mathewhe/aqua_rat huggingface dataset:
Question: if the angles of an n sided polygon are in A.P and a>=20 and d>=20 then wat is the maximum possible value of n?
(A) 12
(B) 14
(C) 21
(D) 25
(E) cant determine
Rationale: Sum of Interior angles of a polygon = (n-2) × 180° where n = number of sides
There will be n angles which are in A.P. Therefore,
Since we need to find maximum value of n, put minimum value for a and d.i.e., take a=20 and d=20
Then sum of the angles
=n/2[2×20+(n−1)20]
Therefore,
10n(n+1)=(n−2)180
n=14.52
Since number of sides must be a positive integer, maximum value of n = 14
ANSWER:B
Answer: (B) 14
Question: In a class Students are seated in 15 rows. There are 15 students in the first row and 16 students in the second row. In each subsequent row there are 2 more students than in the previous row. Find the total number of students in the class?
(A) 406
(B) 420
(C) 521
(D) 460
(E) 421
Rationale: The first row has 15 students. The remaining 14 rows forms an AP with first term 16 and last term 42 with an average of 29. The total number of students in the class is 29*14+15=421
Answer is E.
Answer: (E) 421
Question: By how much is three-fifth of 350 greater than four-seventh of 210 ?
(A) 90
(B) 100
(C) 110
(D) 120
(E) 130
Rationale: Explanation:
3/5 of 350 - 4/7 of 210 = 210 - 120 = 90.
Answer: A
Answer: (A) 90
Question: Each month, after Jill pays for rent, utilities, food, and other necessary expenses, she has one fifth of her net monthly salary left as discretionary income. Of this discretionary income, she puts 30% into a vacation fund, 20% into savings, and spends 35% on eating out and socializing. This leaves her with $111 dollar, which she typically uses for gifts and charitable causes. What is Jill’s net monthly salary?
(A) $2400
(B) $3200
(C) $6000
(D) $6400
(E) $3700
Rationale: let x be the monthly salary
15%of 1/5*x=111
x=3700
answer E
Answer: (E) $3700
Question: If the number 517*324 is completely divisible by 3, then the smallest whole number in the place of * will be:
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 3.
x = 2.
Answer B) 2.
Answer: (B) 2
Question: In a division, divident is 690, divisior is 36 and quotient is 19. Find the remainder.
(A) A)4
(B) B)3
(C) C)2
(D) D)5
(E) E)6
Rationale: Explanation:
690 = 36 x 19 + r
690 = 684 + r
r = 690 - 684 = 6
Answer: Option E
Answer: (E) E)6
Question: A present value of a machine is $900. Its value depletiation rate is 25% per annum then find the machine value before 2 years?
(A) $1500
(B) $1200
(C) $1600
(D) $1000
(E) $1350
Rationale: P= $900
R = 25%
T = 2 years
Machine value before 2 years = P/[(1-R/100)^T]
=900*4/3 * 4/3
=$1600
Answer is C
Answer: (C) $1600
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 30, the dividend is:
(A) A)5322
(B) B)5330
(C) C)2280
(D) D)5340
(E) E)5342
Rationale: Divisor = (5 * 30) = 150
= 10 * Quotient = Divisor
=> Quotient = 150/10 = 15
Dividend = (Divisor * Quotient) + Remainder
Dividend = (150 * 15) + 30 = 2280.
C
Answer: (C) C)2280
Question: The length of the bridge, which a train 200 metres long and travelling at 60 km/hr can cross in 30 seconds, is?
(A) 720
(B) 470
(C) 270
(D) 370 m.
(E) 570
Rationale: Speed = [60 X 5/18] m/sec = [50/3] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30
= 50/3 => (130 + x)/30
= 370=> x
= 370 m.
Answer:D
Answer: (D) 370 m.
Question: 4000 was divided into two parts such a way that when first part was invested at 3% and the second at 5%, the whole annual interest from both the investments is Rs.144, how much was put at 3%?
(A) 3299
(B) 2690
(C) 2800
(D) 2692
(E) 2981
Rationale: (x*3*1)/100 + [(4000 - x)*5*1]/100 = 144
3x/100 + 200 – 5x/100 = 144
2x/100 = 56 è x = 2800.Answer: C
Answer: (C) 2800
Question: There are 30 students in a certain geometry class. If two thirds of the students are boys and three fourths of the boys are under six feet tall, how many boys in the class are under six feet tall?
(A) 6
(B) 12
(C) 15
(D) 24
(E) 27
Rationale: 30*2/3 *3/4= 15
Answer: C
Answer: (C) 15
Question: 96% of the population of a village is 23040. The total population of the village is?
(A) 16800
(B) 1689
(C) 6795
(D) 24000
(E) 12654
Rationale: Explanation:
X * (96/100) = 23040
X = 240 * 100
X = 24000
Answer: D
Answer: (D) 24000
Question: Value of
(256)5/4
(A) 1012
(B) 1024
(C) 1048
(D) 525
(E) None of these
Rationale: Explanation:
=(256)5/4=(44)5/4=4(5)=1024
Option B
Answer: (B) 1024
Question: A car traveled 281 miles in 4 hours 41 minutes. What was the average speed of the car in miles per hour?
(A) 100 miles / hour
(B) 90 miles / hour
(C) 70 miles / hour
(D) 60 miles / hour
(E) 30 miles / hour
Rationale: We first convert the time of 4 hours 41 minutes in minutes
4 hours 41 minutes = 4 ? 60 + 41 = 281 minutes
Average speed S is given by distance / time. Hence
S = 281 miles / 281 minutes = 1 mile / minute
= 60 miles / hour
correct answer D
Answer: (D) 60 miles / hour
Question: The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 50 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is
(A) 90
(B) 99
(C) 92
(D) 94
(E) 97
Rationale: The average score in an examination of 10 students of a class is 60 --> the total score = 10*60 = 600;
The 5 smallest scores have an average of 55 --> the total score of the 5 smallest scores = 275.
From above, the total score of the 5 largest scores = 600 - 275 = 325.
Say the 5 largest scores are a, b, c, d, and e (where a<b<c<d<e, since each of the top five scorers had distinct scores). We want to maximize e. To maximize e, we need to minimize a, b, c, and d. The least value of a, is 55 (The least score of the top 5 , a, should be equal to the highest of the bottom 5 and to minimize the highest of the bottom 5, all scores from the bottom 5 should be equal). In this case the least values of b, c, and d are 56, 57, and 58 respectively:
a + b + c + d + e = 55 + 56 +57 + 58 + e = 325;
e = 99.
Answer: B.
Answer: (B) 99
Question: A student is ranked 21th from right and 11th from left. How many students are there in totality ?
(A) 18
(B) 19
(C) 20
(D) 31
(E) 22
Rationale: From right 21 , From left 11
Total = 21+11-1 = 31
ANSWER:D
Answer: (D) 31
Question: In the formula V = 1/(3r)^4, if r is halved, then V is multiplied by
(A) 64
(B) 8
(C) 16
(D) 1/8
(E) 1/64
Rationale: Say r=2 => V1 = 1/1296
when r=1; V2 = 1/81
V2 = 16*V1.
Answer=C=16
Answer: (C) 16
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
(A) 76 seconds
(B) 18 seconds
(C) 40 seconds
(D) 19 seconds
(E) 45 seconds
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25)
= 40 seconds
Answer: C
Answer: (C) 40 seconds
Question: In the Hillside summer camp there are 50 children. 90% of the children are boys and the rest are girls. The camp administrator decided to make the number of girls only 5% of the total number of children in the camp. How many more boys must she bring to make that happen?
(A) 50
(B) 45.
(C) 40.
(D) 30.
(E) 25.
Rationale: Given there are 50 students , 90% of 50 = 45 boys and remaining 5 girls.
Now here 90% are Boys and 10% are Girls.
Now question is asking about how many boys do we need to add, to make the girls percentage to 5 or 5%..
If we add 50 to existing 45 then the count will be 95 and the girls number will be 5 as it.
Now boys are 95% and girls are 5%. ( out of 100 students = 95 boys + 5 girls ).
Answer: option A is correct.
Answer: (A) 50
Question: At the end of year X, automobile installment credit accounted for 43% of all outstanding consumer installment credit. At that time automobile finance companies extended $50 billion of credit, or 1/4 of the automobile installment credit. How many billion dollars of consumer installment credit was outstanding at that time?
(A) 450
(B) 465.12
(C) 475
(D) 500.15
(E) 200
Rationale: System of Equations
a = (43/100) c
(1/4) a = 50 --> a = 200
Substitution
200 = (43/100) c
c = (100/43) 200
Calculate
200/43 * 100
- The the correct answer is 465.12. The correct answer is B.
Answer: (B) 465.12
Question: Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 45 more revolutions than gear P?
(A) 45
(B) 80
(C) 90
(D) 100
(E) 120
Rationale: Gear Q makes 30 more revolutions each 60 seconds.
The time to make 45 = 30*1.5 more revolutions is 60*1.5 = 90 seconds.
The answer is C.
Answer: (C) 90
Question: A cistern is filled by pipe A in 12 hours and the full cistern can be leaked out by an exhaust pipe B in 18 hours. If both the pipes are opened, in what time the cistern is full?
(A) 50hrs
(B) 60hrs
(C) 36hrs
(D) 80hrs
(E) 90hrs
Rationale: time taken to full the cistern=(1/12-1/18)hrs
=1/36
=36hrs
ANSWER:C
Answer: (C) 36hrs
Question: A 72 gallon solution of salt and water is 10% salt. How many gallons of water must be added to the solution in order to decrease the salt to 8% of the volume?
(A) 8
(B) 12
(C) 18
(D) 14
(E) 16
Rationale: Amount of salt = 7.2
Assume x gallons of water are added.
7.2 / 72 + x = 8/100
720 = 8x + 576
8x = 144
x = 18
Correct Option: C
Answer: (C) 18
Question: A pet shop sells 50 rabbits for Rs. 2000 at a profit of Rs. 12 per rabbit. Find the cost price for one rabbit?
(A) 20
(B) 52
(C) 28
(D) 40
(E) 15
Rationale: SP per rabbit = 2000/50 = Rs. 40Profit per rabbit = Rs. 12 CP per rabbit = 40 - 12= Rs. 28Answer: C
Answer: (C) 28
Question: A computer system uses alphanumeric case sensitive characters for its passwords. When the system was created it required users to create passwords having 4 characters in length. This year, it added the option of creating passwords having 5 characters in length. Which of the following gives the expression for the total number of passwords the new computer system can accept?
Assume there are 62 unique alphanumeric case sensitive characters.
(A) 63^4
(B) 62^5
(C) 62(62^4)
(D) 63(62^4)
(E) 63(62^6)
Rationale: Total number of passwords = number of 4 character password +number of 5 character password
= 62^4 + 62^5 (Since there is no limitation on repetition , each character can be chosen in 62 ways )
=62^4(1+ 62)
=62^4 * 63
Answer D
Answer: (D) 63(62^4)
Question: A can do a work in 20 days. B is 30% more efficient than A. How many days does B alone take to do the same job?
(A) 121/23
(B) 129/12
(C) 198/13
(D) 200/13
(E) 199/18
Rationale: Ratio of times taken by A and B = 130:100 = 13:10
suppose B alone to take x days to do the work
then, 13:10::20:x
13x= 10*20
x=200/13 days
correct option is D
Answer: (D) 200/13
Question: Harry is a trail runner who decides to take a day off work to run up and down a local mountain. He runs uphill at an average speed of 5 miles per hour and returns along the same route at an average speed of 10 miles per hour. Of the following, which is the closest to his average speed, in miles per hour, for the trip up and down the mountain?
(A)  5.5
(B)  5.8
(C)  6.0
(D)  6.3
(E)  6.6
Rationale: to calculate average of 2 speeds a and b when distance is constant
Formula - 2ab/(a+b)
Here Harry's uphill speed = 5 mph
Harry's downhill speed = 10 mph
2*5*10/(5+10) = 100/15 = 6.6
Correct answer - E
Answer: (E)  6.6
Question: P and Q started a business with respective investments of Rs. 4 lakhs and Rs. 10 lakhs. As P runs the business, his salary is Rs. 5000 per month. If they earned a profit of Rs. 2 lakhs at the end of the year, then find the ratio of their earnings?
(A) 1 : 8
(B) 1 : 0
(C) 1 : 2
(D) 1 : 1
(E) 1 : 5
Rationale: Ratio of investments of P and Q is 2 : 5
Total salary claimed by P = 12 * 5000 = Rs. 60000
Total profit = Rs. 2 lakhs.
Profit is to be shared = Rs. 140000
Share of P = (2/7) * 140000 = Rs. 400000
Share of Q = Rs. 100000
Total earnings of P = (60000 + 40000) = Rs. 100000
Ratio of their earnings = 1 : 1
Answer: D
Answer: (D) 1 : 1
Question: When 2/9 of the votes on a certain resolution have been counted, 3/4 of those counted are in favor of the resolution. What fraction f of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution?
(A) 11/14
(B) 13/18
(C) 4/7
(D) 3/7
(E) 3/14
Rationale: If we use variable for total votes there will be too many fractions to manipulate with, so pick some smart #: let set total # of votes is 18.
2/9 of the votes on a certain resolution have been counted--> 4 counted and 18-4=14 votes left to be counted;
3/4 of those counted are in favor of the resolution--> 3 in favor and 1 against;
Ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18*2/3=12 people who voted against, so in the remaining 14 votes there should be 12-1=11 people who voted against. Thus f=11/14 of the remaining votes must be against.
Answer: A.
Answer: (A) 11/14
Question: Twelve participants are participating in a competition. In how many ways can the first three prizes be won?
(A) 1320
(B) 680
(C) 820
(D) 720
(E) 620
Rationale: Out of 12 participants, the first three prizes can be won in,
12P3 = 12! / (12 - 3)!
= 12 X 11 X 10
= 1320 ways
ANSWER:A
Answer: (A) 1320
Question: X,Y and Z can complete a piece of work in 24,6 and 12 days respectively.Working together, they will complete the same work in:
(A) 24/7days
(B) 3/7days
(C) 35/7days
(D) 12/24days
(E) 45/35days
Rationale: X+Y+Z day work = 1/24+1/6+1/12 = 7/24
X,Y,Z complete the work in 24/7 days
ANSWER A
Answer: (A) 24/7days
Question: The last day of the century cannot be:
(A) Sunday
(B) Wednesday
(C) Friday
(D) Saturday
(E) Tuesday
Rationale: SOLUTION :
100 years have 5 odd days. Hence the last day of 1st century is a Friday.
200 years have 10 odd days or 1 week + 3 odd days. Hence, the last day of the 2nd century is a Wednesday.
300 years have 15 odd days or 2 week + 1 odd day. Hence, the last day of the 3rd century is a Monday.
400 years have 0 odd days. Hence, the last day of the 4th century is a Sunday.
ANSWER IS D
Answer: (D) Saturday
Question: The average of seven numbers is 9. The average of first three numbers is 7 and the average of last three numbers is 11. What is the middle number?
(A) 7
(B) 8
(C) 9
(D) 11
(E) 10
Rationale: The total of seven numbers = 7X9 = 63
The total of first 3 and last 3 numbers is = 3 X 7+3 X 11 = 54
So, the middle number is (63 - 54 ) = 9
C
Answer: (C) 9
Question: The first train leaves the station at 6:00 am with a speed of 60 km/hr. The second train leaves at 7:00 am, in the same direction from the same station, with a speed of 80 km/hr. What time will the second train catch the first train?
(A) 9:00 am
(B) 10:00 am
(C) 11:00 am
(D) 12:00 noon
(E) 1:00 pm
Rationale: In one hour, the first train travels 60 km.
The second train catches the first train with a relative speed of 20 km/h.
The second train will catch the first train at 10:00 am.
The answer is B.
Answer: (B) 10:00 am
Question: A family consists of two grandparents, two parents, and four grandchildren. The average age of the grandparents is 66 years, the average age of the parents is 40 years, and the average age of the grandchildren is 7 years. What is the average age (in years) of the family?
(A) 26
(B) 28
(C) 30
(D) 32
(E) 34
Rationale: Total age of the grandparents = 66 Ã— 2 = 132
Total age of the parents = 40 Ã— 2 = 80
Total age of the grandchildren = 7 Ã— 4 = 28
Average age of the family = (132+80+28)/8 = 240/8 = 30 years
The answer is C.
Answer: (C) 30
Question: At a baseball game, 10% of the fans did not wear ball caps, 60% of the remaining fans wore ball caps for the home team. What percentage of the fans wore ball caps for the visiting team?
(A) 64% of the attendees wore ball caps for the visiting team.
(B) 36% of the attendees wore ball caps for the visiting team.
(C) 44% of the attendees wore ball caps for the visiting team.
(D) 54% of the attendees wore ball caps for the visiting team.
(E) None of these.
Rationale: Explanation:Let total number of fans be 100,Then, number of fans not wearing ball caps = 10.Number of fans with home team ball cap= 60% of 90 = 54.Total number of fans with visitor team ball cap = 100 – (10 + 54) = 36.Thus, 36% of the attendees wore ball caps for the visiting team.Answer: Option B.
Answer: (B) 36% of the attendees wore ball caps for the visiting team.
Question: Two trains 180 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 10.24 sec
(B) 18.8 sec
(C) 14.24 sec
(D) 12.24 sec
(E) 11.84 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 180 + 160 = 340 m.
Required time = 340 * 9/250 = 306/25 = 12.24 sec.
Answer: D
Answer: (D) 12.24 sec
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red?
(A) 12/477
(B) 12/487
(C) 12/455
(D) 12/416
(E) 12/419
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
When three marbles are drawn, the probability that one is yellow and two are red
= (²C₁)(⁴C₂)/¹⁵C₃
= (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13)
= 12/455
Answer: C
Answer: (C) 12/455
Question: A 10-meter long wire is cut into two pieces. If the longer piece is then used to form a perimeter of a square, what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point?
(A) 2/3
(B) 3/4
(C) 1/5
(D) 2/5
(E) 3/5
Rationale: The longer wire will form a square with an area more than 4 if the wire is cut at a point within two meters of either end. The probability of this is 4/10 = 2/5.
The answer is D.
Answer: (D) 2/5
Question: 5 - [5 - {5 - 5(5 + 5)}] = ?
(A) 5
(B) -45
(C) 45
(D) 50
(E) 60
Rationale: Explanation:
=> ? = 5 - [5 - {5 - 5 × 10}] = 5 - [5 - (-45)]
= 5 - (50) = - 45
Answer: Option B
Answer: (B) -45
Question: A class consists of 5 boys and 5 girls. Given that one kid can only hold one title, in how many ways can you pick 2 boys to be the class clown and the teacher's pet or 2 girls to be the most beautiful girl in class and the smartest kid on the block?
(A) 9
(B) 18
(C) 32
(D) 40
(E) 240
Rationale: Easiest way is to treat it like an arrangements question in the following manner:
From the boys we need to select 2 to be clown and pet: This can be done in 5*4 ways
Similarly for the girls, we have 4*5 ways.
Thus total = 20+20 = 40 ways. Thus D is the correct answer.
Answer: (D) 40
Question: There are three vessels of equal capacity .Vessel A contains Milk and water in the ratio 7:3 ;Vessel B contains Milk and water in the ratio 2:1 and Vessel C contains Milk and water in the ratio 3:2 .If the mixture in all the three vessels is mixed up.What will be the ratio of milk and water ?
(A) 59:31
(B) 3:2
(C) 118:126
(D) 193:122
(E) 201:132
Rationale: 7:3=>7x+3x=10x
2:1=>2y+1y=3y
3:2=>3z+2z=5z
10x=3y=5z
Take LCM of 10,3,5=30
Or simply;
x=3
y=10
z=6
So,
Ratio of Milk:Water= (7x+2y+3z)/(3x+y+2z)=59/31
Ans:A
Answer: (A) 59:31
Question: Ravi and sunil are partners in a business. Ravi invests Rs.18,000 for 8 months and Sunil invested Rs.10000 for 10 months then after one year ratio of their profits will be
(A) 1:3
(B) 36:25
(C) 3:2
(D) 4:5
(E) 20:45
Rationale: =(18000*8):(10000*10)
=144000:100000
=36:25
ANSWER:B
Answer: (B) 36:25
Question: Two pipes A and B can separately fill a tank in 16 and 18 minutes respectively. A third pipe C can drain off 45 liters of water per minute. If all the pipes are opened, the tank can be filled in 18 minutes. What is the capacity of the tank?
(A) 590 liters
(B) 720 liters
(C) 740 liters
(D) 860 liters
(E) 620 liters
Rationale: 1/16 + 1/18 - 1/x
= 1/18
x = 16
16 * 45 = 720
Answer:B
Answer: (B) 720 liters
Question: the population of a country is increased by 2% in one year and 3% in next year.what is the combined growth of population in these two year
(A) 4.06%
(B) 5.06%
(C) 6.06%
(D) 7.06%
(E) 8.06%
Rationale: concept of successive percentage, total percentage= x+y+xy/100
put x=2 and y=3
combined growth= 2+3+2*3/100
= 5+0.06= 5.06%
ANSWER:B
Answer: (B) 5.06%
Question: A number, x is chosen at random from the set of positive integers less than 10. What is the probability that (7/x) > x?
(A)  1/5
(B)  7/9
(C)  1/3
(D)  2/3
(E)  2/9
Rationale: Number x has to be chosen from numbers 1-9
(7/x) > x
=> 7 > x^2
=>x^2 - 7 < 0
x can have 2 values only 1 , 2
Therefore , probability = 2 / 9
Answer E
Answer: (E)  2/9
Question: Debony normally drives to work in 45 minutes at an average speed of 40 miles per hour. This week, however, she plans to bike to work along a route that decreases the total distance she usually travels when driving by 20% . If Debony averages between 12 and 16 miles per hour when biking, how many minutes earlier will she need to leave in the morning in order to ensure she arrives at work at the same time as when she drives?
(A) 135
(B) 105
(C) 95
(D) 75
(E) 45
Rationale: Debony normally drives to work in 45 minutes at an average speed of 40 miles per hour.
Use formula D = RT
Car:
T1: 45 min
R1: 40 mph
D1: [(40*45)/60] = 30 miles
Bike:
T1:?
R2: 12 - 16 mph
D2: 08*D1 = 24 miles
T1: [(24*60)/12] = 120 min (Only 12 mph speed yields an answer given in the choices)
Therefore, Deb has to leave 120 min - 45 min = 75 min early
ANSWER: D
Answer: (D) 75
Question: What is the area inscribed by the lines y =6, x = 3, y = 2x-4 on an xy-coordinate plane?
(A) a) 1
(B) b) 2
(C) c) 4
(D) d) 8
(E) e) 16
Rationale: First, let's graph the lines y = 6 and x = 3
At this point, we need to find the points where the line y = 2x-4 INTERSECTS the other two lines.
For the vertical line, we know that x = 3, so we'll PLUG x = 3 into the equation y = 2x-4 to get y = 2(3)-4 = 2
Perfect, when x = 3, y = 2, so one point of intersection is (3,2)
For the horizontal line, we know that y = 6, so we'll PLUG y = 6 into the equation y = 2x-4 to get 6 = 2x-4. Solve to get: x = 5
So, when y = 6, x = 5, so one point of intersection is (5,6)
Now add these points to our graph and sketch the line y = 2x-4
At this point, we can see that we have the following triangle.
The base has length 2 and the height is 4
Area = (1/2)(base)(height)
= (1/2)(2)(4)
= 4
Answer:
C
Answer: (C) c) 4
Question: Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.85. How much was lent at 5%?
(A) 228
(B) 2769
(C) 278
(D) 502
(E) 131
Rationale: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 85
5x/100 + 90 – 6x/100 = 85
x/100 = 5
=> x = 500
Answer: D
Answer: (D) 502
Question: Initially, the men and women in a room were in the ratio of 4 : 5. Then, 2 men entered the room and 3 women left the room. Then, the number of women doubled. Now there are 14 men in the room. How many R women are currently in the room?
(A) 12
(B) 14
(C) 15
(D) 24
(E) 36
Rationale: the number of women doubled means that they have become 24 from 12..
and we have to tell the current strength so 24 is the answer..
let the number be 4x and 5x..
given 4x+2=14.. so x=3..
women number=5*3-3=12, then doubled=24..
ans D
Answer: (D) 24
Question: If 3^20 x 2^20 =6^n what is the value of n?
(A) 18
(B) 20
(C) 22
(D) 24
(E) 26
Rationale: 3^20 *2^20 = 6^n
6^20 =6^n therefore n=20
B
Answer: (B) 20
Question: In how many ways can the letters of the word "VENUS" be arranged?
(A) 60
(B) 80
(C) 100
(D) 120
(E) 140
Rationale: The total ways of arranging the letters = 5! = 120
The answer is D.
Answer: (D) 120