RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Elvin's monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for Internet service. Elvin's total telephone bill for January was $40 and Elvin's total telephone bill for February was 76$. If Elvin's charge for the calls he made in February was twice the charge for the calls he made in January, what is Elvin's fixed monthly charge for Internet service?
A.$5
B.$10
C.$14
D.$4
Answer: D.$4
Explanation: Bill = Fixed Charge + Charge of Calls made
in Jan, Bill = Fixed Charge(Let, y) + Charge of calls made in Jan (Let, x) = $40
in Feb, Bill = Fixed Charge (Let, y) + Charge of calls made in Feb (Then, 2x) = $76
i.e. x+y = 40
and 2x+y = 76
Take the difference if two equations
i.e. (2x+y) - (x+y) = 76 - 40
i.e. x = 36
i.e. Fixed Monthly Charge, y = 4
Answer: Option
D
Question: On sport’s day, if 12 children were made to stand in each column, 98 columns could be formed. If 24 children were made to stand in a column, how many columns could be formed ? After a certain music being played the plan was that the children have to stand in concentric circles such that the innermost circle will have one student, the next circle will have two students, the third circle will have 3 students and so on. How many circles will be formed in this manner.
A.48
B.20
C.50
D.29
Answer: A.48
Explanation: no of students will be 98*12=1176
let us consider n circles then 1+2+3+....+n=1176
n(n+1)/2=1176
n=48 circles
ANSWER:A
Question: How many 5 no. digit no. can be formed with digits 1,2,3,4,5,6 which are divisible by 4 and digits not repeated
A.144
B.168
C.192
D.186
Answer: C.192
Explanation: last 2 digits can be 12,16,24,32,36,52,56,64.
so total possible 5 digit numbers = 8*4*3*2= 192 numbers
ANSWER:C
Question: If log3N+log9Nlog3N+log9N is whole number, then how many numbers possible for N between 100 to 100?
A.1, 9, 81
B.1, 9, 89
C.1, 9, 88
D.1, 9, 22
Answer: A.1, 9, 81
Explanation: log3N+log9Nlog3N+log9N = log3N+log32Nlog3N+log32N = log3N+12log3Nlog3N+12log3N =32log3N32log3N
Now this value should be whole number.
Let 32log3N32log3N = w
⇒log3N=23w⇒log3N=23w
N=3(23w)N=3(23w)
As N is a positive integer, So for w = 0, 3, 6 we get N = 1, 9, 81.
Answer:A
Question: The number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is
A.33
B.278
C.75
D.978
Answer: C.75
Explanation: Explanation:
The hour hand moves from pointing to 12 to pointing to half way between 2 and 3. The angle covered between each hour marking on the clock is 360/12 = 30. Since the hand has covered 2.5 of these divisions the angle moved through is 75.
Answer: C) 75
Question: 6000, 1200, 300, 60...
A.30
B.15
C.20
D.36
Answer: B.15
Explanation: 6000/5=1200
1200/4=300
300/5=60
60/4=15
ANSWER:B
Question: A walks with a speed of 6 km/hr and after 5 hr of his start, B starts running towards A at a speed of 8 km/hr. At what distance from start will B catch A.
A.100
B.110
C.120
D.140
Answer: C.120
Explanation: In 5hrs, A will cover 30 km. Now, at some distance ‘x’. So A will cover X distance and B will cover 30 + X.x/6 = (30+x)/8x = 90. So distance from start after which B will catch A = 90+30 =120km Answer : C
Question: The surface of a cube is 150sq cm. Find its volume?
A.8cc
B.9cc
C.125cc
D.4cc
Answer: C.125cc
Explanation: 6a2 = 150 = 6*25
a = 5 => a3 = 125cc
Answer: C
Question: The sum of four consecutive even numbers is 292. What would be the smallest number?
A.22
B.27
C.70
D.28
Answer: C.70
Explanation: Explanation:
Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1)
Their sum = 8x - 4 = 292 => x = 37
Smallest number is: 2(x - 2) = 70.
Answer: C
Question: The present population of a town is 3456. Population increase rate is 20% p.a. Find the population of town before 2 years?
A.2400
B.2100
C.3500
D.3600
Answer: A.2400
Explanation: P = 3456
R = 20%
Required population of town = P/(1 + R/100)^T
= 3456/(1 + 20/100)^2
= 3456/(6/5)^2
= 2400(approximately)
Answer is A
Question: Average of 10 matches is 32, How many runs one should should score to increase his average by 3 runs.
A.A)65
B.B)76
C.C)78
D.D)80
Answer: A.A)65
Explanation: Explanation:
Average after 11 innings should be 35
So, Required score = (11 * 35) - (10 * 32)
= 385 - 320 = 65
Answer: Option A
Question: Walking 4/3 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?
A.22
B.16
C.27
D.28
Answer: B.16
Explanation: Speed Ratio = 1:4/3 = 3:4
Time Ratio = 4:3
1 -------- 4
4 --------- ? 16 m.Answer:B
Question: The population of a town increases by 12% during first year and decreased by 10% during second year. If the present population is 50,400, what it was 2 years ago?
A.40,000
B.35,000
C.50,000
D.60,000
Answer: C.50,000
Explanation: Here A = 50400, x = 12, y = - 10
Therefore, the population 2 years ago
= A /[( 1 + x/100) ( 1 + y/100)]
= 50400 / [( 1 + 12/100) ( 1 - 10/100)]
= (50400 x 100 x 100) / (112 x 90)
= 50,000.
ANSWER:C
Question: A bag contains 10 red jellybeans and 10 blue jellybeans. If 3 jellybeans are removed one at a time, at random and are not replaced, what is the probability Y that all 3 jellybeans removed from the bag are blue?
A.9/100
B.2/19
C.1/8
D.3/20
Answer: B.2/19
Explanation: Method-1
10 red jellybeans and 10 blue jellybeans
Total Outcomes = No. of ways to choose 3 Jelly bean at random out of a total 20 jellybeans = 20C3 = 1140
Favourable Outcomes = No. of ways to choose 3 Jelly bean such that they are all Blue out of 10 Blue = 10C3 = 120
Probability = Favourable Outcomes / Total Outcomes = 10C3 / 20C3
Probability Y= 120 / 1140 = 2/19
Answer: option B
Method-2
Probability of First jelly bean to be Blue = 10/20 [Total 10 Blue out of total 20 jellybeans]
Probability of Second jelly bean to be Blue = 9/19 [Total 9 Blue remaining out of total 19 jellybeans remaining]
Probability of Third jelly bean to be Blue = 8/18 [Total 8 Blue remaining out of total 18 jellybeans remaining]
Required Probability = (10/20)*(9/19)*(8/18) = 2/19
Answer: option B
Question: Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.140. How much was lent at 5%?
A.1500
B.1300
C.1200
D.1000
Answer: D.1000
Explanation: (x*5*1)/100 + [(2500 - x)*6*1]/100 = 140
X = 1000
ANSWER D
Question: An express traveled at an average speed of 100 km/hr, stopping for 3 min after every 75 kn. How long did it take to reach its destination 600 km from the starting point?
A.6 hrs 21 min
B.6 hrs 71 min
C.6 hrs 32 min
D.6 hrs 27 min
Answer: A.6 hrs 21 min
Explanation: Time taken to cover 600 km = 600/100 = 6 hrs.
Number of stoppages = 600/75 - 1 = 7
Total time of stoppages = 3 * 7 = 21 min
Hence, total time taken = 6 hrs 21 min.
Answer:A
Question: Bert left the house with N dollars. He spent 1/3 of this at the hardware store, then $7 at the dry cleaners, and then half of what was left at the grocery store. When he got home, he had $10.50 left in his pocket. What was the value of N?
A.$42
B.$44
C.$52
D.$60
Answer: A.$42
Explanation: started to test answer A
if he had 42, then he spent 13 2/3 at hardware store
now he was left with 27 1/3$
he spent 7 dollars on cleaning, thus he remained with 20 1/3$
he then spent 1/2 of 20 1/3 or 10.5,
hence,right OPTION is A.
Question: The average weight of 49 students in a class is 52 kg. 5 of them whose average weight is 48 kg leave the class and other 5 students whose average weight is 54 kg join the class. What is the new average weight (in kg) of the class ?
A.51 1⁄3
B.52 30/49
C.52 1⁄49
D.43.42
Answer: B.52 30/49
Explanation: Total weight of 49 students
= 49 × 52 = 2548 kg
Total weight of 5 students who leave
= 5 × 48 = 240 kg
Total weight of 5 students who join
= 5 × 54 = 270 kg
Therefore, new total weight of 49 students
= 2548 – 240 + 270 = 2578
⇒ New average weight = 2578⁄49 = 52 30/49 kg
Answer B
Question: Seven children â€” A, B, C, D, E, F, and G â€” are going to sit in seven chairs in a row. Child A has to sit next to both B & G, with these two children immediately adjacent to here on either side. The other four children can sit in any order in any of the remaining seats. How many possible configurations are there for the children?
A.240
B.480
C.720
D.1440
Answer: A.240
Explanation: There are five different â€œthree in a rowâ€ locations for these three children. Now, for any given triplet of seats, we know A has to be in the middle, so the children could be seated B-A-G or G-A-B â€” just those two orders. This means the total number of configurations for these three children is 5*2 = 10.
Now, consider the non-restricted elements, the other four. Once A & B & G are seated, the remaining four children can be seated in any order among the remaining four seats â€” thatâ€™s a permutation of the 4 items â€”- 4P4 = 4! = 24. For any single configuration of A & B & G, there are 24 ways that the other children could be seated in the remaining seats.
Finally, weâ€™ll combine with the Fundamental Counting Principle. We have 10 ways for the first three, and 24 ways for the remaining four. Thatâ€™s a total number of configurations of 24*10 = 240. Answer = A
Question: Four different objects 1, 2, 3, 4 are distributed at random in four places marked 1, 2, 3, 4. What is the probability that none of the objects occupy the place corresponding to its number?
A.6/3
B.3/8
C.1/2
D.5/8
Answer: B.3/8
Explanation: There are 4! i.e. 24 ways in which four objects can be arranged in four places. There are a total of 9 instances where the objects are not occupying the place corresponding to the given number. They are as follows:
(2, 1, 4, 3) (2, 3, 4, 1) (2, 4, 1, 3) (3, 1, 4, 2) (3, 4, 1, 2) (3, 4, 2, 1) (4, 1, 2, 3) (4, 3, 1, 2) (4, 3, 2, 1)
Hence, the required probability = 9/24 = 3/8.
ANSWER:B
Question: In order to fulfill a local school’s request for x cakes, a parents agreed to each bake an equal number of cakes. If p of the parents did not bake any cakes, which of the following represents the additional number of cakes that each of the other parents had to bake in order for the school’s request for x cakes to be fulfilled?
A.px/a
B.px/(a(a-p))
C.px
D.pxa
Answer: B.px/(a(a-p))
Explanation: No of cakes each parent has to bake : x/a
No of parents did not bake cake = p
No of cakes that were not baked by p parents = p*x/a
No of parents has to bake additional cakes = a-p
additional number of cakes that each of the other parents had to bake in order for the school’s request for x cakes = px/(a(a - p))
Answer B
Question: Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes 10 km/hr downstream and 4 km/hr upstream.
A.7 kmph
B.8 kmph
C.9 kmph
D.7 kmph
Answer: A.7 kmph
Explanation: Speed in still water = (10 + 4)1/2 kmph = 7 kmph.
answer :A
Question: Let f(x) = x^2 + bx + c. If f(6) = 0 and f(-2) = 0, then b + c =
A.18
B.15
C.-16
D.-21
Answer: C.-16
Explanation: f(x) = x^2 + bx + c. If f(6) = 0 and f(-2) = 0, then b + c =
f(6) = 0= 36+6b+c--- Taking 36 to the other side
-> 6b+c= -36
f(-2) =0= 4-2b+c --- taking -2b+c to the other side
-> 2b-c=4
When we add these 2 equations, we get 8b= -32---> b= -4
And while substituting b= -4 we get c= -12.
b+c= -16--- Answer C
Question: A bus started its journey from Mumbai and reached Pune in 44min with its average speed of 50 km/hr. If the average speed of the bus is increased by 5km/hr, how much time will it take to cover the same distance?
A.20 min
B.30 min
C.45 min
D.40 min
Answer: D.40 min
Explanation: Sol. Distance between Ramgarh and Devgarh =(50*44)/60=110/3
Average speed of the bus is increased by 5 km/hr then the
speed of the bus = 55 km/hr
Required time = 110/3*60/55 = 40 min
D
Question: The last time Rahul bought Diwali cards, he found that the four types of cards that he liked were priced Rs.9.00, Rs.7.00, Rs.4.50 and Rs.5.50 each. As Rahul wanted 30 cards, he took five each of two kinds and ten each of the other two, putting down the exact number of 20 rupees notes on the counter payment. How many notes did Rahul give?
A.8
B.9
C.10
D.9
Answer: D.9
Explanation: Explanation :
Let the four cards be a, b ,c and d. 'x' be the number of notes.
Then, according to the question,
=> 5a + 5b + 10c + 10d = 20*x.
=> a + b + 2(c+d) = 4 * x . -----------------------------(i)
Since, a + b = 9+7 = 16
And,
=> c + d = 4.50+5.50= 10 .
Putting these values in (i), we get :-
=> 16 + 2 *10 = 4 * x.
=> x = 9 .
Answer : D
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.76 less, he could have gained 25%. What is the cost price?
A.s.380
B.s.375
C.s.375
D.s.350
Answer: A.s.380
Explanation: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
76 ----- ? => 380
ANSWER:A
Question: If the price of petrol increases by 25% and Raj intends to spend only an additional 15% on petrol, by how much will he reduce the quantity of petrol purchased?
A.10%
B.12%
C.8%
D.16%
Answer: C.8%
Explanation: Explanation :
Let the price of 1 litre of petrol be Rs. x and let Raj initially buys 'y' litres of petrol.
Therefore, he would have spent Rs. xy on petrol.
When the price of petrol increases by 25%, the new price per litre of petrol is 1.25x.
Raj intends to increase the amount he spends on petrol by 15%.
i.e., he is willing to spend xy+15% of xy=1.15xy.
Let, the new quantity of petrol that he can get be 'q'.
Then, 1.25x × q=1.15xy.
=>q=1.15xy/1.25x.
=>0.92y.
As the new quantity that he can buy is 0.92y, he gets 0.08y lesser than what he used to get earlier i.e a reduction of 8%.
Answer : C
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.210
B.209
C.212
D.211
Answer: B.209
Explanation: In a group of 6 boys and 4 girls, four children are to be selected such that at least one boy should be there.
Hence we have 4 options as given below
We can select 4 boys ...(option 1)
Number of ways to this = 6C4
We can select 3 boys and 1 girl ...(option 2)
Number of ways to this = 6C3 × 4C1
We can select 2 boys and 2 girls ...(option 3)
Number of ways to this = 6C2 × 4C2
We can select 1 boy and 3 girls ...(option 4)
Number of ways to this = 6C1 × 4C3
Total number of ways
= 6C4 + 6C3 × 4C1 + 6C2 × 4C2 + 6C1 × 4C3
= 6C2 + 6C3 × 4C1 + 6C2 × 4C2 + 6C1 × 4C1[∵ nCr = nC(n-r)]
= 15 + 80 + 90 + 24
= 209
B
Question: At Didymus Corporation, there are just two classes of employees: silver and gold. The average salary of gold employees is $50,000 higher than that of silver employees. If there are 120 silver employees and 160 gold employees, then the average salary for the company is how much higher than the average salary for the silver employees?
A.$24,000
B.$28,000
C.$32,000
D.$36,000
Answer: B.$28,000
Explanation: The answer should be -> B. $28,000
Question: In how many ways can a Chief Minister and a Vice Minister be elected from a team of 10 members?
A.80
B.90
C.100
D.110
Answer: B.90
Explanation: There are 10 choices for the Chief Minister.
Then there are 9 choices for the Vice Minister.
The total number of ways is 10*9 = 90.
The answer is B.
Question: 250% of x is increased by 250% to become 30 . what is the value of x?
A.3.42
B.3.6
C.4.6
D.4.8
Answer: A.3.42
Explanation: Let x = 100 (To make calculation easy.)
250% of 100 = 250
Now,
250 is increased by 250%, then it become = 875
Now comparing,
875 = 30
So, 1 = 30/875
Hence, 100 = (30*100)/875 = 3.42
ANSWER : OPTION A
So, 100 = x = 3.42.
Question: (565945 x 121) = ?
A.68463812
B.68463813
C.68479345
D.68463814
Answer: C.68479345
Explanation: 565945*121=68479345Ans C
Question: Company ABC imported 10,500 widgets made of either brass or aluminum. The widgets are painted blue, red or green. If 10 percent of the widgets are made of brass and of those 30 percent are painted green and 40 percent are painted red how many brass widgets painted blue were imported?
A.420
B.840
C.315
D.1680
Answer: C.315
Explanation: Answer A.
We are told that 10% of all imported widgets are made of brass and of those, 30% are green and 40% are red. Since we know that there are only three colors, the remaining 30% must be blue. 30% blue of 10% brass widgets leads to 3% blue brass widgets out of the total 10,550 widgets.
10,500 /100 * 3 = 315.
Answer C.
Question: A, B and C enter into a partnership with a capital in which A's contribution is Rs. 10,000. If out of a total profit of Rs. 1000, A gets Rs. 500 and B gets Rs. 300, then C's capital is :
A.4000
B.3778
C.2667
D.2887
Answer: A.4000
Explanation: Explanation:
A : B : C = 500 : 300 : 200 = 5 : 3 : 2.
Let their capitals be 5x, 3x and 2x respectively.
Then, 5x = 10000
=> x = 2000.
C's capital = 2x = Rs. 4000.
Answer: A) 4000
Question: Find out the square of a number which when doubled exceeds its one fifth by 9 ?
A.16
B.25
C.19
D.26
Answer: B.25
Explanation: A
Let the number be p, then the square will be p^2
According to question:
2p = (p/5) + 9
=> 10p = p + 45
=> p = 5
p^2 = 5^2 = 25.
Answer : B
Question: If 5 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is?
A.8:5:4
B.8:5:18
C.8:5:12
D.8:5:14
Answer: A.8:5:4
Explanation: 5A = 8B = 10 C
A:B:C = 1/5:1/8:1/10
= 8:5:4
Answer: A
Question: Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1125 as rent for parking his cars, what is the total rent paid by all the four agencies?
A.Rs. 4500
B.Rs. 4800
C.Rs. 5250
D.Rs. 6150
Answer: D.Rs. 6150
Explanation: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15
= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60
Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.
The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k
It is given that A paid Rs. 1125
45k = 1125 => k = 25
246k = 246(25) = Rs. 6150
Thus the total rent paid by all the four agencies is Rs. 6150.
ANSWER:D
Question: Anne bought doughnuts for a class breakfast party. She bought 5 chocolate doughnuts, 6 coconut doughnuts, and 11 jam-filled doughnuts. How many doughnuts did Anne buy in all?
A.22
B.36
C.39
D.21
Answer: A.22
Explanation: Add the numbers of doughnuts.
5 + 6 +11 =22.
Answer is A.
Question: Two pipes A and B can fill a tank in 24 minutes and 32 minutes respectively. If both the pipes are
opened simultaneously, after how much time should B be closed so that the tank is full in 18
minutes?
A.7 minute
B.9 minute
C.10 minute
D.8 minute
Answer: D.8 minute
Explanation: pipe A will work for 18 minutes. suppose pipe B is closed after x minutes than
we have 18/24+x/32=1
x=8 minute.
ANSWER:D
Question: The manufacturing cost of a shoe is Rs.230 and the transportation lost is Rs.500 for 100 shoes. What will be the selling price if it is sold at 20% gains
A.s 282
B.s 216
C.s 220
D.s 210
Answer: A.s 282
Explanation: Explanation :
Total cost of a watch = 230 + (500/100) = 235.
Gain = 20% => SP = 1.2CP = 1.2 X 235 = 282
Answer : A
Question: A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 7x km.
A.56
B.18
C.24
D.19
Answer: A.56
Explanation: Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 7x/(x/8) = 56 kmph
Answer: A
Question: Right triangle ABC is to be drawn in the xy-plane so that the right angle is at A and AB is parallel to the y-axis. If the x- and y-coordinates of A, B, and C are to be integers that are consistent with the inequalities -6 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions?
A.54
B.432
C.2,160
D.2,916
Answer: C.2,160
Explanation: We have the rectangle with dimensions 9*6 (9 horizontal dots and 6 vertical). AB is parallel to y-axis and AC is parallel to x-axis.
Choose the (x,y) coordinates for vertex A: 9C1*6C1;
Choose the x coordinate for vertex C (as y coordinate is fixed by A): 8C1, (9-1=8 as 1 horizontal dot is already occupied by A);
Choose the y coordinate for vertex B (as x coordinate is fixed by A): 5C1, (6-1=5 as 1 vertical dot is already occupied by A).
9C1*6C*8C1*5C1=2160.
Answer: C.
Question: Reena took a loan of $. 1200 with simple interest for as many years as the rate of interest. If she paid $ 588 as interest at the end of the loan period, what was the rate of interest?
A.3.6
B.7
C.18
D.Cannot be determined
Answer: B.7
Explanation: Let rate = R% and time = R years.
Then,1200 x R x R/100= 588
12R2 = 588
R2 = 49
R = 7.
Answer:B
Question: There are r red ball, b blue ball and w white ball in a bag. What is the ratio of the number of blue ball to the total no. of ball in terms of r, b and w.?
A.r / (r + b + w)
B.r / (r + b)
C.(r + b + w)/r
D.r / (b + w)
Answer: A.r / (r + b + w)
Explanation: The total number of marbles is
r + b + w
The total ratio of blue marbles to the total number of marbles is
r / (r + b + w)
A
Question: In how many ways Chief Minister and Minister be elected from a team of 10 members?
A.90
B.95
C.120
D.100
Answer: A.90
Explanation: To do this, if captain is elected first, then we have 10 ways of doing this.
For election of vice-captain, we have only 9 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 10*9 = 90 ways.
A
Question: If 4 women can color 48 m long cloth in 2 days, then 6 women can color 36 m long cloth in
A.2 days
B.1 day
C.4 days
D.3 days
Answer: B.1 day
Explanation: The length of cloth painted by one woman in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 women = 36/ 6 × 6 = 1 day.
B
Question: Each person who attended a company meeting was either a stockholder in the company, an employee of the company or both. If 62 percent of these who attended the meeting were stockholders and 49 percent were employees. What percent were stockholders, who were not employees?
A.52
B.51
C.54
D.55
Answer: B.51
Explanation: I came up with the same answer choice B, but my approach was slightly different!
49% were employees which shall cover those who were only employees and those who were both shareholders and employees.
Thus, the number of attendants who were only shareholders is 100% - 49% = 51%.
Question: One square garden has area of A square feet and the perimeter is p feet. If 3A=3(2p+9), what is the perimeter of the garden, in feet?
A.28
B.36
C.40
D.56
Answer: B.36
Explanation: You can also solve this via using the given numbers in the answer choices!
Of course you need to be aware of the basic properties as outlined by the other posts above (a = x^2 and p = 4x)
Starting with D you will notice that x=14 is way too big for your area (14^2) and will not satisfy: 3A=3(2p+9) or A=2p+9
--> Eliminate D and E
Now pick B (its either too big, then its A, or too small then you know its C or it is B itsself)
And picking B indeed solves the problem! (36/4 --> 9; a= 9^2 = 81 and 81=2x36+9)
Question: Which of the following is equivalent to the pair of inequalities x + 2 > 10 and x - 4 <= 5 ?
A. 2 < x < 16
B. 2 <= x < 4
C. 2 < x <= 8
D. 8 < x <= 9
Answer: D. 8 < x <= 9
Explanation: Solution:
Let’s isolate x in both inequalities, starting with x + 2 > 10.
x + 2 > 10
x > 8
Next we isolate x in the inequality x – 4  5.
x – 4 <= 5
x <= 9
Bringing these two inequalities together we know:
8 < x <= 9
The answer is D.
Question: One used-car salesperson receives a commission of $ 200 plus 4 percent of $ 1,000 less than the car’s final sale price. Another car salesperson earns a straight commission of 6 percent of the car’s final sale price. What is the final sale price of a car if both salespeople would earn the same commission for selling it?
A.$ 5,000
B.$ 6,000
C.$ 8,000
D.$ 10,000
Answer: C.$ 8,000
Explanation: let s1 and s2 be the commission earned by the two salesperson
as per the question,
s1=200+0.04(x-1000) (where x is the sp of the car)
s2=0.06x
also
s1=s2
or,
200+0.04(x-1000)=0.06x
200+0.04x-40=0.06x
0.02x=160
x=8000
ANSWER:C