RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
A.10
B.99
C.88
D.66
Answer: A.10
Explanation: Speed of the boat in still water = (60+80)/2 = 70 kmph. Speed of the stream = (80-60)/2 = 10 kmph. Answer:A
Question: The sum of two numbers is 40 and their product is 1050. What will be the sum of their reciprocals?
A.(4/105)
B.(11/210)
C.(35/4)
D.(75/8)
Answer: A.(4/105)
Explanation: Solution
x+y=40 xy=1050 1/x+1/y=x+y/xy 40/1050 = (4/105).
Answer A
Question: A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio:
A.16:15
B.15:16
C.12:11
D.11:13
Answer: A.16:15
Explanation: Let the Face Value of Stock giving dividend 9% be Rs. x, whose Market Value is Rs.96.
Let the Face Value of Stock giving dividend 12% be Rs. y, whose Market Value is Rs.120.
By given formula,
Face Value * Dividend % / Market Value = Annual income.
Annual Income from 1st Stock = 9x/96.
Annual Income from 2nd Stock = 12y/120.
To obtain equal dividends from both,
Annual Income from 1st Stock = Annual Income from 2nd Stock.
= 9x/96 = 12y/120.
= x/y = 96/90.
We find GCD of 96, 90 = 6.
= x/y = 16*6 / 15*6.
= Required ratio = x:y = 16:15.
answer : A
Question: 0.05 x 0.03 = ?
A.0.00015
B.0.015
C.0.0015
D.0.15
Answer: C.0.0015
Explanation: 5 x 3 = 15.
Sum of decimal places = 4
0.05 x 0.03 = 0.0015
Answer: Option C
Question: Dan's age after 18 years will be 8 times his age 3 years ago. What is the present age of Dan?
A.4
B.6
C.8
D.10
Answer: B.6
Explanation: Let Dan's present age be x.
x+18 = 8(x-3)
7x = 42
x = 6
The answer is B.
Question: 81,162,49,98,25,50,55
A.110
B.127
C.129
D.128
Answer: A.110
Explanation: 81*2=162
49*2=98
25*2=50
55*2=110
ANSWER:A
Question: A zinc-copper alloy with 6 kg of pure zinc would contain 90% of zinc. The alloy with 3 kg of 90% zinc alloy contains 84% of zinc. Calculate the weight and percentage of zinc in the zinc-copper alloy.
A.2.4 kg or 80%
B.1.4 kg or 88%
C.3.4 kg or 60%
D.4.9 kg or 81.4%
Answer: D.4.9 kg or 81.4%
Explanation: Right Answer Explanation:
x : 6
y : 100
90
10 : 90 – y
(90-y)/6 = 10/x = ………..(1)
In the second case,
x 3
y 90
84
6 84-y
Therefore (84-y)/3 = 6/x ………..(2)
Dividing (1) and (2)
=
270 – 3y = 840 – 10y
7y = 570
y = 81.4
x = 60/(90-80) = 60/10 = 6 kg
Quantity of zinc in x = 81.4% of x
= 0.814 6
= 4.9 kg
Weight and percentage of zinc is 4.9 kg or 81.4%
D
Question: A machine fills 150 bottles of water every 8 minutes. How many minutes it takes this machine to fill 675 bottles?
A.12 min
B.34 min
C.32 min
D.45 min
Answer: C.32 min
Explanation: 8 minutes are needed to fill 150 bottles. How many groups of 150 bottles are there in 675 bottles?
675 ÷ 150 = 4.5 = 4 and 1/2
For each of these groups 8 minutes are needed. For 4 groups and 1/2
8 × 4 + 4 = 32 + 4 = 36 minutes. (4 is for 1/2 a group that needs half time)
We can also find the final answer as follows
4.5 x 8 = 32 minutes
correct answer is C) 32 min
Question: Set G consists of all even integers between 2 and 100, inclusive. Set X is derived by reducing each term in set G by 50, set Y is derived by multiplying each term in set G by 1.5, and set Z is derived by dividing each term in set G by -4. Which of the following represents the ranking of the three sets in descending order of standard deviation?
A. X, Y, Z
B. X, Z, Y
C. Y, Z, X
D. Y, X, Z
Answer: D. Y, X, Z
Explanation: Set G - {2, 4, ..., 100};
Set X - {-48, -46, ..., 50};
Set Y - {3, 6, ..., 150};
Set Z - {-2/4, -4/4, ..., -100/4} = {-1/2, -1, -3/2, ..., -25}.
If we add or subtract a constant to each term in a set the SD will not change, so sets G and X will have the same SD.
If we increase or decrease each term in a set by the same percent (multiply by a constant) the SD will increase or decrease by the same percent, so set Y will have 1.5 times greater SD than set G and set Z will have 4 times less SD than set G (note SD can not be negative so SD of Z wil be SD of G divided by 4 not by -4).
So, the ranking of SD's in descending order is: Y, G=X, Z.
Answer: D.
Question: The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the width of this rectangle.
A.5
B.10
C.15
D.20
Answer: C.15
Explanation: L * W = 300 : area , L is the length and W is the width.
2 L + 2 W = 70 : perimeter
L = 35 - w : solve for L
(35 - W) * W = 300 : substitute in the area equation
W = 15 and L = 20 : solve for W and find L using L = 35 - w.
correct answer C
Question: A military garrison in a wild frontier has 60 men who have provisions to last 26 weeks. At the end of 6 weeks they are joined by another 30 men. How long will the provisions last?
A.13 1/3
B.12 1/3
C.11 3/3
D.12 1/2
Answer: A.13 1/3
Explanation: Total provisions=600*26*7=10920
Provisions used for in 6 weeks=6*7*600=2520
remaining provisions=8400
remaining provisions need to be split between 90(60+30) people.
Number of provisions per person= 8400/90
we need to find the answer in terms of weeks=(8400/90)/7=40/3
Answer:A
Question: By selling an article at Rs.900, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?
A.s.600
B.s.480
C.s.500
D.s.540
Answer: D.s.540
Explanation: SP = 900
Profit = 25%
CP = (SP)*[100/(100+P)]
= 900 * [100/125]
= 720
Loss = 25% = 25% of 720 = Rs.180
SP = CP - Loss = 720 - 180 = Rs.540
ANSWER:D
Question: If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value A of z - x?
A.6
B.7
C.8
D.9
Answer: D.9
Explanation: x<y<z
To find the least possible value for z-x; we need to find the values for z and x that can be closest to each other. If x is some even number, then what could be minimum possible odd z.
If x is some even number
y-x>5; y>x+5; minimum value for y=x+5+2=x+7[Note: x+5 is as even+odd=odd and nearest odd greater than x+5 is x+5+2]
Minimum value for z=y+2=x+7+2=x+9 [Note: z=y+2 because both z and y are odd. Difference between two odd numbers is 2]
A=z-x = x+9-x= 9
Ans:D
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m ?
A.127.5 m
B.254 m
C.184 m
D.212 m
Answer: A.127.5 m
Explanation: Explanation:
When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 x 700)/800 = 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C
= (600 x 212.5)/1000 = 127.5 m.
ANSWER IS A
Question: There are a total of 11 students in Mr. Michael's gym class. Over the course of a badminton unit, each of the 11 students will compete exactly once against every other student in the class. How many total games of badminton will be played?
A.58
B.51
C.52
D.55
Answer: D.55
Explanation: there are 11 students , if each play with all other members .
then total games can be calculated as 10+9....+1 = 55.
alternate approach is to choose 2 distinct out of 11 = 11c2 = 55
Answer is D.
Question: J is faster than P. J and P each walk 24 km. Sum ofthe speeds of J and P is 7 kmph. Sum of time taken by them is 14 hours. Then J speed is equal to?
A.4
B.5
C.6
D.7
Answer: A.4
Explanation: let j's speed is x then p's speed would be 7-x.
and given,
sum of time taken by them is 14 hours
=>(24/x)+(24/(7-x)=14
=>x=4,3
therefore j's speed will be 4 as j walks faster than p.
ANSWER:A
Question: A box contains 2 red balls and 5 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?
A.1/4
B.7/5
C.1/2
D.5/8
Answer: B.7/5
Explanation: My complicated version of your simple approach
Let the 5 black balls be BBBBB and 2 Red Balls be RRR
They can be arranged in 8 slots _ _ _ _ _ _ _ _
in (7!)/ (5!x2!)
If the fourth slot is Black ball then the arrangement will be to fill
_ _ _ B _ _ _ _
we have 6 slots and 4 Black (BBBB) and 2 Red (RRR)
They can be arranged in (7!)/ (4!x2!)
Hence required probability = [(7!)/ (5!x2!)]/[(6!)/ (4!x2!)]=7/5
B
Question: A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 55%. Staff are allowed a further 50% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?
A.0.275D
B.0.225D
C.0.265D
D.0.245D
Answer: B.0.225D
Explanation: Effective discount = a + b + ab/100 = - 55 - 50 + (-55)(-50)/100 = 77.5
Sale price = D * ( 1 - 77.5/100)
Sale price = .225 * D
Answer (B)
Question: If the number 481 * 673 is completely divisible by 9, then the smallest whole number in place of * will b
A.4
B.5
C.7
D.8
Answer: C.7
Explanation: Sum of digits = (4 + 8 + 1 + x + 6 + 7 + 3) = (29 + x), which must be divisible by 9.
x = 7.
C)
Question: Two trains of equal length, running with the speeds of 60 and 90 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
A.3.2
B.2.6
C.6.6
D.32.2
Answer: C.6.6
Explanation: RS = 60 -40 = 20 * 5/18 = 100/18
T = 50
D = 50 * 100/18 = 2500/9
RS = 60 + 90 = 150 * 5/18
T = 2500/9 * 18/750 = 6.6 sec.Answer: C
Question: If a^2x = b^y, then
A.log a/b= x/y
B.log a/ log b = x/y
C.log a/ log b = y/2x
D.log b/a = x/y
Answer: C.log a/ log b = y/2x
Explanation: a^2x = b^y => log a^2x = log b^y => 2x log a = y log b
=> log a/ log b = y/2x
ANSWER:C
Question: A can complete the job in 4 hours and B can complete the same job in 3 hours. A works for 1 hour and then B joins and both complete the job. What fraction of the job did B complete
A.1/7
B.3/10
C.1/2
D.5/6
Answer: A.1/7
Explanation: A=1/7
Question: A , B , and C started a partnership business by investing $45,000 , $63,000 , and $72,000 respectively. At the end of the year, the profit was distributed among them. If C's share of profit is $20,000, what is the total profit?
A.$38,000
B.$42,000
C.$46,000
D.$50,000
Answer: D.$50,000
Explanation: A:B:C = 45000:63000:72000 which is a ratio of 5:7:8.
Let the total profit be x.
x * 8/20 = 20000
x = 20000*20/8 = 50,000.
The answer is D.
Question: the sum of 2nd and 19th term of A.P. is equal to the sum of 8th , 15th and 12 th term . find the term which is 0
A.12
B.13
C.14
D.15
Answer: C.14
Explanation: t2 + t19 = t8 + t15 + t12
=> a+d + a+18d = a+7d + a+14d + a+11d
=> a + 13d = 0
=> t14 = 0 i.e. 14th term is zero.
ANSWER:C
Question: A retailer buys 40 pens at the market price of 36 pens from a wholesaler ,if he sells these pens giving a discount of 1% ,what is the profit % ?
A.15%
B.5%
C.10%
D.25%
Answer: C.10%
Explanation: let the market price of each pen be Rs 1
then,C.P of 40 pens = Rs 36
S.P of 40 pens =99% of Rs 40=Rs 39.60
profit %=((3.60*100)/36) %=10%
Answer is C.
Question: In an examination 80% failed in Math and 20% failed in French. If 24% failed in both. What % of students passed in both.
A.25%
B.24%
C.20%
D.30%
Answer: B.24%
Explanation: Passed in Math = 100 - 80 = 20%
Passed in French = 100 - 20 = 80%
Students who passed Math or French = 100 -24 = 76%
Students passed in Math and French = (Passed in Math) + (Passed in French) - (Students who passed Math or French) = 20+80-76 =24%
ANSWER:B
Question: The grade point average of the entire class is 80. If the average of one fourth of the class is 92, what is the average of the rest of the class?
A.73
B.74
C.75
D.76
Answer: D.76
Explanation: Let x be the number of students in the class.
Let P be the average of the rest of the class.
80x = (1/4)92x + (3/4)(P)x
320 = 92 + 3P
3P = 228
P = 76.
The answer is D.
Question: Of the three numbers, the first is twice as second and three times the third. The average of the three numbers is 66, and the three numbers in order are?
A.116,58,36
B.98,49,33
C.126,63,36
D.108,54,36
Answer: D.108,54,36
Explanation: Explanation :
Solution: Let A =x,
B =x/2, C = x/3.
=x + x/2 + x/3 / 3 = 66
By solving we will get x = 108.
Hence A= 108
B= 108/2= 54
C= 108/3 = 36
Answer : D
Question: A bag contains nine yellow balls, three white balls and four red balls. In how many ways can two balls be drawn from the bag?
A.⁹C₂
B.³C₂
C.¹⁶C₂
D.¹²C₂
Answer: C.¹⁶C₂
Explanation: Explanation:
Total number of balls = 9 + 3 + 4
Two balls can be drawn from 16 balls in ¹⁶C₂ ways.
ANSWER IS C
Question: Given a unit square, two points are chosen uniformly at random within the square. Compute
the probability that the line segment connecting those two points touches both diagonals of the
square.
A.1/4
B.2/4
C.3/4
D.4/4
Answer: A.1/4
Explanation: If we draw both diagonals, then the desired event happens if and only if the two
points appear in dierent triangles that do not share an edge. Given the triangle where one
point lands, the other point has probability
1/4
of landing in the other triangle.
correct answer A
Question: Set X consists of 5 integers and has median of 20 and a range of 20. What is the value of the greatest possible integer that can be present in the set?
A.20
B.37
C.C.40
D.43
Answer: A.20
Explanation: Note that both median and range do not restrict too many numbers in the set. Range is only concerned with the smallest and greatest. Median only cares about the middle.
Quick check of each option starting from the largest:
(E) 50
Range of 20 means the smallest integer will be 30. So 20 cannot lie in between and hence cannot be the median.
(D) 43
Range of 20 means the smallest integer will be 23. So 20 cannot lie in between and hence cannot be the median.
(C) 40
Range of 20 means the smallest integer will be 20. 20 can lie in between such as:
20, 20, 20, 20, 20
This is possible. Hence it is the greatest such number.
Answer (A)
Question: A train is running at a speed of 40 km/hr and it crosses a post in 25.2 seconds. What is the length of the train?
A.190 metres
B.160 metres
C.280 metres
D.120 metres
Answer: C.280 metres
Explanation: Speed of the train, v = 40 km/hr = 40000/3600 m/s = 400/36 m/s
Time taken to cross, t = 25.2 s
Distance Covered, d = vt = (400/36)Ã— 25.2 = 280 m
Distance covered is equal to the length of the train = 280 m
Correct answer is 280 metres
C
Question: A circular path of 19 m radius has marginal walk 2 m wide all round it. Find the cost of leveling the walk at 25p per m2?
A.rs.49.25
B.rs.40.50
C.rs.44.20
D.rs.62.85
Answer: D.rs.62.85
Explanation: Explanation:
π (21^2 - 19^2) = 22/7 * (441-361) = 251.43
251.43 * 1/4 = Rs.62.85
Answer: Option D
Question: Rahul went to a shop and bought things worth Rs. 26, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
A.19.7
B.20.7
C.22
D.21.4
Answer: B.20.7
Explanation: Total cost of the items he purchased = Rs.26
Given that out of this Rs.26, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (26−30/100−x)6/100 = 30/100
⇒ 6(26 −0.3 −x) = 30
⇒ (26 − 0.3 − x) = 5
⇒ x = 26 − 0.3 − 5 = 20.7
B
Question: How many of the positive divisors of 480 are also multiples of 4 not including 480?
A.15
B.16
C.19
D.20
Answer: A.15
Explanation: 480 = 2^6 * 3 * 5 = (4) * 2^3 * 3 * 5
Besides (4), the exponents of 2, 3, and 5 are 3, 1, and 1.
There are (3+1)(1+1)(1+1) = 16 ways to make multiples of 4.
We must subtract 1 because one of these multiples is 480.
The answer is A.
Question: .
On dividing a number by 357, we get 39 as remainder. On dividing the same number 17, what will be the remainder ?
A.0
B.3
C.5
D.8
Answer: C.5
Explanation: Let x be the number and y be the quotient. Then,
x = 357 x y + 39
= (17 x 21 x y) + (17 x 2) + 5
= 17 x (21y + 2) + 5)
Required remainder = 5.
Answer: Option C
Question: x percent of y percent of z is decreased by y percent. find the result?
A.(xz - y) / 100
B.(100xyz - xy^2z) /1,000,000
C.(xz - y) / 10,000
D.(xyz - 2y) / 100
Answer: B.(100xyz - xy^2z) /1,000,000
Explanation: We're told that X percent of Y percent of Z is DECREASED by Y percent. We're asked for the result of all of this math.
IF....
X = 10
Y = 50
Z = 100
First, 50% of 100 = 50
Next, 10% of 50 = 5
Finally, 5 decreased by 50% of itself is 2.5
So we're looking for an answer that equals 2.5 when X=10, Y=50 and Z=100.
Answer A. (100xyz - xy^2z) / 1,000,000 = (5,000,000 - 2,500,000)/1,000,000 = 2,500,000/1,000,000 = 2.5
Anwer is B
Question: There are 7 boxes numbered from 1 to 7. Either a red ball or a green ball will be placed in each box in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. How many different ways can this be done?
A.26
B.28
C.30
D.32
Answer: B.28
Explanation: 1 green ball: 7 ways
2 green balls: 6 ways
3 green balls: 5 ways
4 green balls: 4 ways
5 green balls: 3 ways
6 green balls: 2 ways
7 green balls: 1 way
The total number of ways is 7*8/2=28
The answer is B.
Question: Three numbers are randomly selected, with replacement, from the set of integers {0, 1, 2, 3, 4, 5, 6, 7, 8}. If the first number selected is w, the second number selected is x, and the third number is y, what is the probability that w < x < y ?
A.28/243
B.31/243
C.35/729
D.83/729
Answer: A.28/243
Explanation: The number of ways to select w, x, and y is: 9*9*9=729
The number of ways to choose three different numbers from the set is 9C3=84.
There are six permutations for each group of three different numbers, but only one permutation satisfies w < x < y.
The probability that w < x < y is 84/729 = 28/243
The answer is A.
Question: A boat moves down stream at the rate of 1 km in 6 minutes and
upstream at the rate of 1 km in 10 minutes. The speed of current is
A.2 kmph
B.3 kmph
C.4 kmph
D.5 kmph
Answer: A.2 kmph
Explanation: If speed(in kmph) of the boat=b and current=c, then
In downstream time taken(in hrs.)=1/(b+c)=6/60=1/10 or b+c=10 ---(i) &
In upstream time taken(in hrs.)=1/(b-c)=10/60=1/6 or b-c=6 ---(ii)
From (i) & (ii), b=8, c=2
ANSWER:A
Question: If a, b, w are integers, 33 = abw, and a < b < w, what is the smallest possible value of a?
A.-33
B.-3
C.1
D.3
Answer: A.-33
Explanation: Given : a * b * w = 33.
33 is a Positive Odd number.Side Note:Thus, all 3 numbers will be odd.
Prime factorization will also give you numbers. 1, 3, 11. The 3 numbers will be combination of these 3 numbers with possible variation in sign(+/-).
We could have any 2 digits as negative. --> negative * negative * positive. We have negative values in answer option, so eliminate C, D and E from answer choices.
-33 * -1 * 1 = 33.
Correct answer is A
Question: If you multiply two integers together and
then add 4, the result is 40. Which of the
following could NOT be the sum of the
two numbers?
A.12
B.13
C.15
D.18
Answer: D.18
Explanation: Let the two integers equal x and y, and then create the following equation and simplify:
xy + 4 = 40
xy = 36
So x and y are a pair of integers that equal 36. Try adding all possible combinations of two
integers that multiply out to 36:
1 × 36 = 36 1 + 36 = 37
2 × 18 = 36 2 + 18 = 20
3 × 12 = 36 3 + 12 = 15
4 × 9 = 36 4 + 9 = 13
6 × 6 = 36 6 + 6 = 12
This list of sums includes 12, 13, 15, and 20, but not 18. Thus, no pair of integers both
satisfies the original equation and adds up to 18
correct answer D)18
Question: Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 184 cms. What was the ratio A of men to women?
A. 5:2
B. 5:1
C. 4:3
D. 4:1
Answer: A. 5:2
Explanation: (A) A=184 x 5 + 170 x 2 = 1260.A
Question: Find the arithmetic mean P of all roots of the following equation- see an attachment.
A.2
B.1
C.0.5
D.-1/3
Answer: C.0.5
Explanation: arithmetic mean P your answer C and E are same, can you correct one of them please. thanks.C
Question: The product of two numbers is 336 and the sum of their squares is 289. The sum of the number is?
A.A)23
B.B)25
C.C)27
D.D)31
Answer: D.D)31
Explanation: Let the numbers be x and y.
Then, xy = 336 and x2 + y2 = 289.
(x + y)2 = x2 + y2 + 2xy = 289 + (2 x 336) = 961
x + y =31.
Option D
Question: Jamshid can paint a fence in 50 percent less time than Taimour can when each works alone. When they work together, they can paint the fence in 5 hours. How long would it take Taimour to paint the fence alone?
A.6 hours
B.8 hours
C.15 hours
D.24 hours
Answer: C.15 hours
Explanation: I believe the answer is C. Please see below for explanation.
if Jamshid can paint a dence in 50 percent less time then Taimour we can infer the following rate J = 2T
if working together they can do the job in 8 hours we can infer 1 = 2T+T * 5 => 1/15
Working alone Taimour can do the job in 1 = 1/15* hours => 15
Answer C
Question: Crazy Eddie has a key chain factory. Eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price, and thus increased the profit from the sale of each key chain from 35% of the selling price to 50% of the selling price. If the manufacturing cost is now $50, what was it before the decrease?
A.$20
B.$65
C.$50
D.$80
Answer: B.$65
Explanation: Deargoodyear2013,
I'm happy to help.This is a relatively straightforward problem, not very challenging. BTW,Crazy Eddiewas the actually name of an electronics chain on the East Coast of the USA back in the 1970s.
Manufacturing now is $50. They now are making a 50% profit, so the selling price must be $100.
They had this same selling price, $100, before they made the change, and had a profit of 35%, so the manufacturing must have been $65. Answer = (B).
Question: There are 2 sections A and B in a class, consisting of 50 and 70 students respectively. If the average weight of section A is 50kg and that of section B is 70kg, Find the average of the whole class?
A.50.78kg
B.49.32kg
C.61.67kg
D.69.15kg
Answer: C.61.67kg
Explanation: Total weight of 50+70 students = 50*50 + 70*70 = 7400
Average weight of the class is = 7400/120 = 61.67 kg
Answer is C
Question: The sum of two consecutive numbers is 37. What are they?
A.18 and 19
B.18 and 21
C.18 and 23
D.19 and 20
Answer: A.18 and 19
Explanation: Two consecutive numbers are like 8 and 9, or 51 and 52.
Let x, then, be the first number. Then the number after it is x + 1.
The problem states that their sum is 37:
word problem = 37
2x = 37 − 1
= 36.
x = 36
2
= 18.
The two numbers are 18 and 19.
Option is A
Question: In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/8. For a group of 200 newborn members of the population, approximately how many would be expected to survive the first 3 months of life?
A.134
B.146
C.152
D.162
Answer: A.134
Explanation: The probability of survival for each of the first 3 months of life is 1-1/8= 7/8, so of 200 newborn 200*7/8*7/8*7/8=~134 is expected to survive.
Answer: A.
Question: In a class of 50 students, 20 play Tennis, 15 play Cricket and 11 play Football. 7 play both Tennis and Cricket, 4 play Cricket and Football and 5 play Tennis and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports?
A.10
B.20
C.25
D.30
Answer: A.10
Explanation: {Total}={Hockey}+{Cricket}+{Football}-{HC+CH+HF}+{All three}+{Neither} For more check ADVANCED OVERLAPPING SETS PROBLEMS
50=20+15+11-(7+4+5)+{All three}+18 --> {All three}=2;
Those who play ONLY Hockey and Cricket are 7-2=5;
Those who play ONLY Cricket and Football are 4-2=2;
Those who play ONLY Hockey and Football are 5-2=3;
Hence, 5+2+3=10 students play exactly two of these sports.
{Total}={Hockey}+{Cricket}+{Football}-{HC+CH+HF}+{All three}+{Neither} For more check ADVANCED OVERLAPPING SETS PROBLEMS
50=20+15+11-(7+4+5)+{All three}+18 --> {All three}=2;
Those who play ONLY Hockey and Cricket are 7-2=5;
Those who play ONLY Cricket and Football are 4-2=2;
Those who play ONLY Hockey and Football are 5-2=3;
Hence, 5+2+3=10 students play exactly two of these sports.
Answer A