RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Suppose that 25% of all the wise people are nice and half of all the nice
people are wise. Suppose further that 25% of all the people are neither
wise nor nice. What percent of all the people are both wise and nice?
A.10%
B.15%
C.20%
D.25%
Answer: B.15%
Explanation: Let k be the number of all the people who are both nice and wise. Then, the
number of wise people is 4k and the number of nice people is 2k. The number of people
who are either wise or nice or both is 4k + 2k − k = 5k. If the number of all people is
x, then x − 0.25x = 5k, so x = 20k/3.
correct answer B
Question: A firm has 4 senior partners and 4 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner. (2 groups are considered different if at least one group member is different)
A.40
B.44
C.48
D.52
Answer: D.52
Explanation: The total number of ways to form a group of 3 is 8C3 = 56
The number of groups without a senior partner is 4C3 = 4
The number of groups which include a senior partner is 56-4 = 52
The answer is D.
Question: If you wanted to plant a certain number of flowers, but knew that 1 in 5 would not grow, how many flowers would you need to plant if you want a total of 20?
A.20
B.30
C.28
D.25
Answer: D.25
Explanation: 20 / (5-1) = 5
5 * 5 = 25
25 - (5-1) = 20
The correct answer is D
Question: The average of 10 numbers is calculated as 15. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
A.10
B.13
C.16
D.18
Answer: C.16
Explanation: Explanation:
10 * 15 + 36 – 26 = 160/10 = 16
C)
Question: [1+(1/5)]^n=2?
What is the value of n?
A.1.999
B.2.999
C.3.88
D.4.88
Answer: C.3.88
Explanation: 1+1/5 = 6/5 = 1.2
1.2*1.2 = 1.44 *1.2 = 1.728 *1.2 = 2.0736
so if N is integer, N=4. if not, N = 3.8
(1.2)^3.8 = 1.999
ANSWER:C
Question: If x, y, and s are positive numbers such that 10*x/(x+y)+ 20*y/(x+y)=s and if x is less than y, which of the following could be the value of s?
A.10
B.12
C.15
D.18
Answer: D.18
Explanation: Answer choice C: s= 15
(10x + 20y)/(x+y) = 15
10x + 20y = 15x + 15y
5y = 5x
y = x
Doesn't work because the problem states that x<y.
We need y to be larger, so let's try answer choice D: s=18
10x + 20y = 18x + 18y
2y = 8x
y/x = 8/2
Success! x<y.
The correct answer is D.
Question: The sum of the first five terms of a G.P is 363. If the common ratio is 1/3 find the first term.
A.323
B.243
C.232
D.332
Answer: B.243
Explanation: Sum of the first n terms of a G.P = a (1 -rn )/1 - r ,
a [ 1 - (1/3) 5 ]/ (1 - 1/3) = 363
a = 363 [ 1-1/3 ] /1- (1/3) 5 = ( 363* 2/3) / ( 1- 1/242 ) = 242/ ( 242/243 )
a = 243
ANSWER:B
Question: If an object travels 200 feet in 4 seconds, what is the object's approximate speed in miles per hour? (Note: 1 mile = 5280 feet)
A.36
B.34
C.356
D.12
Answer: B.34
Explanation: 1 mile = 5280 feet
=> 1 feet = 1/5280 miles
If the object travels 200 feet in 4 sec
then it travels 200/4 * 60 * 60 feet in 1 hour (1 hr = 60 min * 60 sec)
= 3600 * 50 feet in 1 hour
= 180000 feet in 1 hr
= 180000/5280 miles in 1 hour
= 18000/528 miles/hr ~ 34 miles/hr
Answer - B
Question: In a certain country 1/7 of 8 = 5. Assuming the same proportion, what would be the value of 1/5 of 40 ?
A.54
B.25
C.45
D.35
Answer: D.35
Explanation: D
35
Question: A scuba diver descends at a rate of 80 feet per minute. a diver dive from a ship to search for a lost ship at the depth of 4000feet below the sea level..how long will he take to reach the ship?
A.70 minutes
B.72 minutes
C.50 minutes
D.66 minutes
Answer: C.50 minutes
Explanation: Time taken to reach = 4000/80= 50 minutes
ANSWER:C
Question: A boy rides his bicycle 10 km at an average speed of 12 km/hr and again travels 12 km at an average speed of 10 km/hr. His average speed for the entire trip is approximately?
A.10.8 km/hr
B.12.8 km/hr
C.11.8 km/hr
D.16.8 km/hr
Answer: A.10.8 km/hr
Explanation: A
10.8 km/hr
Total distance traveled = 10 + 12 = 22 km /hr.
Total time taken = 10/12 + 12/10 = 61/30 hrs.
Average speed = 22 * 30/61 = 10.8 km/hr.
Question: If one root of the equation 2x^2 + 3x – k = 0 is 5, what is the value of k?
A.65
B.79
C.68
D.87
Answer: A.65
Explanation: We just enter this root into the equation in order to recieve an equation to find the answer!
2*5^2+3*5-k=0
k=50+15=65
The answer is A
Question: For 600 km journey it will take 8hrs, if 120 km is done by bus and the rest by car. It takes 20 minutes more, if 200 km is done by busand the rest by car. The ratio of the speed of the train to that of the cars is?
A.1 : 3
B.3 : 4
C.1 : 6
D.2 : 7
Answer: B.3 : 4
Explanation: Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120 + 480 = 8 1 + 4 = 1 ....(i)
x y x y 15
And, 200 + 400 = 25 1 + 2 = 1 ....(ii)
x y 3 x y 24
Solving (i) and (ii), we get: x = 60 and y = 80.
Ratio of speeds = 60 : 80 = 3 : 4
B
Question: Three walls have wallpaper covering a combined area of 300 square meters. By overlapping the wallpaper to cover a wall with an area of 180 square meters, the area that is covered by exactly two layers of wallpaper is 34 square meters. What is the area that is covered with three layers of wallpaper?
A.43 Square Meters
B.36 Square Meters
C.42 Square Meters
D.83.3 Square Meters
Answer: A.43 Square Meters
Explanation: 300 - 180 = 120 sq m of the wallpaper overlaps (in either two layers or three layers)
If 36 sq m has two layers, 120 - 34 = 86 sq m of the wallpaper overlaps in three layers. 86 sq m makes two extra layers hence the area over which it makes two extra layers is 43 sq m.
Answer (A).
Question: One hour after Sid started walking the 60 miles from X to Y, James started walking from X to Y as well. Sid walks 3 miles per hour and James walks 1 mile per hour faster than Sid . How far from X will James be when he catches up to Sid ?
A.8 miles
B.9 miles
C.12 miles
D.11 miles
Answer: C.12 miles
Explanation: First, determine how far Sid has walked in the one hour. he has walked three miles which means he is three miles ahead of James when he sets off. James walks at four miles/hour which means that every hour, james will get one mile closer to Sid . If he gets one mile closer every hour, it will take him three hours to catch up to him which means he travels 3hours * 4 miles/hour = 12 miles and he travels 4 hours * 3 miles/hour = 12 miles. He will be 12 miles from X when he catches up to her.
A slightly different way to solve...
We don't know how long they will walk before they catch up to one another but we do know that A walks for one hour more than J. J = T and A = T+1. We are looking for the distance at which they meet up which means the distance will be the same. D=r*t so,
r*t (james) = r*t (Sid )
r*(t) = r*(t+1)
4t = 3t+3
t=3
d=r*t
d=4*3
d=12
C) 12 miles
Question: The price of 2 sarees and 4 shirts is $1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?
A.3800
B.3300
C.2400
D.4200
Answer: C.2400
Explanation: C
$2400
Let the price of a saree and a shirt be $x and $y respectively.
Then, 2x + 4y = 1600 .... (i)
and x + 6y = 1600 .... (ii)
Divide equation (i) by 2, we get the below equation.
=> x + 2y = 800. --- (iii)
Now subtract (iii) from (ii)
x + 6y = 1600 (-)
x + 2y = 800
----------------
4y = 800
----------------
Therefore, y = 200.
Now apply value of y in (iii)
=> x + 2 x 200 = 800
=> x + 400 = 800
Therefore x = 400
Solving (i) and (ii) we get x = 400, y = 200.
Cost of 12 shirts = $(12 x 200) = $2400.
Question: If doubling a number and adding 20 to the result gives the same answer as multiplying the number by 8 and taking away 4 from the product, the number is
A.2
B.3
C.4
D.6
Answer: C.4
Explanation: Solution
Let the number be x.	= Then, 2x+20 = 8x–4
= 6x = 24
‹=›x = 4.
Answer C
Question: Indu gave Bindu Rs.6500 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
A.12.8
B.20
C.10.4
D.11.6
Answer: C.10.4
Explanation: 6500 = D(100/4)2
D = 10.4
Answer: C
Question: Anand and Deepak started a business investing Rs. 27,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is?
A.7728
B.2888
C.8400
D.2882
Answer: A.7728
Explanation: Ratio of their shares = 27500 : 35000 = 11:14
Deepak's share = 13800 * 14/25 = Rs. 7728.
Answer: A
Question: A math teacher has 27 cards, each of which is in the shape of a geometric figure. Half of the cards are rectangles, and a third of the cards are rhombuses. If 8 cards are squares, what is the maximum possible number of cards that re circles.
A.9
B.10
C.11
D.12
Answer: B.10
Explanation: a square is a special kind of rhombus (sides are perpendicular)
a square is a special kind of rectangles (sides with same length)
Among the 27 cards with have:
15 rectangles
10 rhombus
8 squares
Among the 15 rectangles, there could be 8 special ones (with sides of same length) that are squares. That lets at least 7 rectangles that are not square.
Among the 10 rectangles, there could be 8 special ones (with sides perpendicular) that are squares. That lets at least 2 rhombus that are not square.
We have 8 squares.
So the minimum different cards that represent a square, a rhombus or a rectangle is 2 + 7 + 8 = 17
Which means that the maximum number of circles that you could have is 27 - 17 = 10
Answer (B)
Question: Dexter was born between October 6th and 10th (6th and 10th excluding). His year of birth is also known. What is the probability of Dexter being born on a Saturday?
A.0 or 1/3
B.1/7 or 3/7
C.1/3 or 1/7
D.1/3 or 1/4
Answer: A.0 or 1/3
Explanation: Explanation :
Since the year of birth is known, the birthday being on Saturday can have a zero probability.
Also since between 6th and 10th, there are three days i.e. 7th,8th and 9th.
Therefore, probability of birthday falling on Saturday can be 1/3.
Answer : A
Question: A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?
A.177
B.199
C.800
D.171
Answer: C.800
Explanation: 25 = E/(1000 - E) * 100
1000 - E = 4E
1000 = 5E => E = 200
1000 - 200 = 800
Answer: C
Question: From a group of boys and girls, 15 girls leave. They are then left 2 boys for each girl. After this, 72 boys leave. There are then 5 girls for each boy. Find the number of girls in the beginning
A.20
B.10
C.30
D.55
Answer: D.55
Explanation: Assume the number of boys at present = x
Then, the number of girls at present = 5x
Before the boys left, the number of boys were (x+72) and number of girls were 5x
Hence, 2(5x) = x + 72
=> 10x = x + 72
=> x = 8
Number of girls in the beginning = (5x + 15) = (5×8 + 15) = 55
Answer is D.
Question: When positive integer N is divided by positive integer J, the remainder is 27. If N/J = 204.09, what is value of J?
A.300
B.320
C.360
D.410
Answer: A.300
Explanation: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 204.09
Here 204 is the quotient.
Given that Remainder = 27
So, 204.09= 204 + 27/J
So, J = 300
Answer: A
Question: The length of a train and that of a platform are equal. If with a speed of 180 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
A.1500
B.266
C.299
D.750
Answer: A.1500
Explanation: Speed = [180 * 5/18] m/sec = 50 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 50 => x = 50 * 60 / 2 = 1500
Answer: A
Question: If you drew a dot on the edge of a wheel and traced the path of the dot as the wheel rolled one complete revolution along a line, then the path formed would be called a cycloid, combining both forward and circular motion. What is the length of the path formed by one complete revolution? Assume the wheel has a radius of r.
A.8r
B.4r
C.9r
D.7r
Answer: A.8r
Explanation: Hint: (1-cos(t))0.5 = 20.5×sin(t/2)
The answer is 8r.
Imagine the circle resting on coordinate (0,0) and moving east.
Also magine the point on the circle to start at (0,0).
Let t be the angle between the point on the circle and the center of the circle.
The position of the point on the circle, relative to t, is:
x = rt - r×sin(t)
y = r - r×cos(t)
Taking the derivatives:
dx/dt = r - r×cos(t)
dy/dt = r×sin(t)
The change in arc length can be defined as ( (dx/dt)2 + (dy/dt)2 ) 1/2.
So the total arc length is the integral from 0 to 2pi of ( (dx/dt)2 + (dy/dt)2 ) 1/2.
After a few steps this integral becomes:
r×21/2 × (1-cos(t))1/2.
Using the hint:
r×21/2 × 21/2 × integral of sin(t/2) dt from 0 to 2×pi
= 2×r × (-2×cos(t/w) from 2×pi to 0)
= 8r
correct answer A
Question: Seven 6 faced dice are thrown together. The probability that all the three show the same number on them is?
A.1/32
B.1/46656
C.1/33
D.1/38
Answer: B.1/46656
Explanation: The three dice can fall in 6 * 6 * 6 * 6 * 6 * 6 * 6 = 279936 ways.
Hence the probability is 6/279936
= 1/46656
Answer: B
Question: In a hostel there were 100 students. 20 students left the hostel,the average budget is increased by rupees 10. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?
A.2200
B.1660
C.5400
D.2400
Answer: D.2400
Explanation: Let average is x
100x + 400 = 80(x+10)
x = 20
100 * 20 + 400 = 2400
Answer:D
Question: man can row upstream at 30 kmph and downstream at 40 kmph, and then find the speed of the man in still water?
A.30
B.35
C.40
D.70
Answer: B.35
Explanation: US = 30
DS = 40
M = (30 + 40)/2
= 35
Answer:B
Question: Find the odd man out
6, 13, 29, 61, 125, 253, 509
A.6
B.13
C.29
D.125
Answer: A.6
Explanation: 1*2+3 = 5
5*2+3 = 13
13*2+3 = 29
29*2+3 = 61
61*2+3 = 125
125*2+3 = 253
253*2+3= 509
ANSWER:A
Question: The equation of line a is y = 4/3*x - 100. What is the smallest possible distance in the xy-plane from the point with coordinates (0, 0) to any point on line a?
A.48
B.50
C.60
D.75
Answer: C.60
Explanation: This can be solve in two steps and without any complex calculation.
Given : equation of line a as y=(4/3)x -100. So the line intercept the axes at (0,-100) and (75,0).
This can be considered a right angle triangle with right angle at (0,0) . So Base=100 , Height=75 and Hypotenuse =125 (By Pythagoras triplet)
So a perpendicular from the (0,0) to hypotenuse will be the answer.
Area of triangle= 0.5*100*75=0.5*125* x
=> x=60;
SO answer is 60=C
Question: A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 2, 4 and 6, which can be repeated. If the product of the digits in the area code must be even, how many different codes can be created?
A.27
B.22
C.24
D.26
Answer: A.27
Explanation: Total # of codes possible is 3*3*3 = 27. Oit of those 27 codes
Answer: A
Question: Insert the missing number.
8, 7, 11, 12, 14, 17, (....)
A.27
B.20
C.22
D.17
Answer: D.17
Explanation: There are two series (8, 11, 14, 17) and (7, 12, 17) increasing by 3 and 5 respectively.
answer : D
Question: From a group of boys and girls, 15 girls leave. They are then left 2 boys for each girl. After this, 63 boys leave. There are then 5 girls for each boy. Find the number of girls in the beginning
A.20
B.10
C.30
D.50
Answer: D.50
Explanation: Assume the number of boys at present = x
Then, the number of girls at present = 5x
Before the boys left, the number of boys were (x+63) and number of girls were 5x
Hence, 2(5x) = x + 63
=> 10x = x + 63
=> x = 7
Number of girls in the beginning = (5x + 15) = (5×7 + 15) = 50
Answer is D.
Question: Six students are equally divided into 3 groups, then, the three groups were assigned to three different topics. How many different arrangements R are possible?
A. 30
B. 60
C. 90
D. 180
Answer: C. 90
Explanation: 90 is the number of ways you can assign 3 teams formed out of 12 people to 3 different tasks.
But now you can order the 3 tasks in 3! ways. T1 T2 T3 or T2 T1 T3.... etc etc.
I was confused between 90 and 540 but since question used the wordarrangementsdecided to go with complete arrangements R INCLUDING the order of tasks.
could you explain the highlighted step... i'm getting 90 = 15 * 3!
suppose the students are numbered 1,2,3,4,5,6 and tasks are X,Y and Z
one of the 15 possible ways of forming teams is 12, 34, 56. these teams can be assigned to 3 tasks in 3! = 6 ways
X--	Y--	Z
12--	34--	56
12--	56--	34
34--	12--	56
34--	56--	12
56--	12--	34
56--	34--	12
so the answer should be 15*6 = 90
But now you can fruther decide which task you want to perform first X Y or Z..C
Question: How many no.'s with 3 different digits, 2, 3, 5, 6, 7 and 9, which are divisible by 5?
A.10
B.20
C.40
D.35
Answer: B.20
Explanation: Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.
The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place.
The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.
Required number of numbers = (1 x 5 x 4) = 20
B
Question: Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
A.375
B.400
C.450
D.350
Answer: A.375
Explanation: A+B+C = 1500
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1500 => 375
ANSWER A
Question: If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
A.288
B.162
C.878
D.168
Answer: B.162
Explanation: 12 m/s = 12 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 12 * 18/5 * 15/4 km = 162 km.
Answer: B
Question: If 10 crates have 96 apples each and how many apples more is required in order to make 100 apples in each crate?
A.5
B.10
C.40
D.20
Answer: C.40
Explanation: Each crate requires 4 apples and totally there are 10 crates so required apples = 10 * 4 = 40
Answer: C
Question: 85% of a number is added to 24, the result is the same number. Find the number?
A.277
B.267
C.222
D.160
Answer: D.160
Explanation: (85/100) * X + 24 = X
3X = 480
X = 160
Answer:D
Question: If the sides of a rectangle are increased by 35%, what is the percentage increase in the area?
A.38.25%
B.40.25%
C.82.25%
D.50%
Answer: C.82.25%
Explanation: If sides are a and b, after increase sides would be 1.35a and 1.35 b.
Percentage increase in area = (1.35a*1.35b - ab) *100/ab = 82.25
Answer : C
Question: The average weight of 10 person's increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
A.100 kg
B.102.5 kg
C.85 kg
D.Data inadequate
Answer: A.100 kg
Explanation: Explanation:
Total weight increased = (10 x 3.5) kg = 35 kg.
Weight of new person = (65 + 35) kg = 100 kg.
Answer: A
Question: Equal amount of water were poured into two empty jars of different capacities, which made one jar 1/6 full and other jar 1/5 full. If the water in the jar with lesser capacity is then poured into the jar with greater capacity, what fraction of the larger jar will be filled with water?
A.1/7
B.2/7
C.1/3
D.7/12
Answer: C.1/3
Explanation: Same amount of water made bigger jar 1/6 full, thenthe same amount of water(stored for a while in smaller jar) were added to bigger jar, so bigger jar is 1/6+1/6=2/6= 1/3 full.
Answer: C.
Question: The difference between the value of a number increased by 12.5% and the value of the original number decreased by 25% is 30. What is the original number?
A.60
B.80
C.40
D.120
Answer: B.80
Explanation: Explanatory Answer
Let the original number be x.
Let A be the value obtained when x is increased by 12.5%.
Therefore, A = x + 12.5% of x
Let B be the value obtained when x is decreased by 25%.
Therefore, B = x - 25% of x
The question states that A - B = 30
i.e., x + 12.5% of x - (x - 25% of x) = 30
x + 12.5% of x - x + 25% of x = 30
37.5% of x = 30
x = 30/37.5*100 = 80
The correct choice is (B)
Question: A person saved $10 in buying an item on sale. If he spent $100 for the item, approximately how much percent he saved in the transaction?
A.8%
B.10%
C.2%
D.5%
Answer: B.10%
Explanation: Actual price = 100+10 = $110
Saving = 10/110 * 100 = 100/11 =10% approximately
Answer is B
Question: If a tire rotates at 400 revolutions per minute when the car is traveling 72km/h, what is the circumference of the tire?
A.2 meters
B.6 meters
C.5 meters
D.3 meters
Answer: D.3 meters
Explanation: 400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 72,000 m : C is the circumference
C = 3 meters
correct answer D
Question: In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
A.159
B.194
C.205
D.209
Answer: D.209
Explanation: We may have 1 boy and 3 girls or 2 boys and 2 girls or 3 boys and 1 girl or 4 boys
Required number of ways = (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + 6C4
= (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + 6C2
= (6 x 4) +[(6x5)/(2x1) x (4x3)/(2x1)] + [(6x5x4)/(3x2x1)) x 4] +[(6x5)/(2x1)]
= 24 + 90 + 80 + 15 = 209
Answer D.
Question: A man sold two chairs at Rs. 1,200 each. On one he gained 20% and on the other he lost 20%. His gain or loss in the whole transaction is:
A.1% loss
B.2% loss
C.4% loss
D.15 gain
Answer: C.4% loss
Explanation: Solution: In the case where loss and gain percentage is common on same selling price, always a loss incurs in total deal. And this can be calculated by a short-cut:
Loss on total deal,
= (Common loss or gain percentage /10)2 = (20/10)2
= 4%
Alternatively, It can be also calculated through Graphic Change Method: This can be given by,
100==20% gain ==>120==20% loss==>96.
Loss = 4% (As 100 became 96).
Answer: Option C
Question: A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?
A.277
B.276
C.800
D.271
Answer: C.800
Explanation: 25 = E/(1000 - E) * 100
1000 - E = 4E
1000 = 5E => E = 200
1000 - 200 = 800
Answer: C
Question: C and D start a business with Rs.4000 and Rs.10000 respectively. Hoe should they share their profits at the end of one year?
A.5:2
B.2:5
C.5:3
D.3:5
Answer: B.2:5
Explanation: They should share the profits in the ratio of their investments.
The ratio of the investments made by C and D =
4000 : 10000 => 2:5 .
Answer:B
Question: What is the area inscribed by the lines y = 10, x = 1, y = 3x+1 on an xy-coordinate plane?
A.a) 1
B.b) 2
C.c) 3
D.d) 6
Answer: D.d) 6
Explanation: First, let's graph the lines y = 10 and x = 1
At this point, we need to find the points where the line y = 3x+1 INTERSECTS the other two lines.
For the vertical line, we know that x = 1, so we'll PLUG x = 1 into the equation y = 3x+1 to get y = 3(1)+1 = 4
Perfect, when x = 1, y = 5, so one point of intersection is (1,4)
For the horizontal line, we know that y = 10, so we'll PLUG y = 10 into the equation y = 3x+1 to get 10 = 3x+1. Solve to get: x = 3
So, when y = 10, x = 3, so one point of intersection is (3,10)
Now add these points to our graph and sketch the line y = 3x+1
At this point, we can see that we have the following triangle.
The base has length 2 and the height is 6
Area = (1/2)(base)(height)
= (1/2)(2)(6)
= 6
Answer:
D
Question: The perimeters of two squares are 40 cm and 28 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares .
A.22 cm
B.28.4 cm
C.26 cm
D.28 cm
Answer: B.28.4 cm
Explanation: Explanation:
We know perimeter of square = 4(side)
So Side of first square = 40/4 = 10 cm
Side of second square = 28/4 = 7 cm
Area of third Square = 10*10 - 7*7
= 51 cm
So side of third square = 7.1 [because area of square = side*side]
Perimeter = 4*Side = 4*7.1 = 28.4 cm
Answer: Option B