, how many hours did the secretary who worked the longest spend on the project?
A.80
B.55
C.56
D.16
Answer: B.55
Explanation: 10x = 110
=> x = 11
Therefore the secretary who worked the longest spent 11 x 5 = 55 hours on the project
Option (B)
Question: Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?
A.2(10)
B.2(9)
C.3 * 2(8)
D.3 * 2(9)
Answer: D.3 * 2(9)
Explanation: Explanatory Answer
When a coin is tossed once, there are two outcomes. It can turn up a head or a tail.
When 10 coins are tossed simultaneously, the total number of outcomes = 210
Out of these, if the third coin has to turn up a head, then the number of possibilities for the third coin is only 1 as the outcome is fixed as head.
We need to find out what happens to the remaining 9 coins?
The remaining 9 coins can turn up either a head or a tail. Each of the 9 coins has 2 possibilities.
Number of outcomes for the remaining 9 coins = 2(9)
∴ the number of outcomes in which the 3rd coin turns a head = 1 * 2(9) = 2(9).
Choice D
Question: 12*18*6 is the volume of some material. How many cubes of edge 3 can be insert into it?
A.48
B.49
C.50
D.51
Answer: A.48
Explanation: no. of such cubes = volume of material / volume of one cube
(12*18*6)/(3*3*3)= 48
ANSWER:A
Question: The vertices of a rectangle in the standard (x,y) coordinate place are (0,0), (0,4), (10,0) and (10,4). If a line through (1,1) partitions the interior of this rectangle into 2 regions that have equal areas, what is the slope of this line?
A.1/2
B.1/3
C.1/4
D.1/5
Answer: C.1/4
Explanation: We should know that a rectangle can be divided into two equal areas by a straight line only when the straight line passes through the center of the rectangle.
The center of the rectangle is the point (5,2).
The slope of line passing through points (1,1) and (5,2) = (2-1)/(5-1) = 1/4
The answer is C.
Question: A(n+1)=1+(1/A(n)) and A(1)=1. What is the value of A(10)?
A.89/55
B.91/57
C.93/59
D.95/61
Answer: A.89/55
Explanation: A(n+1)=1+(1/A(n))
A(1) = 1
A(2) = 2
A(3) = 3/2
A(4) = 5/3
A(5) = 8/5
A(6) = 13/8
A(7) = 21/13
A(8) = 34/21
A(9) = 55/34
A(10) = 89/55
The answer is A.
Question: Eleven people are planning to share equally the cost of a rental van. If one person withdraws from the arrangement and the others share equally the cost of the rental van, then the share of each of the remaining people will increase by...?
A.1/10
B.1/9
C.1/8
D.11/10
Answer: A.1/10
Explanation: Let P = total cost of the rental van.
The original share per person is P/11.
The new share per person is P/10.
P/10 = P/11 * 11/10 = (1 + 1/10)*original share
The answer is A.
Question: Which of the following numbers completes
the sequence 3, 8, 14, 21, 29, 38, 48, 59, 71 ___?
A.35
B.36
C.37
D.84
Answer: D.84
Explanation: The numbers increase at a somewhat steady rate, so you have to figure out how much
you have to add to each number to produce the next in the sequence: 3 + 5 = 8; 8 + 6 = 14;
14 + 7 = 21; 21 + 8 = 29, and so on. The rule for the sequence is to add successively larger
numbers to each number; therefore, the next number is 71 + 13 = 84.
correct answer D)84