RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is?
A.1/98
B.1/2
C.1/6
D.1/2
Answer: B.1/2
Explanation: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(E) = 1 - 1/2 = 1/2.
Answer: B
Question: If x and y are positive integers such that x < y and z=x/y, which of the following must be true?
I. z>(x − 1)/(y + 1)
II. z<(x + 1)/(y + 1)
III. z>(x + 1)/(y - 1)
A.I only
B.I and II
C.II and III
D.II only
Answer: B.I and II
Explanation: x < y --> Let x = 2 and y = 3 --> z = 2/3
I. z>(x − 1)/(y + 1) --> 2/3 > 1/4 --> True
II. z<(x + 1)/(y + 1) --> 2/3 < 3/4 --> True
III. z>(x + 1)/(y - 1) --> 2/3 > 3/2 --> False
Answer: B
Question: The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, how many subsequent flights need to depart from Phoenix on-time, for the airport's on-time departure rate to be higher than 50%?
I will see what is the quickest way to solve it then I will provide the explanation
A.3
B.7
C.9
D.10
Answer: A.3
Explanation: The following approach might be the easiest one and less error prone.
We need on-time departure rate to be higher than 5/10, so it should be at least 6/11, which means that 6 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then 6-3=3 subsequent flights need to depart on-time.
Answer: A
Question: Find the remainder of the division (2^14)/7.
A.1
B.2
C.3
D.4
Answer: D.4
Explanation: Find the pattern of the remainders after each power:
(2^1)/7 remainder 2
(2^2)/7 remainder 4
(2^3)/7 remainder 1 -->this is where the cycle ends
(2^4)/7 remainder 2 -->this is where the cycle begins again
(2^5)/7 remainder 4
Continuing the pattern to (2^14)/7 gives us a remainder of 4
Final Answer:
D) 4
Question: A number when divided by 296 leaves 75 as remainder. When the same number is divided by 37, the remainder will be:
A.5
B.4
C.1
D.2
Answer: C.1
Explanation: Explanation:
Let x = 296q + 75
= (37 x 8q + 37 x 2) + 1
= 37 (8q + 2) + 1
Thus, when the number is divided by 37, the remainder is 1.
Answer C
Question: Six years ago Rahul was P times as old as Sachin was. If Rahul is now 17 years old, how old is Sachin now in terms of P ?
A.11/P + 6
B.P/11 +6
C.17 - P/6
D.17/P
Answer: A.11/P + 6
Explanation: let's call Sachin age six years ago is x
so six years ago Rahul was: 17-6 = 11 years old
and six years ago Rahul was P times as old as Sachin was
=> 11/x = P
=> x = 11/P
=> Now Sachin's age will be : x+6 = 11/P+6
=> the answer is A
Question: P, Q and R have Rs.7000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R?
A.Rs.3000
B.Rs.3600
C.Rs.2400
D.Rs.2800
Answer: D.Rs.2800
Explanation: Let the amount with R be Rs.r
r = 2/3 (total amount with P and Q)
r = 2/3(7000 - r) => 3r = 14000 - 2r
=> 5r = 14000 => r = 2800.
ANSWER:D
Question: A motorist travels to a place 150 km away at an average speed of 50 km/hr and returns at 30 km/hr. His average speed for the whole journey in km/hr is?
A.37.9
B.37.2
C.37.5
D.37.1
Answer: C.37.5
Explanation: Average speed = (2xy) /(x + y) km/hr
= (2 * 50 * 30) / (50 + 30) km/hr.
37.5 km/hr.
Answer: C
Question: Let a,b,c,d,e,f be non-negative real numbers. Suppose that a + b + c + d + e + f = 1 and
ad + be + cf >= 1/18 . Find the maximum value of ab + bc + cd + de + ef + fa.
A.7/36
B.6/36
C.5/36
D.4/36
Answer: A.7/36
Explanation: We partially factor
ab + bc + cd + de + ef + fa = a(b + f) + c(b + d) + e(d + f):
Notice that the terms in the parenthesis are very close to (b+d+f), except each part is missing
one term. We can add ad + cf + eb to this expression to get
a(b + f) + c(b + d)e(d + f) + ad + cf + eb
= a(b + d + f) + c(b + d + f) + e(b + d + f)
= (a + c + e)(b + d + f)
Let x = a+c+e and y = b+d+f. We have x+y = 1, so AM-GM gives us x+y
2
p
xy, hence
(a + c + e)(b + d + f) - 1
4 . Subtracting away ad + be + cf - 1
18 gives us
ab + bc + cd + de + ef + fa -
1/4
-1/18
=
7/36
where equality holds when a + c + e = b + d + f = 1
2 and ad + be + cf = 1/18 . We can verify that
equality holds when a = e = 1/9 , b = d = 1/4 ,c = 5/18, f = 0.
correct answer A
Question: A basket contains 3 blue, 3 red and 3 yellow marbles. If 3 marbles are extracted from the basket at random, what is the probability that a marble of each color is among the extracted?
A.2/21
B.3/25
C.1/6
D.9/28
Answer: D.9/28
Explanation: Probability of getting each color marble = (3C1*3C1*3C1)/9C3
= (3*3*3)/84
= 27/84 = 9/28
So answer is D
Question: You walk one mile to school every day. You leave home at the same time each
day, walk at a steady speed of 3 miles per hour, and arrive just as school begins. Today you
were distracted by the pleasant weather and walked the first half mile at a speed of only 2
miles per hour. At how many miles per hour must you run the last half mile in order to arrive
just as school begins today?
A.4
B.6
C.8
D.10
Answer: B.6
Explanation: Recall the formula s = v *t, where in this case, s is distance (in miles) traveled at a
constant speed of v (miles per hour), for a time of t hours. The first statement indicates that
it usually takes you only 20 minutes to go to school (solve for t in 1 = 3 * t and change units)
Today, it took you 15 minutes to cover the first half mile (solve for t in 1=2 = 2 * t and
change units). You only have 5 more minutes to arrive (that is 1/12th of an hour), and need
to cover another half mile. Solve for v in the equation 1/2 = (1/12) *v.
correct answer B
Question: In how many ways letters of the word LICENSING be arranged?
A.362880
B.12540
C.65320
D.48962
Answer: A.362880
Explanation: LICENSING has 9 letters, out of which I repeated 2 times, N repeated 2 times. Hence total ways = 10!/(2!*2!)= 362880 ways
A
Question: A ratio between two numbers is 3 : 4 and their L.C.M. is 180. The first number is
A.60
B.45
C.20
D.15
Answer: B.45
Explanation: Sol.
Let the required numbers be 3x and 4x. Then, their L.C.M. is 12x.
∴ 12x = 180⇔ x = 15. Hence, the first number is 45.
Answer B
Question: A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 50 percent of the drive from the center, what percent of the round-trip has the technician completed?
A.70
B.65
C.60
D.75
Answer: D.75
Explanation: round trip means 2 trips i.e.to and fro. He has completed one i.e 50% completed. then he traveled another 50% of 50% i.e 25%. so he completed 50 +25 =75 % of total trip.
D
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is?
A.4:9
B.4:3
C.4:5
D.4:1
Answer: B.4:3
Explanation: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √16 : √9
= 4:3
Answer:B
Question: A, B and C shared profits in ratio of 3 : 7 : 6. Theypartnered for 14months, 8months and 7months respectively. What was he ratio of their investments ?
A.12 : 49 : 64
B.20 : 49 : 64
C.10 : 19 : 64
D.20 : 29 : 64
Answer: A.12 : 49 : 64
Explanation: Simply multiply profit sharing ratio with investment ratio to get investment amount ratio.
Let X is the total investment
â‡’14 x = 3
â‡’ 8 x = 7
â‡’ 7x = 8
â‡’ Final investment ratio = 12 : 49 : 64
A
Question: Machine A can put caps on a set of bottles in 8 hours at a constant rate. If Machine A does the job for 6 hours and Machine B does the rest of the job, which works at 1/4 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job?
A.4hrs
B.6hrs
C.8hrs
D.10hrs
Answer: C.8hrs
Explanation: machine A will do 6/8 in 6 hrs, so A does 3/4 of the work ..
Therefore, B will do the remaining 1/4 th work alone..
As the speed of B is 1/4 rate of A, B will do the 1/4th work in same time that A takes to complete full job...
ans 8
C
Question: If x is an integer, then x(x - 1)(x - v) must be evenly divisible by three when v is any of the following values EXCEPT
A.-4
B.-2
C.-1
D.2
Answer: B.-2
Explanation: here's another approach
x(x - 1)(x - v)
all three are consecutive, so the product MUST be a multiple of 3
we don't know the value of v just yet ... so let's extend the series ... the extension itself reveals the answers
..(x-5)..(x-2)(x-1)x(x+1)..(x+4)..
we can see the possible values of v too from the series
v = 2 OR 2+3n [25]
v = -1 OR -1+3n [-1-4]
B i.e. -2 does not fit in any value of v
so B it is
Question: One fourth of one third of two fifth of a number is 35. What will be40% of that number
A.A)140
B.B)420
C.C)180
D.D)200
Answer: B.B)420
Explanation: Explanation:
(1/4) * (1/3) * (2/5) * x = 35
then x = 35 * 30 = 1050
40% of 1050 = 420
Answer: Option B
Question: An internet service provider charges $3.10 for the first 1/5 of a day plus $0.40 for each additional 1/5 of a day. What would this company charge for an internet usage that was 8 days long?
A.$15.60
B.$16.00
C.$17.80
D.$18.70
Answer: D.$18.70
Explanation: first 1/5 day = $3.10
rest of the days = 8 - (1/5) = 39/5
charge for the rest of the days = 39 *0.4 = 15.6
total charge = 3.10+15.6 = 18.7
Answer is D.
Question: The ratio of sodium chloride to ammonium in 100 kg of mixed ammonium normally used by three chemists is 1: 3. The amount of sodium chloride to be added to 100 kg of mixed ammonium to make the ratio 9 :25 is
A.2 kg
B.6.625 kg
C.6.25 kg
D.6.35 kg
Answer: A.2 kg
Explanation: sodium chloride in 100 kg = 1/4 x 100 = 25 kg
ammonium in 100 kg = 3 / 4 x 100 = 75 kg
Now 75 is 25 parts out of (25 + 9) = 34 parts.
Hence 9 parts = 9/25 x 75 = 27
Amount to be added = 27 - 25= 2 Kg
ANSWER:A
Question: There are 172 lights which are functional and each is controlled by a separate On/Off switch. Two children A and B start playing with the switches. A starts by pressing every third switch till he reaches the end. B, thereafter, presses every fifth switch till he too reaches the end. If all switches were in Off position at the beggining, How many lights are switched On by the end of this operation?
A.83
B.85
C.87
D.79
Answer: D.79
Explanation: Editing my solution:
Number of switches = 172
Number of switches turned on by A: 3, 6, ... 171 = 57
Number of switches turned on by B: 5, 10, ....170 = 34
Few switches are turned on by A and later turned off by B: LCM(3,5) = 15x = 15, 30,....90 = 6.
Subtract the above 6 switches from both A and B as they are turned off.
Number of switches that are turned on = (57- 6) + (34 - 6) = 79
Answer: D
Question: What is the measure of the angle W made by the diagonals of the any adjacent sides of a cube.
A.30
B.45
C.60
D.75
Answer: C.60
Explanation: C.. 60 degrees
All the diagonals are equal. If we take 3 touching sides and connect their diagonals, we form an equilateral Triangle. Therefore, each angle would be 60.C
Question: The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.
A.48.55
B.49
C.51
D.61
Answer: A.48.55
Explanation: Required average
= (50.25 x 16 + 45.15 x 8)/(16 + 8)
= (804 + 361.20)/24
= 1165.20/24
= 48.55
Answer is A
Question: The sum of the heights of two high-rises is x feet. If the second high rise is 37 feet taller than the first, how tall will the first high rise be after they add an antenna with a height of z feet to the top?
A.(x+z)/2 + 37
B.2x−(37+z)
C.(x−37)/2 + z
D.x/2 - 37 + z
Answer: C.(x−37)/2 + z
Explanation: I will note h1 the height of high-rise 1 and h2 the height of high-rise 2. SO:
h1 + h2 = x
and h2 = h1 + 37 =>
Q: h1+ z = ?
h21+ h1 + 37 = x => 2h1= x-37 =? h1 = (x-37)/2
=> h1+ z = (x-37)/2 + z, CORRECT ANSWER C
Question: In how many ways, a committee of 12 members can be selected from 8 men and 7 ladies, consisting of 7 men and 5 ladies?
A.150
B.167
C.200
D.168
Answer: D.168
Explanation: (7 men out 8) and (5 ladies out of 7) are to be chosen
Required number of ways = 8C7*7C5 = 168
Answer is D
Question: 61 small identical cubes are used to form a large cube. How many more cubes are needed to add one top layer of small cube all over the surface of the large cube ?
A.64
B.128
C.152
D.155
Answer: D.155
Explanation: 61 small cube will make a large cube with 4 cubes in each line i.e.
Adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line.
Total number of small cubes in new cube = 6^3 = 216
Extra cube required = 216 - 61 = 155
Hence, D is the answer.
Question: A card game called “high-low” divides a deck of 52 playing cards into 2 types, “high” cards and “low” cards. There are an equal number of “high” cards and “low” cards in the deck and “high” cards are worth 2 points, while “low” cards are worth 1 point. If you draw cards one at a time, how many ways can you draw “high” and “low” cards to earn 6 points if you must draw exactly 3 “low” cards?
A.1
B.20
C.3
D.4
Answer: B.20
Explanation: Great question Ravih. This is a permutations problem (order matters) with repeating elements. Given thatlowcards are worth 1 pt andhigh cards2 pts, and you must draw 3 low cards, we know that you must also draw 1 high card. The formula for permutations problems with repeating elements isN!/A!B!...where N represents the number of elements in the group and A, B, etc. represent the number of times that repeating elements are repeated. Here there are 4 elements and thelowcard is repeated 3 times. As a result, the formula is:
5!/3! which represents (5*4*3*2*1)/(3*2*1) which simplifies to just 20, giving you answer B.
Question: A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 3 different offices?
A.5
B.6
C.27
D.8
Answer: C.27
Explanation: Ans. Each employee can go into any of the two offices. Thus we have
=> 3 * 3 * 3= 27
Answer : C
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 1800. He sold both the items together for Rs. 31150. What percentage of profit did he make?
A.30%
B.75%
C.40%
D.70%
Answer: B.75%
Explanation: The total CP = Rs. 16000 + Rs. 1800 = Rs. 17800 and SP = Rs. 31150
Profit(%) = (31150 - 17800)/17800* 100 = 75%
ANSWER:B
Question: A drink vendor has 80 liters of Maaza, 144 liters of Pepsi and 368 liters of Sprite. He wants to pack them in cans, so that each can contains the same number of liters of a drink, and doesn't want to mix any two drinks in a can. What is the least number of cans required?
A.35
B.37
C.42
D.30
Answer: B.37
Explanation: The number of liters in each can = HCF of 80, 144 and 368 = 16 liters.
Number of cans of Maaza = 80/16 = 5
Number of cans of Pepsi = 144/16 = 9
Number of cans of Sprite = 368/16 = 23
The total number of cans required = 5 + 9 + 23 = 37 cans.
ANSWER:B
Question: If the product of two numbers is 84942 and their H.C.F. is 33, find their L.C.M.
A.2574
B.2500
C.1365
D.1574
Answer: A.2574
Explanation: Explanation:
HCF * LCM = 84942, because we know
Product of two numbers = Product of HCF and LCM
LCM = 84942/33 = 2574
Option A
Question: A man traveled a total distance of 1800 km. He traveled one-third of the whole trip by plane and the distance traveled by train is three-fifth of the distance traveled by bus. If he traveled by train, plane and bus, then find the distance traveled by bus?
A.239
B.247
C.277
D.270
Answer: D.270
Explanation: Explanation:
Total distance traveled = 1800 km.
Distance traveled by plane = 600 km.
Distance traveled by bus = x
Distance traveled by train = 3x/5
=> x + 3x/5 + 600 = 1800
=> 8x/5 = 1200 => x = 750 km.
Answer: D
Question: A reduction of 12% in the price of oil enables a house wife to obtain 6kgs more for Rs.1200, what is the reduced price for kg?
A.24
B.27
C.40
D.28
Answer: A.24
Explanation: 1200*(12/100) = 144 ---- 6
? ---- 1 => Rs.24
Answer:A
Question: Laura took out a charge account at the General Store and agreed to pay 6% simple annual interest. If she charges $35 on her account in January, how much will she owe a year later, assuming she does not make any additional charges or payments?
A.$2.10
B.$37.10
C.$37.16
D.$38.10
Answer: B.$37.10
Explanation: Principal that is amount taken by Laura at year beginning = 35$
Rate of interest = 6%
Interest = (6/100)*35 = 2.10$
Total amount that Laura owes a year later = 35+2.1 = 37.1 $
Answer B
Question: If a person walks at 12 km/hr instead of 8 km/hr, he would have walked 20 km more. The actual distance traveled by him is?
A.50
B.40
C.45
D.60
Answer: B.40
Explanation: Let the actual distance traveled be x km. Then,
x/8 = (x + 20)/12
x - 40 =>x = 40 km.
Answer: B
Question: 364, 361, 19, 16, 4, 1, ?
A.0
B.1
C.2
D.3
Answer: B.1
Explanation: 364-3=361
sqrt(361)=19
19-3=16
sqrt(16)=4
4-3=1
sqrt(1)=1
ANSWER:B
Question: What is the ratio between perimeters of two squares one having 2.5 times the diagonal then the other?
A.4: 5
B.1: 3
C.2.5: 1
D.3.5: 1
Answer: C.2.5: 1
Explanation: d = 2.5d d = d
a√2 = 2.5d a√2 = d
a = 2.5d/√2 a = d/√2 =>2.5: 1
Answer: C
Question: In 1 hour, a boat goes 8 km along the stream and 12 km against the stream. The speed of the boat in still water (in km/hr) is :
A.3 km/hr.
B.2 km/hr.
C.10 km/hr.
D.8 km/hr.
Answer: C.10 km/hr.
Explanation: Speed in still water = 1/2(8 + 12) km/hr
= 10 km/hr. ANSWER :C
Question: A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed?
A.32
B.88
C.67
D.11
Answer: D.11
Explanation: One day work of A, B and C = 1/24 + 1/30 + 1/40 = 1/10 Work done by A and B together in the last 4 days = 4*(1/24 + 1/30) = 3/10
Remaining work = 7/10
The number of days required for this initial work = 7 days.
The total number of days required = 4 + 7 = 11 days.
Answer:D
Question: The number 69 can be written as the sum of squares of 3 integers. Which of the following could be the difference between the largest and smallest integers of the 3?
A.2
B.5
C.7
D.8
Answer: B.5
Explanation: Notice that the question asks which of the followingcouldbe the difference between the largest and smallest integers, not must be. The 3 integers could be: +/-2, +/-4 and +/-7 so the difference could be 5,3 or 11. Since only one of them is among the choices, then it must be the correct answer.
Answer: B
Question: If four students are made to sit in a row, then 3 don't have seats. If 15 students are made to sit in a row, then two rows are empty. How many students have to sit a row such that each row has equal number of students and all students are seated?
A.0
B.1
C.4
D.5
Answer: D.5
Explanation: Let there be a rows.
Then 4a + 3= 15(a-2) [equating the number of students]
=> a= 3
and total number of students = 15
Therefore 5 students much sit in each row such that each row has an equal number of students and all students are seated.
Option (D)
Question: In how many different number of ways 5 men and 2 women can sit on a shopa which can accommodate persons?
A.200
B.230
C.240
D.250
Answer: B.230
Explanation: Option 'B'
7p3 = 7 × 6 × 5 = 210
Question: Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is:
A.10
B.12
C.14
D.16
Answer: C.14
Explanation: Explanation:
A,B,C together fill the tank in 6 hours.
=> Part filled by pipes A,B,C together in 1 hr =1/6
All these pipes are open for only 2 hours and then C is closed.
Remaining part =1−1/3=2/3
This remaining part of 2/3 is filled by pipes A and B in 7 hours
Therefore, part filled by pipes A and B in 1 hr
=(2/3)/7=2/21
Part filled by pipe C in 1 hr
=(1/6-2/21)=7-4/42 =3/42 =1/14
i.e., C alone can fill the tank in 14 hours.
Answer: Option C
Question: A sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is?
A.33.3
B.33.6
C.33.0
D.33.4
Answer: C.33.0
Explanation: Let B = 100
A = 50
C * (150/100) = 50
3C = 100
C = 33.3 then 'C' Cheapest
Answer:C
Question: A class of students consists of 6 senior and 2 junior students. If a class council is created with 3 senior and 1 junior student, in how many ways can the class council be formed?
A.12
B.20
C.40
D.57
Answer: C.40
Explanation: Choose 3 senior from 5 senior and choose 1 junior from 3 junior:
3C6 * 1C2 = 20*2 = 40
Ans: C
Question: The 100-milliliter solution of sugar and water is 15% sugar. How much water (in milliliters) must be added to make a solution that is 8% sugar?
A.72.5
B.77.5
C.82.5
D.87.5
Answer: D.87.5
Explanation: In the original solution the amount of sugar is 0.15*100=15 ml.
Let the volume of the new solution be V.
0.08V=15 ml.
V=187.5 ml.
The amount of water we need to add is 187.5 - 100 = 87.5 ml.
The answer is D.
Question: An office supply store stocks three sizes of notebooks, each in five colors: blue, green, yellow, red, or pink. The store packs the notebooks in packages that contain either 4 notebooks of the same size and the same color or 4 notebooks of the same size and of 4 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?
A.18
B.24
C.30
D.45
Answer: C.30
Explanation: First let's consider the small notebooks.
There are 5 ways to choose notebooks of the same color.
The number of ways to choose four notebooks with different colors is 5C4=5.
There are 10 different packages we can make with the small notebooks.
We can use the same process to find 10 different packages with medium and large notebooks.
The total number of different packages is 30.
The answer is C.
Question: If p/q = 2/7 , then 2p+q= ?
A.11
B.14
C.13
D.15
Answer: A.11
Explanation: let p=2, q=7 then 2*2+7=11
so 2p+q=11.
ANSWER:A
Question: A company produces computers with 7 different speeds, and the ratio of each speed to the next one is a fixed ratio. If the fastest computer is 5.4 GHz, while slowest speed is 0.2 GHz, what is the speed of the second slowest computer?
A.(3^1/2) (0.2)
B.(27^1/7) (0.2)
C.(5.2/7) + 0.2
D.(0.2)^2
Answer: A.(3^1/2) (0.2)
Explanation: 1st speed=0.2
Let x be ratio,then 1st/2nd=x
0.2/2nd =x------>2nd=0.2/x------(a)
.
.
.
7th=0.2/x^6=5.4
x^6=0.2/5.4=1/27----->1/3^3
x=1 / 3^(3*1/6)------->1/3^1/2
therefore 2nd speed(from (a)) =0.2/(1/3^1/2)-------->3^1/2*0.2
Ans A
Question: The product of two numbers is 266 and their difference is 5. What is the bigger number ?
A.13
B.15
C.19
D.24
Answer: C.19
Explanation: Explanation:
Let the two numbers be A and B, here A > B
AB = 266
B = 266/A -----------------(I)
Given,
A – B = 5 ----------- (II)
Substitute from (I) in (II), we get
A – 266/A = 5
A2 – 5A + 266 = 0
(A – 19)(A – 14) = 0
Therefore , A = 19 or A = 14
Hence, bigger number = A = 19
ANSWER: C
Question: The probability of rain showers in Barcelona on any given day is 0.3. What is the probability that it will rain on exactly one out of three straight days in Barcelona?
A.0.441
B.0.072
C.0.432
D.0.72
Answer: A.0.441
Explanation: IMO This is just for first day! It can rain on 2nd day or 3 rd day (and not rain on other days) in 3 consecutive days!
Hence,
0.3*0.7*0.7 + 0.7*0.3*0.7 + 0.7*0.7*0.3 = 0.441
Option - A
Question: How many odd, positive divisors does 640 have?
A.6
B.8
C.12
D.15
Answer: C.12
Explanation: Make a prime factorization of a number: 540=2^2*3^3*5 --> get rid of powers of 2 as they give even factors --> you'll have 3^3*5 which has (3+1)(1+1)=12 factors.
Another example: 60=2^2*3*5 it has (2+1)(1+1)(1+1)=12 factors out of which (1+1)(1+1)=4 are odd: 1, 3, 5 and 15 the same # of odd factors as 60/2^2=15 has.
Answer: C.
Question: A certain animal shelter has 28 cats and 46 dogs. How many dogs must be adopted and taken away from the animal shelter so that 70 percent of the animals in the shelter will be cats?
A.6
B.12
C.28
D.34
Answer: D.34
Explanation: (28 + 46 - x)*0.7 = 28
x = 34.
Answer: D.