mathewhe/aqua_rat huggingface dataset:
Question: On a certain transatlantic crossing, 15 percent of a ship's passengers held round-trip tickets and also took their cars aboard the ship. If 60 percent of the passengers with round-trip tickets did not take their cars aboard the ship, what percent of the ship's passengers held round-trip tickets?
(A) 33 1/3%
(B) 40%
(C) 37.5%
(D) 60%
(E) 66 2/3%
Rationale: On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?
Solution: Let total number of passengers be 100
According to Q stem 40% of passengers who had round-trip tics have taken cars - let number of passengers with round trip be X then
40% of X = 15 => X= 37.5.
Answer C
Answer: (C) 37.5%
Question: Look at this series: 5.2, 4.8, 4.4, 4, ... What number should come next?
(A) 4.1
(B) 3.6
(C) 2.6
(D) 5.0
(E) 5.5
Rationale: B
3.6
In this simple subtraction series, each number decreases by 0.4.
Answer: (B) 3.6
Question: If n is an integer, what is the greatest possible value for n that would still make the following statement true: 11*10^n < 1/10 ?
(A) –4
(B) –3
(C) –2
(D) –1
(E) 0
Rationale: Just putting values, the LHS becomes
n=0 --> 11
n=-1 --> 11/10
n=-2 --> 11/100
n=-3 --> 11/1000
Anything lower will be smaller than 11/1000. n=-2, equality doesnt hold but it does for n=-3.
Answer is B.
Answer: (B) –3
Question: The area of a circular field is 17.56 hectares. Find the cost of fencing it at the rate of Rs. 3 per metre approximately
(A) 4457
(B) 4567
(C) 4235
(D) 4547
(E) 4675
Rationale: Explanation:
Area = (17.56 x 10000) m2= 175600 m2.
ΠR2 = 175600 ⇔ (R)2 = (175600 x (7/22)) ⇔ R = 236.37 m.
Circumference = 2ΠR = (2 x (22/7) x 236.37) m =1485.78 m.
Cost of fencing = Rs. (1485.78 x 3) = Rs. 4457.
Answer: Option A
Answer: (A) 4457
Question: The population of a town is 8000. It decreases annually at the rate of 20% p.a. What will be its population after 2 years?
(A) 5100
(B) 5120
(C) 5130
(D) 5140
(E) 5160
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
8000 × 80/100 × 80/100 = 5120
B
Answer: (B) 5120
Question: Statement: "In order to bring punctuality in our office, we must provide conveyance allowance to our employees."
Assumptions:
1)Conveyance allowance will not help in bringing punctuality.
2)Discipline and reward should always go hand in hand.
(A) Only assumption I is implicit
(B) Only assumption II is implicit
(C) Either I or II is implicit
(D) Neither I nor II is implicit
(E) Both I and II are implicit
Rationale: Assumption I goes against the statement. So, it is not implicit. The allowance will serve as a reward to the employees and shall provoke them to come on time. So, II is implicit.
B)
Answer: (B) Only assumption II is implicit
Question: Steel company has four empty trucks that will head out in the morning, all four to the same destination. The clerk has four different boxes to ship to that same destination. All four boxes could go on any one of the trucks, or the boxes could be split up into any groupings and given to the trucks in any combinations (ie. two to one truck, one to another, and one to another). In how many different ways could the boxes be put on the four trucks?
(A)  16
(B)  64
(C)  256
(D)  576
(E)  4096
Rationale: MAGOOSHOFFICIAL SOLUTION:
Steel company has four empty trucks that will head out in the morning, all four to the same destination.Where we put one box has absolutely no bearing on where we put any of the other boxes. The placement of the four boxes is completely independent of one another. For each box, we have four choices.
N = 4*4*4*4 = 16*16 = 256
Answer = (C)
Answer: (C)  256
Question: If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 18 more than n. What is y in terms of x ?
(A)  20 - x
(B)  18 - x
(C)  x + 18
(D)  x + 2
(E)  x - 2
Rationale: Original Digits=xy i.e. Number=10x+y
After reversing the digits:
Digits=yx i.e. Number=10y+x
10y+x is 9 more than 10x+y
10x+y+18=10y+x
10x-x+18=10y-y
9x+18=9y
x+2=y
OR
y=x+2
Ans:D
Answer: (D)  x + 2
Question: The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 15, how many more dollars, in terms of x, will it cost per person?
(A)  x/6
(B)  x/16
(C)  x/40
(D)  3x/40
(E)  3x/80
Rationale: Choose x as a multiple of 16, I chose 64:
So for 10 people, that's 6.4 each and for 16 people it's 4 USD each... Pick one of the options that gives you 6.4 - 4 = 2.4... The answer is D.
Answer: (D)  3x/40
Question: Reb 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 Reb 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: Reb 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: How many pieces of 0.40 meteres can be cut from a rod 47.5 meteres long
(A) 100
(B) 118
(C) 120
(D) 125
(E) 70
Rationale: Explanation:
We need so simple divide 47.5/0.40,
=(4750/40) = 118
Option B
Answer: (B) 118
Question: The average age of a class of 20 students is 18 years. The average increased by 2 when the teacher's age also included. What is the age of the teacher?
(A) 40 years
(B) 41 years
(C) 42 years
(D) 43 years
(E) 44 years
Rationale: If age of the teacher was 18, average would not have changed.
Since average increased by 2,
Age of the teacher=18+22×1=40
ANSWER:A
Answer: (A) 40 years
Question: If 3x=9y=z, what is x+y, in terms of z?
(A) z/2
(B) 2z
(C) z/3
(D) 3z/5
(E) 4z/9
Rationale: 3x=9y=z
x = z/3
and y = z/9
x+y = z/3 + z/9 = 4z/9
Answer is E
Answer: (E) 4z/9
Question: Machine A and machine B are each used to manufacture 660 sprockets. It takes machine A 10 hours longer to produce 660 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produces?
(A) 6
(B) 6.6
(C) 60
(D) 100
(E) 110
Rationale: B takes x hours
A takes x + 10 hours
rate of A = 660/x+10
rate of B = 660/x
thus, 660/x = (660/x+10)*1.10
x = 100
so B = 100
A = 110 sprockets per hour
660/110 = 6
ANSWER:A
Answer: (A) 6
Question: If a book is sold at 8% profit instead of 8% loss, it would have brought Rs 12 more. Find out the cost price of the book
(A) Rs 75
(B) Rs 72
(C) Rs 60
(D) Rs 70
(E) Rs 80
Rationale: Let C.P. of the book be Rs. ’X’
Given, 1.08 X - 0.92X = 12
=> 0.16 X = 12 = 12/0.16 = Rs 75
ANSWER:A
Answer: (A) Rs 75
Question: Two trains 140 m and 170 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) 11.16 sec
(B) 11.8 sec
(C) 27.7 sec
(D) 10.8 sec
(E) 17.8 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 170 = 310 m.
Required time = 310 * 9/250 =11.16 sec.
Answer: A
Answer: (A) 11.16 sec
Question: A and B together can do a work In 2 days. A alone can do it in 12 days. What time B will take to do the work alone?
(A) 2.4 days
(B) 8 days
(C) 1.2 days
(D) 1.0 days
(E) 5 days
Rationale: Explanation:
A and B 1day's work = 1/2
A alone can do 1day's work = 1/12
what time B will take to do the work alone?
B = (A+B) - A = (1/2) - (1/12) = 2.4 Days
Answer: Option A
Answer: (A) 2.4 days
Question: In the following sequence: [x, y, z, 5, 7, 16, 28] each number is equal to the sum of the three numbers preceding it. What is x-y?
(A) 6
(B) 3
(C) 4
(D) 5
(E) 7
Rationale: lets start from z, as per the question stem
z + 5 + 7 = 16
-->> z= 4
similarly, y + 4 + 5 = 7
--> y = -2
similarly,, x + -2 + 4 = 5
--> x = 3
hence , x-y = 3+2 = 5
ANSWER:D
Answer: (D) 5
Question: A computer store offers employees a 15% discount off the retail price. If the store purchased a computer from the manufacturer for $500 dollars and marked up the price 15% to the final retail price, how much would an employee save if he purchased the computer at the employee discount (15% off retail price) as opposed to the final retail price.
(A) 52.5
(B) 54.5
(C) 55.5
(D) 57.5
(E) 59.5
Rationale: Cost price=500
Profit=15% =15% of 500=75
selling price=CP+ Profit
SP=575
a Discount of 10% to employees means 10% off on 575
so 10% of 575= 57.5
Ans D
Answer: (D) 57.5
Question: A shop owner sells 40mtr of cloth and gains SP of 10 mtrs. Find the gain %?
(A) 33.33%
(B) 40%
(C) 50%
(D) 66.67%
(E) 70%
Rationale: Here, selling price of 10 m cloth is obtained as profit.
Profit of 10 m cloth = (S.P. of 40 m cloth) – (C.P. of 40 m cloth)
Selling price of 30 m cloth = Selling Price of 40 m of cloth
Let cost of each metre be Rs. 100.
Therefore, cost price of 30 m cloth = Rs. 3000 and S.P. of 30 m cloth = Rs. Rs. 4000
Profit% = 10/30 × 100 = 33.33%
Profit of 33.33% was made by the merchant.
A
Answer: (A) 33.33%
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
(A) 77
(B) 66
(C) 20
(D) 21
(E) 24
Rationale: M = 15
S = 5
DS = 15 + 5 = 20
Answer: C
Answer: (C) 20
Question: Solve the given two equations and find the inequality of X and Y. (a) X^2- 365 = 364 and (b) y- (324) ^(1/2) = (81)^(1/2)
(A) If x>y
(B) If x>=y
(C) If x<y
(D) If x<=y
(E) x=y or relationship cannot be established
Rationale: Solution:-
X=4,-5
Y= -4,6
E
Answer: (E) x=y or relationship cannot be established
Question: In a group of 28 junior high school students, 5 take French, 10 take Spanish, and 4 take both languages. The students taking both French and Spanish are not counted with the 7 taking French or the 10 taking Spanish. How many students are not taking either French or Spanish?
(A) 7
(B) 13
(C) 9
(D) 12
(E) 10
Rationale: B
13
Add 1 + 10 + 4 to get 15.
Then subtract 21 from the total students ⇒ 28 – 15 = 13.
Answer is B
Answer: (B) 13
Question: A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 15 days before the project is completed, in how many days total will the project be completed?
(A) 18
(B) 21
(C) 24
(D) 27
(E) 30
Rationale: A's rate is 1/20 of the project per day.
B's rate is 1/30 of the project per day.
The combined rate is 1/12 of the project per day.
In the last 15 days, B can do 1/2 of the project.
Thus A and B must complete 1/2 of the project, which takes 6 days.
The total number of days is 6 + 15 = 21.
The answer is B.
Answer: (B) 21
Question: If each participant of a chess tournament plays exactly one game with each of the remaining participants, then 171 games will be played during the tournament. What is the number of participants?
(A) 15
(B) 16
(C) 17
(D) 18
(E) 19
Rationale: Let n be the number of participants.
The number of games is nC2 = n*(n-1) / 2 = 171
n*(n-1) = 342 = 19*18 (trial and error)
The answer is E.
Answer: (E) 19
Question: Henry gives a certain amount to his friend at 12% p.a. simple interest. If he wants to get thrice the amount given how many years does it take?
(A) 16 years 8 months
(B) 12 years
(C) 10 years 7 months 4 days
(D) 15 years
(E) 20 years
Rationale: Solution: simple interest question
B=A[1+ (tr/100)]; where A is principal amount, B final amount, t time in years and r interest rate
after putting the values 12
3= [1+(12t/100)]
t= 50/3 which is (48+2)/3= 16 + 2/3 means 16 years and (12*2)/3 = 8 months.
Answer is A
Answer: (A) 16 years 8 months
Question: A good train and a passenger train are running on parallel tracks in the same direction. The driver of the goods train observes that the passenger train coming from behind overtakes and crosses his train completely in 60 sec. Whereas a passenger on the passenger train marks that he crosses the goods train in 40 sec. If the speeds of the trains be in the ratio 1:2. Find the ratio of their lengths.
(A) 2:1
(B) 3:1
(C) 5:2
(D) 1:1
(E) None of these
Rationale: Explanation :
Let, the speeds of the two trains be s and 2s m/s respectively.
Also, suppose that the lengths of the two trains are P and Q metres respectively.
Then,
=>(P+Q)/(2s−s)=60. --------------(1)
And,
=>P/(2s−s)=40. --------------(2)
On dividing (1) by (2), we get :-
=>(P+Q)/P=60/40.
The required ratio is P:Q = 2 : 1.
Answer : A
Answer: (A) 2:1
Question: Tim came second in Math. When his mother asked him how much he had scored, he answered that he got the sum of the first 5 even numbers. His mother immediately worked out the answer. How much had he scored in Math?
(A) 80
(B) 30
(C) 40
(D) 70
(E) 60
Rationale: B
30
Sum = (n x n) + n
Hence, 5 x 5 = 25 + 5 = 30
Answer: (B) 30
Question: In what ratio must water be mixed with milk to gain 16(2/3)% on selling the mixture at cost price?
(A) 1 : 6
(B) 6 : 1
(C) 2 : 3
(D) 4 : 3
(E) 3 : 2
Rationale: Explanation:
Let C.P. of 1 litre milk be Re. 1.
S.P. of 1 litre of mixture = Re.1, Gain =	50/3 %
C.P. of 1 litre of mixture =(100 x	3/350 x 1)=6/7
By the rule of alligation, we have:
Ratio of water and milk =	1/7:6/7=1:6.
ANSWER IS A
Answer: (A) 1 : 6
Question: What will be the difference between simple interest and compound interest @ 10% per annum on a sum of Rs. 1000 after 3 years?
(A) 22
(B) 77
(C) 26
(D) 19
(E) 31
Rationale: Explanation:
S.I. = Rs. [(1000 x 10 x 3) / 100] = Rs. 300
C.I. = Rs. [1000 x (1 + (10/100))3 - 1000] = Rs. 331
Difference = Rs. (331 - 300) = Rs. 31
ANSWER:E
Answer: (E) 31
Question: 3 candidates in an election and received 1256, 7636 and 11628 votes respectively. What % of the total votes did the winning candidate gotin that election?
(A) 56.7%
(B) 55%
(C) 57%
(D) 60%
(E) 62%
Rationale: Total number of votes polled = (1256 + 7636 + 11628) = 20520
So, Required percentage = 11628/20520 * 100 = 56.7%
A
Answer: (A) 56.7%
Question: What is the smallest number which when increased by 3 is divisible by 9, 70, 25 and 21?
(A) 2927
(B) 3147
(C) 3387
(D) 3567
(E) 3797
Rationale: When increased by 3, the number must include at least 2*3^2*5^2*7 = 3150
The answer is B.
Answer: (B) 3147
Question: What is the difference between the C.I. on Rs. 4000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly?
(A) s.2.04
(B) s.2.08
(C) s.1.63
(D) s.2.83
(E) s.2.42
Rationale: C.I. when interest is compounded yearly
= [4000 * (1 + 4/100) * (1 + (1/2 * 4)/100]
= 4000 * 26/25 * 51/50 = Rs. 4243.2
C.I. when interest is compounded half-yearly
= [4000 * (1 + 2/100)2]
= (4000 * 51/50 * 51/50 * 51/50)
= Rs. 4244.83 Difference
= (4244.83 - 4243.2)
= Rs.1.63.
Answer: C
Answer: (C) s.1.63
Question: Of the five-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two?
(A) 24440
(B) 36440
(C) 72440
(D) 181440
(E) 216440
Rationale: Of the five-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two?
A. 24
B. 36
C. 72
D. 144
E. 216
Choosing the digit for p - 9 ways;
Choosing the digit for q - 8 ways;
Choosing the digit for r - 7 ways;
Choosing the digit for s - 6ways;
# of permutations of 3 digits in ppqrs - 5!/2!
Total: 9*8*7*6*5!/2!=181440.
Answer: D.
Answer: (D) 181440
Question: Jim is twice as old as Stephanie, who, four years ago, was three times as old as Kate. If, five years from now, the sum E of their ages will be 51, how old is Stephanie ?
(A) 6
(B) 10
(C) 14
(D) 20
(E) 24
Rationale: 1) take C (14y.o.), so mean that S=14, J=28, their sum itself is 42+10 years from now is 52, it is over the 51,
so eliminate C,D,E
2) take B (10y.o.),E= meaning S=10,J=20, so 20+10+10=40 and for K=10-4/3=2+9=11, finally 40+11=51. It is correct
B
Answer: (B) 10
Question: Two years ago, John put $5,000 into a savings account. At the end of the first year, his account had accrued $500 in interest bringing his total balance to $5,500. The next year, his account balance increased by 10%. At the end of the two years, by what percent has John's account balance increased from his initial deposit of $5,000 ?
(A) 19%
(B) 21%
(C) 20%
(D) 22%
(E) 25%
Rationale: investment 5000 dollars
1 st year total gained = 500
total amount end of first year = 5500
second year account increased by 10 % = 5500*0.1 = 550
therefore total amount by second year end = 6050
so total percentage increase in money = (6050-5000)*100/5000 = 21 %
Correct Answer B=21%
Answer: (B) 21%
Question: if 1 is absent rest of people can be divided into 6 equal parts if 2 is absent rest of them are divided into 7 equal parts ,how many students are present
(A) 34
(B) 35
(C) 36
(D) 37
(E) 38
Rationale: x-1/6=(x-2)/7+1,solve it ans 37
ANSWER:D
Answer: (D) 37
Question: If the product of 12 integers is negative, at most how many of the integers can be negative?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 11
Rationale: The product of12 integers is negative
Thus an odd number of integers need to be negative to have a negative product
We are asked at most how many are required.
So, the highest odd integer before 6,i.e. 11
Correct Option : E
Answer: (E) 11
Question: The simple interest on a sum of money is 4/9 of the principal and the number of years is equal to the rate percent. Find the rate and the time?
(A) 6 2/3%
(B) 6 2/8%
(C) 6 9/3%
(D) 6 2/3%
(E) 6 2/1%
Rationale: 4/9 P = (P*R*R)/100
R = 20/3 = 6 2/3%
Answer: A
Answer: (A) 6 2/3%
Question: The length and breadth of a rectangle is increased by 10% and 25% respectively. What is the increase in the area?
(A) 67.5%
(B) 37.5%
(C) 77.5%
(D) 47.5%
(E) 27.5%
Rationale: 100 * 100 = 10000
110 * 125 = 13750
-----------
3750
10000 ------ 3750
100 ------- ? => 37.5%
Answer:B
Answer: (B) 37.5%
Question: A certain ornaments was marked down 10% the first week and another 30% the next week. What percent of the regular price was the final cost of the ornaments after the two markdowns?
(A) 30%
(B) 36%
(C) 40%
(D) 63%
(E) 64%
Rationale: If the price of the ornament is 100, and it is marked down by 10% then by 70% or charged 90% of the price first and 70% of the price of reduced price, the final price is :-
100*70*90/10000= 63
63% is the final price of old price.
D is the answer
Answer: (D) 63%
Question: A number x is 4 times another number y. The percentage that y is less than x is
(A) 12.5%
(B) 75%
(C) 80%
(D) 11%
(E) 1%
Rationale: Say y=1 and x=4.
Then y=1 is less than x=4 by (4-1)/4*100=3/4*100=75%.
Answer: B.
Answer: (B) 75%
Question: Two trains A and B are 100 m and 150 m long and are moving at one another at 54 Km/hr and 36 Km/hr respectively. Arun is sitting on coach B1 of train A. Calculate the time taken by Arun to completely cross Train B.
(A) 10 s
(B) 6 s
(C) 4 s
(D) 8 s
(E) 12 s
Rationale: DETAILED SOLUTION
Speed of A = 54∗1000/60∗60 = 15 m/s
Speed of B = 36∗1000/60∗60 = 10 m/s
Relative speed = S1 + S2 = 15 + 10 m/s = 25 m/s
The length that needs to be crossed = length of train B = 150 m. Therefore time taken = 150/25 = 6s.
What is the time taken for trains to completely cross each other? The length that needs to be crossed = 100 + 150 = 250 m. Time taken = 250/25 = 10 s.
CORRECT ANSWER B.
Answer: (B) 6 s
Question: What is x if 2x - y = 14 and y = 2?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 14
Rationale: Substitute y by 2 in 2x - y = 14
2x - 2 = 14
2x = 16
If we substitute x by 8 , we have 2(8) = 16. Hence
x = 8 correct answer B
Answer: (B) 8
Question: The number of positive integers valued pairs (x, y) satisfying 4x -17y = 1 and x <= 1000 (x is less than or equal to 1000) is
(A) fifty nine
(B) 57
(C) 55
(D) 58
(E) 60
Rationale: 4x-17y=1
y=(4x-1)/17
x has to be a positive integer such that 1 <=x<=1000(4x-1) is a factor of 17 so that y is also a positive integer
So we need to know how many numbers in the set {3,7,11,15,....,3999} are divisible by 17
Lets try to observe the pattern
1. 3 mod 17 = 3
2. 7 mod 17 = 7
3. 11 mod 17 = 11
4. 15 mod 17 = 15
5. 19 mod 17 = 2
6. 23 mod 17 = 6
7. 27 mod 17 = 10
8. 31 mod 17 = 14
9. 35 mod 17 = 1
10. 39 mod 17 = 5
11. 43 mod 17 = 9
12. 47 mod 17 = 13
13.51 mod 17 = 0
14. 55 mod 17 = 4
15. 59 mod 17 = 8
16. 63 mod 17 = 12
17. 67 mod 17 = 16
... and after this the remainders will repeat (this is no co-incidence that the cyclicity is also 17)
So the right choices are x=13,13+17,13+17+17,.....
The number of such numbers is 59 (highest one being 999) A
Answer: (A) fifty nine
Question: A trader marks his books 40% more than the cost price. If he allows 40% discount, then find his gain or loss percent?
(A) 2% profit
(B) 16% loss
(C) 4% loss
(D) No profit No loss
(E) None of these
Rationale: Let CP of an book = 100
MP of an book = 140
Discount 40 % on 140 = 56
SP of the book = 140 - 56 = 84
loss = 16%
Answer : B
Answer: (B) 16% loss
Question: In the x- y plane, there are 4 points (0,0), (0,4), (8,4), and (8,0). If these 4 points makes a rectangle, what is the probability that x+y<4?
(A) 1/2
(B) 1/3
(C) 2/3
(D) 1/4
(E) 2/5
Rationale: The line y=-x+4 intersects the rectangle and these three points of intersection (0,0), (0,4) and (4,0) form a triangle.
The points below the line y=-x+4 satisfy x+y<4.
The area of this triangle is (1/2)(4)(4)=8
The area of the rectangle is 32.
P(x+y<4) = 8/32 = 1/4
The answer is D.
Answer: (D) 1/4
Question: A man can row his boat with the stream at 10 km/h and against the stream in 6 km/h. The man's rate is?
(A) 2 kmph
(B) 7 kmph
(C) 98 kmph
(D) 6 kmph
(E) 4 kmph
Rationale: DS = 10
US = 6
S = ?
S = (10 - 6)/2 = 2 kmph
Answer: A
Answer: (A) 2 kmph
Question: The number of boys in a class is three times the number of girls. Which one of the following numbers cannot represent the total number of children in the class ?
(A) 48
(B) 44
(C) 42
(D) 40
(E) 38
Rationale: Explanation:
Let number of girls = x and number of boys = 3x.
Then, 3x + x = 4x = total number of students.
Thus, to find exact value of x, the total number of students must be divisible by 4.
Answer: C
Answer: (C) 42
Question: Find the area of a parallelogram with base 24 cm and height 16 cm?
(A) 298 cm2
(B) 384 cm2
(C) 278 cm2
(D) 286 cm2
(E) 276 cm2
Rationale: Area of a parallelogram = base * height = 24 * 16
= 384 cm2
Answer:B
Answer: (B) 384 cm2
Question: 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be:
(A) 20 cm
(B) 23 cm
(C) 25 cm
(D) 30 cm
(E) 32 cm
Rationale: L*b*h=Total water displaced=200(given)
To find height i.e rise in the water level
h=200/L*B
H=25cm
answer :C
Answer: (C) 25 cm
Question: Nails and screws are manufactured at a uniform weight per nail and a uniform weight per screw. If the total weight of one screw and one nail is half that of 6 screws and one nail, then the total weight of 3 screws, and 3 nails is how many times that of 1 screws and 5 nails?
(A) a. 4
(B) b. 5/2
(C) c. 2
(D) d. 3/2
(E) e. 5/4
Rationale: let the weight of nail be n and that of screw be s..
so s+w=1/2 * (6s+1n)...
or 1n = 4s..
lets see the weight of 3 s and 3n= 3s+3*4s=15s..
and weight of 1s and 5n= 1s+5*1s=6s..
ratio= 15s/6s=15/6=5/2
B
Answer: (B) b. 5/2
Question: A grocery shop has a sale of Rs. 6535, 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) 4857
(B) 4184
(C) 4012
(D) 4891
(E) 5291
Rationale: Let the sale in the sixth month =x
Then
(6535+6927+6855+7230+6562+x)/6 =6500
=>6535+6927+6855+7230+6562+x =6×6500
=> 34109+x=39000
=> x=39000−34109
=4891
ANSWER:D
Answer: (D) 4891