mathewhe/aqua_rat huggingface dataset:
Question: What is the greatest of 3 consecutive integers whose sum is 18 ?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 5
Rationale: The sum of three consecutive integers can be written as n + (n + 1) + (n + 2) = 3n + 3
If the sum is 24, we need to solve the equation 3n + 3 = 18;
=> 3n = 15;
=> n = 5
The greatest of the three numbers is therefore 5 + 2 = 7 Answer: B
Answer: (B) 7
Question: The speed of a car is 90 km in the first hour and 60 km in the second hour. What is the average speed of the car?
(A) 15 kmph
(B) 18 kmph
(C) 19 kmph
(D) 12 kmph
(E) 11 kmph
Rationale: S = (90 + 60)/2
= 75 kmph
Answer:B
Answer: (B) 18 kmph
Question: What would be the minimum number of pumps required to fill a tank of 1000 m3 to 85% in one hour? The capacity of the pump is 150 m3/hour and operates at an efficiency of 75%.
(A) 6
(B) 8
(C) 10
(D) 11
(E) 12
Rationale: Volume handled by pump in one hour=150x.75=112.5
Volume of the tank that needs to be filled=1000x.85=850
Number of pumps needed=850/112.5=7.55â‰ˆ8
Answer:B
Answer: (B) 8
Question: If the wheel is 12 cm then the number of revolutions to cover a distance of 1056 cm is?
(A) 18
(B) 27
(C) 26
(D) 14
(E) 19
Rationale: 2 * 22/7 * 12 * x = 1056
=> x = 14
Answer: D
Answer: (D) 14
Question: 39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
(A) 10
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: According to the chain rule,
M1 x T1 = M2 x T2
Therefore, 36 x 12 x 5 = 30 x 6 x X
X = 13
Hence, the number of days = 13.
ANSWER:B
Answer: (B) 13
Question: Number of the students in a school 5000. It decreases annually at the rate of 10% p.a. What will be its number of the students after 3 years?
(A) 3635
(B) 3500
(C) 4000
(D) 4500
(E) 3750
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
8000 Ã— 90/100 Ã— 90/100 x 90/100 = 3635
A
Answer: (A) 3635
Question: A type E machine can complete a job in 5 hours and a type B machine can complete the job in 7 hours. How many hours will it take 2 type E machines and 3 type B machines working together and independently to complete the job?
(A) 1/5
(B) 29/35
(C) 5/6
(D) 35/29
(E) 35/12
Rationale: now D should be the answer.
E need 5 hours to complete
and B needs 7 hours to compete
so 2E + 3B will complete 2/5 + 3/7 or 29/35 portion of the job in 1 hour
so the whole job will take 35/29 hours....=D
Answer: (D) 35/29
Question: John makes $50 a week from his job. He earns a raise and now makes $70 a week. What is the % increase?
(A) 16%
(B) 16.66%
(C) 17.9%
(D) 20%
(E) 40%
Rationale: Increase = (20/50)*100 = (2/5)*100 = 40%.
E
Answer: (E) 40%
Question: 3,6,12,24,48,__
(A) 88
(B) 90
(C) 92
(D) 94
(E) 96
Rationale: 6=3*2
12=12*2
24=24*2
48=24*2
96=48*2
ANSWER:E
Answer: (E) 96
Question: In a group of 80 children and 10 youngsters, each child got sweets that are 15% of the total number of children and each youngster got sweets that are 25% of the total number of children. How many sweets were there?
(A) 1160
(B) 2881
(C) 2678
(D) 2321
(E) 2879
Rationale: Number of sweets each child got = 15% of 80 = 15/100 * 80 = 12.
Number of sweets 80 children got = 80 * 12 = 960.
Number of sweets each youngster got = 25% of 80 = 25/100 * 80 = 20.
Number of sweets 10 youngsters got = 10 * 20 = 200.
Total number of sweets = 960 + 200 = 1160.
Answer:A
Answer: (A) 1160
Question: 8 is 2% of a, and 2 is 8% of b. c equals b/a. What is the value of c?
(A) 1/16
(B) 1/4
(C) 1
(D) 4
(E) 8
Rationale: 2a/100 = 8
a = 400
8b/100 = 2
b = 25
c = b/a = 25/400 = 1/16
The answer is A.
Answer: (A) 1/16
Question: In a games hour 4 different types of players came to the ground? cricket 11, hockey 15, football 21, softball 15. In these 4 people play both cricket and hockey, 3people play both softball and football. 2 people play both cricket and football. How many people play only cricket?
(A) 11
(B) 5
(C) 8
(D) 3
(E) 9
Rationale: people play only cricket = total players in cricket- both cricket and football- both cricket and hockey.
people play only cricket = 11-4-2 = 5
Answer is B
Answer: (B) 5
Question: 38 69 22 73 31 47 13 82 66 97 41 79
Which of the following numbers is greater than three fourths of the numbers but less than one fourth of the numbers in the list above?
(A) 71
(B) 76
(C) 81
(D) 92
(E) 97
Rationale: Arrange the numbers in ascending order:
13, 22, 31, 38, 41, 47, 66, 69, 73, 79, 82, 97 (Just cross check the count to ensure that you didn't miss anything)
How many numbers do we see?
12, alright.
What's (1/4)12?
3.
What's (3/4)12?
9.
We're asked to find a number that are greater than 6 numbers in the list AND smaller than the remaining two.
13, 22, 31, 38, 41, 47, 66, 69, 73, 79, 82, 97
13, 22, 31, 38, 41, 47, 66, 69, 73: Find a number greater than any of these numbers.
79, 82, 97: Find a number smaller than any of these numbers.
Only 76 fits the description.
Ans:B
Answer: (B) 76
Question: The price of lunch for 20 people was $300 including a 20% gratuity for service. What was the average price per person, EXCLUDING the gratuity?
(A) 11.73
(B) 12.5
(C) 13.8
(D) 14
(E) 15.87
Rationale: Clearly B is the answer
I used POE here
Lets consider option (B)
20*12.5= 250 now 250(120/100)=300
=> possible ANSWER IMO B
Answer: (B) 12.5
Question: In a particular game, there can be eight players at one time on the pitch and they last for seventy minutes. In the total duration, six players substitute with each player. All the players are then for the same time on the pitch including the substitutes.
Can you calculate the time each player was on the pitch?
(A) 40 Min
(B) 37 Min
(C) 42 Min
(D) 45 Min
(E) 50 Min
Rationale: A
40 minutes
The total number of players = 8 + 6 = 14
According to the question, only eight players can be present on the field. Thus calculating the total time:
70 * 8 = 560
We know that there are 14 players in total so dividing the total time by 14 will give us the time spent by each player.
560/14 = 40 minutes
Answer: (A) 40 Min
Question: Suresh started a business, investing Rs.18000. After 3 months and 4 months respectively, Rohan and Sudhir joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.3872. What is the difference between Rohan’s and Sudhir’s share in the profit?
(A) s.345
(B) s.350
(C) s.352
(D) s.362
(E) s.368
Rationale: Suresh : Rohan : Sudhir
Ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8
= 6 : 3: 2
The difference between Rohan’s and Sudhir’s share = 1 share
:.i.e. = Rs. 3872 × 1/11 = Rs.352.
C
Answer: (C) s.352
Question: A person purchases tomatoes from each of the 4 places at the rate of 1 kg, 2 kg, 3 kg, 4 kg per rupee respectively. On an average he has purchased x kg of tomatoes per rupee. Then the value of x is
(A) 2
(B) 2.5
(C) 1.92
(D) None of these
(E) Cannot be determined
Rationale: x = 10/4 = 2.5
Answer: B.
Answer: (B) 2.5
Question: a car cover a distance of 715 km. with some speed.if speed of car is 10km/hour more,then it take 2 hour less to cover that distance.then initially what was the speed of the car?
(A) 45km/h
(B) 50km/h
(C) 55km/h
(D) 65km/h
(E) none of these
Rationale: let speed=x km./hour.then,
715/x-715/(x+10)=2,1/x-1/(x+10)=2/715;(x+10)-x/x(x+10)=2/715
2x(x+10)=7150;2x^2+20x-7150=0
x^2+10x-3575=0;x^2+65x-55x-3575=0
x(x+65)-55(x+65)=0;(x+65)(x-55)=0
x=55,because x can't be -65
answer C
Answer: (C) 55km/h
Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 4 hours to fill the tank. The leak can drain all the water in ?
(A) 2hr
(B) 1hr
(C) 3hr
(D) 4hr
(E) 6hr
Rationale: Work done by the leak in 1 hour = 1/2 - 1/4 = 1/4
Leak will empty the tank in 4 hours
Answer is D
Answer: (D) 4hr
Question: What is 15% of 2/3 of 0.8?
(A) 0.08
(B) 0.8
(C) 9
(D) 90
(E) None of the above
Rationale: The best way to solve these questions is to convert every term into fraction
(15/100)*(2/3)*(8/10) = 240/3000 = 0.08
Option A
Answer: (A) 0.08
Question: Find the value of (√1.5)/(√0.81) + (√1.44)/(√0.49) is
(A) 195/63
(B) 145/63
(C) 155/63
(D) 125/63
(E) 3.075
Rationale: (√1.5)/(√0.81) + (√1.44)/(√0.49)
=> 3.075
Answer is E.
Answer: (E) 3.075
Question: Martha has 6 dogs and 4 cats. She takes each animal separately for a daily walk. She can take the animals for a walk to the park or to the barber shop. How many different options for a walk with a single animal does Martha have?
(A) 8
(B) 9
(C) 10
(D) 18
(E) 20
Rationale: 5 dogs, 4 cats; park/barber shop
1 dog - 2 options - either park or barber shop, so, 6 dogs - 12 options and 4 dogs - 8 options.
Total = 20 options.
E
Answer: (E) 20
Question: 128 students represent x percent of the boys at a school. If the boys at the school make up 50% of the total school population of x students, what is x?
(A) 160
(B) 190
(C) 225
(D) 250
(E) 500
Rationale: Let B be the number of boys in the school.
128 = xB/100
B = 0.5x
12800=0.5x^2
x^2 = 25600
x = 160
The answer is A.
Answer: (A) 160
Question: If to a certain number, 720 be added, and the sum be divided by 125 ; the quotient will be equal to 7392 divided by 462. What is that number?
(A) 1280
(B) 1270
(C) 1260
(D) 1250
(E) None
Rationale: Solution
Let x = the number required.
a = 720 d = 7392
b = 125 h = 462
Then by the conditions of the problem (x + a)/b = d/h
Therefore x = (bd - ah)/h
Restoring the numbers,x = [(125.7392) - (720.462)]/462 = 1280.
Answer A
Answer: (A) 1280
Question: In a class, the average age of 35 boys is 10 years and the average of 25 girls is 15 years. what is the average age of the whole class?
(A) 11 Years
(B) 12.1 Years
(C) 13 Years
(D) 13.5 Years
(E) 14 Years
Rationale: Total age of 60 students
(35X 10+25 X 15) = 725
Average = 725/60 = 12.1 Years
B)
Answer: (B) 12.1 Years
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is?
(A) 17/25
(B) 17/24
(C) 17/29
(D) 17/20
(E) 17/21
Rationale: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20
Answer: D
Answer: (D) 17/20
Question: From the below series find the remainder from below? 1201 × 1203 ×1205 × 1207 is divided by 6
(A) 3
(B) 5
(C) 6
(D) 7
(E) 9
Rationale: If you don't know the above rule, this problem is really calculation intensive.
But by applying the above rule, when 1201, 1201, 1203, 1204 divided by 6, leaves remainders 1, 3, 5, 1. The product of these remainders = 15.
When 15 is divided by 6, Remainder is 3
A
Answer: (A) 3
Question: a is x % of b, b is x% more than a. Find x.
(A) 50%
(B) 62%
(C) 75%
(D) 37%
(E) 39%
Rationale: DETAILED SOLUTION
a = bx
b = a (1 + x), substituting this in the previous equation, we get
x (x + 1) = 1
x2 + x - 1 = 0
or x is approximately 0.62 or 62%.
Correct Answer: (B).
Answer: (B) 62%
Question: A train 110 m long travels at 60 kmph. How long does it take to pass a telegraph post by the side of the track ?
(A) 3.4
(B) 2.4
(C) 6.6
(D) 2.8
(E) 2.6
Rationale: Speed of train = 60 ×5/18 m/s = 50/3 m/s ∴ Time taken to cross the telegraph post = 110/(50/3)
= 6.6 seconds
Answer: C
Answer: (C) 6.6
Question: The distance between two cities A and B is 465 Km. A train starts from A at 8 a.m. and travel towards B at 60 km/hr. Another train starts from B at 9 a.m and travels towards A at 75 Km/hr. At what time do they meet?
(A) 09
(B) 07
(C) 12
(D) 05
(E) 03
Rationale: Explanation:
Suppose they meet x hrs after 8 a.m
then,
[Distance moved by first in x hrs] + [Distance moved by second in (x-1) hrs] = 465
Therefore, 60x + 75(x-1) = 465
=> x=3.
So,they meet at (8+4) i.e, 12 noon
Answer: C)
Answer: (C) 12
Question: Can you solve the alphametic?
ENLIST + SILENT + LISTEN = ANAGRAM
(A) 1816412
(B) 1416312
(C) 1516312
(D) 1216312
(E) 1116312
Rationale: Correct Answer : B
assume numeric values for alphabetics. like a=0, b=1, c=2, c=3, d=4, e=5,...
solution
547809+087549+780954 = 1416312
Answer: (B) 1416312
Question: A man is 35 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
(A) 14 years
(B) 18 years
(C) 20 years
(D) 22 years
(E) 33 years
Rationale: Let the son's present age be x years. Then, man's present age = (x + 24) years.
(x + 35) + 2 = 2(x + 2)
x + 37 = 2x + 4
x = 33.
answer :E
Answer: (E) 33 years
Question: If (x + 2)(x - a) = px2x2 + qx + 8, what are the values of the constants a, p and q?
(A) 299
(B) 278
(C) -4,1,6
(D) 2378
(E) 2771
Rationale: (x + 2)(x - a) = px2px2 + qx + 8
⇒x2⇒x2 + 2x - ax - 2a = px2px2 + qx + 8
⇒x2⇒x2 + (2 - a) x - 2a = px2px2 + qx + 8
Equating the coefficients of x2x2 , x and constant terms on both sides.
p = 1; q = 2 - a
-2a = 8
Solving, we get a = -4, p = 1, q = 6
Answer:C
Answer: (C) -4,1,6
Question: A grocer has a sale of Rs 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs, 6500 ?
(A) 4991
(B) 3435
(C) 2365
(D) 2443
(E) 2349
Rationale: Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs.[(6500 x 6) - 34009]
= Rs. (39000 - 34009)
= Rs. 4991.
Answer: A
Answer: (A) 4991
Question: A certain number when divided by 80 leaves a remainder 25, what is the remainder if the same no.be divided by 15?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 9
Rationale: Explanation:
80 + 25 = 105/15 = 7 (Remainder)
D
Answer: (D) 7
Question: Write 870,000,000,000 in scientific notation.
(A) 8.7 * 10^11
(B) 800.900 * 10^11
(C) 8.900 * 10^11
(D) 80.9000* 10^11
(E) 08.900 * 10^11
Rationale: a * 10 n , where a is a real number such that 1 * |a| < 10 and n is an integer.
870,000,000,000 = 8.7* 100,000,000,000 = 8.7 * 10 11**
correct answer A
Answer: (A) 8.7 * 10^11
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 13 cm.
(A) 335 cm2
(B) 885 cm2
(C) 285 cm2
(D) 247 cm2
(E) 725 cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (13)
= 247 cm2
Answer: D
Answer: (D) 247 cm2
Question: A sum of Rs.4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
(A) 8120
(B) 3120
(C) 8776
(D) 2879
(E) 1267
Rationale: Let A be the amount received at the end of the three years.
A = 4800[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4800 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7920
So the interest = 7920 - 4800 = Rs.3120
Answer: B
Answer: (B) 3120
Question: A tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride. The proportion of sodium chloride in the tank is 50% by volume and the capacity of the tank is 24 gallons. If the water evaporates from the tank at the rate of 0.5 gallons per hour, and the amount of sodium chloride stays the same, what will be the concentration of water in the mixture in 2 hours?
(A) 32%
(B) 36%
(C) 40%
(D) 44%
(E) 48%
Rationale: The number of gallons in the tank is (1/4)24 = 6 gallons
The amount of sodium chloride is 0.5(6) = 3 gallons
At the start, the amount of water is 0.5(6) = 3 gallons
After 2 hours, the amount of water is 3 - 0.5(2) = 2 gallons
The concentration of water is 2 / (3+2) = 2/5 = 40%
The answer is C.
Answer: (C) 40%
Question: David is 18 years older than his daughter Rosy. In 6 years David will be twice as old as Rosy. What is Rosy current age.
(A) 12
(B) 14
(C) 18
(D) 24
(E) 23
Rationale: Now: Rosy = x, David =x+18
In 6 years Rosy = x+6, David = x+18+6 or 2(x+6)
x+24= 2x+12
x= 12
Rosy is 12 years old
Answer : A
Answer: (A) 12
Question: Light glows for every 14 seconds . How many times did it between 1:57:58 and 3:20:47 am
(A) 381
(B) 382
(C) 383
(D) 384
(E) 355
Rationale: the diff in sec between 1:57:58 and 3:20:47 is 4969 sec, 4969/14 = 354
so total 355 times light ll glow
ANSWER:E
Answer: (E) 355
Question: The area of the cardboard(in cm2) needed to make a box of size 25 cm * 15 cm * 8 cm will be?
(A) 1390 cm2
(B) 695 cm2
(C) 1280 cm2
(D) 1220 cm2
(E) 1240 cm2
Rationale: 2(25 * 15 + 15 * 8 + 25 * 8)
2(375 + 120 + 200) => 1390
ANSWER:A
Answer: (A) 1390 cm2
Question: What annual installment will discharge a debt of Rs. 4600 due in 4 years at 10% simple interest?
(A) 1000
(B) 1030
(C) 1100
(D) None of these
(E) 1101
Rationale: Let the 1st installment = 100/-
It is 3yrs before due
IInd is 2yr before due
III3rd is 1yr before due
IVth is 0 yrs before due
On 1st installment interest will be paid for 3yrs
2nd installment interest will be paid for 2yrs
3rd installment interest will be paid for 1yr
4th installment interest will be paid for 0yr
Interest = P[(100(3+2+1+0)x10)/100] = 60/-
Total loan discharged = 4*100+60/- = 460/-
Now installment of 100/- loan discharged = 460/-
Loan discharged 4600/- ? Installment = 1000/-
Answer: A.
Answer: (A) 1000
Question: What is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder?
(A) 1108
(B) 1683
(C) 2000
(D) 3300
(E) 4000
Rationale: LCM of 5,6,7 and 8 = 840
hence => (840*1)+3 = 843 which is not divisible by 9
if k = 2, no = (840*2)+3=1683 is divisble by 9
ANSWER B
Answer: (B) 1683
Question: What approximate value should come in place of question mark (?) in the following equation
287.532 + 1894.029 – 657.48 = 643.095 + ?
(A) 870
(B) 790
(C) 880
(D) 770
(E) 890
Rationale: ? = 285 + 1895 – 655 – 645 or, ? = 880
Answer C
Answer: (C) 880
Question: If 5400 mn = k^4, where m, n, and k are positive integers, what is the least possible value of 2m + n?
(A) 11
(B) 18
(C) 20
(D) 25
(E) 35
Rationale: k^4=5400∗mn
k^4=3^3.2^3.5^2.mn
In order to make RHS a perfect power of 4, we require it to be multiplied by 3, 2 & 5^2
mn=3.2.5^2
mn = 150 = 10 * 15 (Least possible)
Answer = 2*10 + 15 = 35
ANSWER:E
Answer: (E) 35
Question: A sum of money becomes triple itself in 5 years at simple interest. How many years will it become five times at the same rate?
(A) 12 Â½ years
(B) 62 Â½ years
(C) 18 Â½ years
(D) 10 Â½ years
(E) 12 Â½ years
Rationale: 100 ---- 200 ---- 5
200 ---- 5
100 ---- 2 1/2
------------------
500 ---- 10 Â½ years
Answer:D
Answer: (D) 10 Â½ years
Question: Which of the following is satisfied with |x-4|+|x-3|<4?
(A) 1<x<5
(B) 2<x<5
(C) 1.5<x<5.5
(D) 2.5<x<4
(E) 3<x<4
Rationale: --> If there is addition when there are 2 absolute values, you can just ignore the middle. That is, |x-4|+|x-3|<4 -> |x-4+x-3|<4 -> |2x-7|<4, -4<2x-7<4, 3<2x<11, 3/2<x<11/2 -> 1.5<x<5.5
Therefore, the answer is C.
Answer: (C) 1.5<x<5.5
Question: Salley's internet provider offers unlimited traffic which costs $0.5 per day charged off at 12 a.m. The service is discontinued when client's debt exceeds $5. If today in the morning Salley makes a payment of $7, for how many days, including today, will she be connected to the internet without any additional payments, given her initial balance was $0?
(A)  15
(B)  24
(C)  25
(D)  26
(E)  13
Rationale: day 0- payment of $7 is made in the morning (after 12 am midnight)
day 1 onwards (after 12 am midnight) internet service will begin and will run for 7*2=14 days i.e. at the end of day 15 balance will be zero.
now salley can still use the internet till her debt reaches $5 which means total of 5*2=10 days.
now the question states for how many days, including today, will she be connected to the internet without any additional paymentsi.e. we will have to include day0 also in our final answer. therefore total no. of days =1+14+10=25=C
Answer: (C)  25
Question: Rs.1010/- distributed among A,B and C such that on decreasing their shares by RS.25,RS.10 and RS.15 respectively, The balance money would be divided among them in the ratio 3:2:5. Then, C’s share is:?
(A) Rs.485
(B) Rs.495/-
(C) Rs.575
(D) Rs.685
(E) Rs.592
Rationale: A:B:C = 3:2:5
Total parts = 10
C's share is = 5 parts
10-----> Rs.960/-
3 -----> Rs.480/-
A's total =480 + 15 = Rs.495/-
B)
Answer: (B) Rs.495/-
Question: A boat round trip in a river goes upstream at an average speed of 30 miles per hour. On the trip back downstream boat goes at an average speed of 90 miles per hour. What is her approximate average speed for the round trip in miles per hour?
(A) 40
(B) 45
(C) 60
(D) 61.7
(E) 70
Rationale: Average speed = total distance/total time
Here distance upstream and back is same as boat follows the same route.
D = 30T1 and D=90T2
Therefore, T1 = D/30 and T2 = D/90
T1+T2 = 4d/90
Therefore, average speed = 2d/4d/90
=2d * 90/4d
Answer is 45
Answer is B
Answer: (B) 45
Question: The sum of all solutions for x in the equation x^2 – 8x + 21 = |x – 4|+ 3 is equal to:
(A) –7
(B) 7
(C) 20
(D) 12
(E) 14
Rationale: x^2 - 8x + 18 = |x-4|
RHS can be -ve or +ve
x^2 - 9x + 22 = 0
x^2 - 7x + 14 = 0
x= 11,7,2
We test all 3 values in original equation, all ok.
Thus, Sum = 11 + 7 +2 = 20
Ans (C)
Answer: (C) 20
Question: A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
(A) 270
(B) 297
(C) 278
(D) 208
(E) 277
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 870
= 270
Answer:A
Answer: (A) 270
Question: A train traveling at 42 kms/ hr passes a cyclist going in the same direction in 9 secs. If the cyclist had been going in the opposite direction, the train would have passed him in 5 secs. Find the length of the train.
(A) 75 meters
(B) 60 meters
(C) 90 meters
(D) 80 meters
(E) 70 meters
Rationale: Let the length of the train be x meter
and the speed of the cyclist is y m/s
Now when the train and the cyclist are in the same direction, the relative speed is :(35/3-y)m/s[converting 42km/h to m/s-35/3m/s]
Now distance/relative speed =9 seconds
Substituting the values, we get x+9y.....................(1)
Similarly calculate the relative speed when they are in the opposite direction
The relative speed is (35/3+y)
Now distance/relative speed is equivalent to 5 seconds
Substituting the values, we get the equation
3x-15y=175.................................(2)
Solving (1) and (2), we get x=75 meters
ANSWER:A
Answer: (A) 75 meters
Question: Twenty eight meters of wire is available to fence off a flower bed in the form of a circular sector. What must the radius of the circle in meters be, if we wish to have a flower bed with the greatest possible surface area?
(A) 2√2
(B) 2√5
(C) 5
(D) 7
(E) none of these
Rationale: Area of Sector, A = x/360*pi*r^2
Circumference of the sector = 28
=> x/360*2*pi*r +2r= 28
=> 2A/r+2r=28
=> A= r14-r^2
= r14-r^2
We will now max using derivations
Max value of A will found at A=0
i.e 14-2r=0
r=7
D
Answer: (D) 7
Question: A car is traveling 68 kilometers per hour. How many meters does the car travel in one minute?
(A) 1,250 meters / minute
(B) 1,133 meters / minute
(C) 1,450 meters / minute
(D) 1,550 meters / minute
(E) 1,650 meters / minute
Rationale: Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify
68 kilometers per hour = 68 km/hr
= (68 * 1000 meters) / (60 minutes) = 1,133 meters / minute
correct answer B
Answer: (B) 1,133 meters / minute
Question: In a kilometer race, A beats B by 80 meters or 10 seconds. What time does A take to complete the race?
(A) 290 sec
(B) 190 sec
(C) 199 sec
(D) 115 sec
(E) 193 sec
Rationale: Time taken by B run 1000 meters
= (1000 * 10)/80 = 125 sec.
Time taken by A = 125 - 10 = 115 sec.
Answer: D
Answer: (D) 115 sec
Question: IF 2+3=10 ; 2+5=27 ; 2+7=53 Then 2+11=?
(A) 124
(B) 129
(C) 128
(D) 125
(E) 120
Rationale: 2^0 + 3^2= 1 + 9 = 10
2^1 + 5^2= 2 + 25 = 27
2^2 + 7^2= 4 + 49 = 53
and
2^3 + 11^2= 8 + 121 = 129
ANSWER:B
Answer: (B) 129
Question: Find the no.of ways of arranging the boy and 8 guests at a circular table so that the boy always sits in a particular seat?
(A) 4!
(B) 8!
(C) 10!
(D) 11!
(E) 12!
Rationale: Ans.(B)
Sol. Total number of persons = 9 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 8P8 = 8! Ways ... The number of required arrangements = 8! x 1= 8! = 8! ways
Answer: (B) 8!
Question: The C.P of 15 books is equal to the S.P of 20 books. Find his gain% or loss%?
(A) 16 2/3%
(B) 16 2/8%
(C) 16 2/5%
(D) 16 2/1%
(E) 25%
Rationale: 15 CP = 20 SP
20--- 5 CP loss
100 --- ? => 25% loss.Answer: E
Answer: (E) 25%