mathewhe/aqua_rat huggingface dataset:
Question: A school bus travels from kormangala to Electronic City. There are four children in the bus. Each child has four backpacks with him. There are four dogs sitting in each backpack. Every dog has four puppies with her. All these dogs have four legs, with four toes at each leg.
(A) 5150
(B) 5160
(C) 5170
(D) 5180
(E) 5190
Rationale: 16 backpacks(Each child has 4 backpacks)
64 dogs (Each backpack has 4 dogs)
256 puppies (Each dog has 4 puppies)
Now 256 puppies had total= 256*4 legs =1024 * 4 toes = 4096 toes
64 dogs had total = 64 * 4 legs = 256 * 4 toes =1024 toes
4 chidren had total =4 * 10 toes = 40 toes
So the total toes on bus will be(except driver) = 4096+1024+40= 5160 toes
or
If considering driver answer will be = 5160 + 10 =5170
ANSWER:C
Answer: (C) 5170
Question: A and B are partners in a business. A contributes 1/4 of the capital for 15 months and B received 2/3 of the profit. For how long B's money was used ?
(A) 10
(B) 37
(C) 27
(D) 18
(E) 19
Rationale: Let the total profit be Rs. z. Then,
B's share = Rs. 2z/3, A's share = Rs. ( z - 2z/3 ) = Rs. z/3.
A : B = z/3 : 2z/3 = 1:2
Let the total capital be Rs, X and suppose B's money was used for x months. Then.
(1(x) / 4 * 15) / (3x) / 4 * y) = 1/2 <=> y = (15 * 2 / 3) = 10 .
Thus, B's money was used for 10 months.
Answer: A) 10 months
Answer: (A) 10
Question: Given that E and F are events such that P(E) = 36, P(F) = 24 and P(E n F) = 36,
find P (E|F) and P(F|E)
(A) 5
(B) 8
(C) 2
(D) 6
(E) 12
Rationale: Here, E and F are events
P(E|F) = P(EnF)/P(F) = 36/36 = 1
P(F|E) = P(EnF)/P(E) = 36/24 = 2.
C)
Answer: (C) 2
Question: If after 250 grams of water were added to the 24%-solution of alcohol, the strength of the solution decreased by one-third, how much of the 24%-solution was used?
(A) 180 grams
(B) 220 grams
(C) 250 grams
(D) 350 grams
(E) 500 grams
Rationale: The 24% alcohol solution decreases by 1/3 once the 250 grams of water is added so 250/.08 =3125*.16% (2/3 of 24%) is 500 grams, thus answer is E.
Answer: (E) 500 grams
Question: If 0.5% of A =85 paise, then the value of A is ?
(A) Rs. 170
(B) Rs. 17
(C) Rs. 1.70
(D) Rs. 4.25
(E) None
Rationale: Answer
∵ 0.5/100 of A = 85/100
∴ A = Rs. (85 / 0.5) = Rs. 170
Correct Option: A
Answer: (A) Rs. 170
Question: If six persons sit in a row, then the probability that three particular persons are always together is?
(A) 1/4
(B) 1/8
(C) 1/5
(D) 1/9
(E) 1/2
Rationale: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6!
= 1/5
Answer: Option C
ExplanaC
Answer: (C) 1/5
Question: At what angle the hands of a clock are inclined at 15 minutes past 5?
(A) 135/9
(B) 135/2
(C) 135/1
(D) 135/7
(E) 135/73
Rationale: Sol:
Apply the formula:
θ=∣∣∣30h−112m∣∣∣θ=|30h−112m|
⇒ Angle = 30 × 5 –11/2 × 15 = 150 – 165/2 = 135/2
Answer:B
Answer: (B) 135/2
Question: Two trains 300m and 400m long run at the speed of 36kmph and 18 kmph in opposite directions in parallel tracks. The time which they take to cross each other is?
(A) 5.6sec
(B) 46.67 sec
(C) 10.8sec
(D) 12.6sec
(E) 15sec
Rationale: Relative speed = 36+18 = 54 kmph * 5/18 = 15 m/s
Distance covered in crossing each other = 300+400 = 700m
Required time = 700*1/15=46.67 sec
Answer is B
Answer: (B) 46.67 sec
Question: A specialized type of sand consists of 40% mineral X by volume and 60% mineral Y by volume. If mineral X weighs 3.5 grams per cubic centimeter and mineral Y weighs 3 grams per cubic centimeter, how many grams does a cubic meter of specialized sand combination weigh? (1 meter = 100 centimeters)
(A) 5,500,000
(B) 3,200,000
(C) 55,000
(D) 28,000
(E) 280
Rationale: Let the volume be 1 m^3 = 1m * 1m * 1m = 100cm * 100cm * 100cm = 1,000,000 cm^3
By volume
40% is X = 400,000 cm^3
60% is Y = 600,000 cm^3
By weight,
In 1 cm^3, X is 3.5 gms
In 400,000 cm^3 , X = 3.5 * 400,000 = 1,400,000 grams
In 1 cm^3, Y is 3 gms
In 600,000 cm^3, Y = 3 * 600,000 = 1,800,000 gms
Total gms in 1 m^3 = 1,400,000 + 1,800,000 = 3,200,000
ANSWER:B
Answer: (B) 3,200,000
Question: A car travels uphill at 30 km/hr and downhill at 70 km/hr. It goes 100 km uphill and 50 km downhill. Find the average speed of the car?
(A) 32kmph
(B) 33kmph
(C) 34kmph
(D) 35kmph
(E) 37kmph
Rationale: avg speed=total distance/total time.
total distance traveled=100+50=150km;
time taken for uphill journey=100/30=10/3;
time taken for down hill journey=50/60=5/7;
avg speed=150/(10/3+5/7)=37kmph
ANSWER:E
Answer: (E) 37kmph
Question: If six persons sit in a row, then the probability that three particular persons are always together is -.
(A) 1/5
(B) 1/7
(C) 1/9
(D) 1/2
(E) 2/7
Rationale: 3!4! Required probability = 3!4!/6! = 1/5
ANSWER A
Answer: (A) 1/5
Question: A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is ?
(A) 25/42
(B) 25/49
(C) 25/27
(D) 25/19
(E) 25/25
Rationale: Total fruits = 9
Since there must be at least two apples,
(⁵C₂ * ⁴C₁)/⁹C₃ + ⁵C₃/⁹C₃
=25/42.
Answer:A
Answer: (A) 25/42
Question: Sum of two numbers is 80. Greater number exceeds by 5 from four times of the smaller. Find the numbers?
(A) 65,15
(B) 40,15
(C) 30,20
(D) 35,20
(E) 40,50
Rationale: x + y = 80
x â€“ 4y = 5
x = 65 y = 15
ANSWER A
Answer: (A) 65,15
Question: Two pipes A and B can fill a tank in 12 hours and 15 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
(A) 20 hours
(B) 15 hours
(C) 10 hours
(D) 12 hours
(E) 7 4/9 hours
Rationale: Part filled by A in 1 hour = 1/12
Part filled by B in 1 hour = 1/15
Part filled by (A+B) in 1 hour = 1/12 + 1/15 = 9/60
Both the pipes together fill the tank in 60/9 = 7 4/9 hours
Answer is E
Answer: (E) 7 4/9 hours
Question: If a+ |a| + b= 7 and a+ |b| - b=6 , then a+ b=
(A) 3
(B) 4
(C) 5
(D) 6
(E) 9
Rationale: If a+ |a| + b= 7 and a+ |b| - b=6 , then a+ b=
can be done in 2.3 mins :
there are 4 cases to be tested :
1) a is -ve and b is -ve
substituting in the equation , we get a-a+b=7 and a-b-b=6 solve for a and b we get a=20 and b=7 , so a+b=27 REJECT
2)a is +ve and b is +ve
substitute in the equation, we ger a+a+b=7 and a+b-b=6 solve for a and b we get a=6 and b=-5 ,therefore a+b=1 not on list so REJECT
3) a is -ve and b is +ve
substitute , we get a-a=b=7 and a+b-b=6 solve fo a and b we get a=6 and b=7, a+b=13 not on list so REJECT
4) a is +ve and b is -ve
substitute , we get a+a=b=7 and a-b-b=6 solve for a and b , we get a=4 and b= -1 ,a+b=3 , ANSWER A
Answer: (A) 3
Question: x is a positive integer less than 500. When x is divided by 7, the remainder is 1; when x is divided by 3, the remainder is 2. How many x are there?
(A) 21
(B) 22
(C) 23
(D) 24
(E) 25
Rationale: when x divided by 7 and leave reminder 1. x could be 1,8,15,....
when divided by 3 and leave reminder 2- x could be 2,5,8,....
so x must be of the form 21m+8 where m=0,1,2,.....
first no will be 8 and last no will be 491.
so total no. less than 500 will be 24.
Answer:D
Answer: (D) 24
Question: Tough and Tricky questions: Combinations.
Five contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?
(A) 6
(B) 7
(C) 15
(D) 16
(E) 24
Rationale: Number of ways First-place medal can be awarded to four contestants = 5
Number of ways Second-place medal can be awarded to contestants after awarding First-place medal =3
Therefore number of possibilities = 5 *3 =15
Answer:C
Answer: (C) 15
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
(A) 287 Sec
(B) 190 Sec
(C) 277 Sec
(D) 177 Sec
(E) 667 Sec
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1900 m
T = D/S
T = 1900/10
T = 190 Sec
Answer:B
Answer: (B) 190 Sec
Question: Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. What are the marks obtained by them?
(A) 42, 33
(B) 42, 36
(C) 44, 33
(D) 44, 36
(E) 45, 46
Rationale: Explanation:
Let the marks secured by them be x and (x + 9)
Then sum of their marks = x + (x + 9) = 2x + 9
Given that (x + 9) was 56% of the sum of their marks
=>(x + 9) = 56/100(2x + 9)
=> (x + 9) = 14/25 (2x+9)
=> 25x + 225 = 28x + 126
=> 3x = 99 => x = 33
Then (x + 9) = 33 + 9 = 42
Hence their marks are 33 and 42
Answer: Option A
Answer: (A) 42, 33
Question: On the x-y coordinate plane there is a parabola, y=x(4-x). Which of the following points is in the region that is enclosed by this parabola and the x-axis?
I. (1, 4) II. (2, 3) III. (4, 1)
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I, II, and III
Rationale: Since co-efficient of x^2 is negative, the parabola will be downward facing. So the parabola and the x axis will enclose some points where the y-values of the parabola are positive.
When x = 1, y = 3 lies on the parabola, so (1, 4) will not be enclosed by the parabola and x axis.
When x = 2, y = 4 lies on the parabola, so (2, 3) will lie below it and this point will be enclosed by the parabola and x axis.
When x = 4, y = 0 lies on the parabola, so (4, 1) will not be enclosed by the parabola and x axis.
The answer is B.
Answer: (B) II only
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.75 less, he could have gained 25%. What is the cost price?
(A) 176
(B) 375
(C) 355
(D) 326
(E) 281
Rationale: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
75 ----- ? => 375
Answer: B
Answer: (B) 375
Question: (y^n - b^n) is completely divisible by (y - b), when
(A) n is odd natural number
(B) n is even natural number
(C) n is any natural number
(D) n is prime
(E) None
Rationale: For every natural number n, (y^n - b^n) is completely divisible by (y - b).
C
Answer: (C) n is any natural number
Question: A rectangular with dimensions 35 inches by 45 inches is to be divided into squares of equal size. Which of the following could be a length of a side of the squares?
(A) a) 4 inches
(B) b) 6 inches
(C) c) 5 inches
(D) d) 8 inches
(E) e) 10 inches
Rationale: you need to divide the width and length of the rectangular to equal pieces where L = W
you can solve this using GCF
35=5*7
45=3*3*5
GCF = 5
P.S you can make squares with side of 5
Answer : C
Answer: (C) c) 5 inches
Question: A 8% product yields 10%. The market value of the product is:
(A) Rs. 60
(B) Rs. 40
(C) Rs. 70
(D) Rs. 80
(E) Rs. 50
Rationale: Let the face value of the product is Rs.100
It yields Rs.8
Market value of the stock=(8/10)*100=Rs.80
ANSWER:D
Answer: (D) Rs. 80
Question: Which answer is closest to the √36?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Try some examples.....
4 x 4 = 16
5 x 5 = 25
Answer C
Answer: (C) 6
Question: If positive integer k is divided by 4, the quotient is m and the remainder is 2, then which of the following must be true?
I. k + m is even
II. k cannot be a even number
III. k is divisible by 3
(A) None
(B) I
(C) II
(D) III
(E) I and II only
Rationale: k = 4m+2 = 2(2m+1)
I. k + m = 2(2m+1) + m => even if only m is even, however m can be odd => not always true
II. k can not be a prime: not always true:
m=0 => k=2 : a prime
III. not true if m is even
Ans: none of the above
Answer: (A) None
Question: An choclate store received shipments of ingredients on Monday and Tuesday . Tuesday's shipment had 3 different packages, with an average (arithmetic mean) of 11 and 2/3 pounds. Wednesday's shipment included 7 packages, weighing an average of 9 and 3/7 pounds. What was the average package weight, in pounds, of the shipments received on both days?
(A) 0 and 1/10 pounds
(B) 9 and 6/7 pounds1
(C) 10 and 2/5 pounds
(D) 11 pounds
(E) 11 and 1/7 pounds
Rationale: Solution: Average weight = Total weight/number of packages. The total weight on Monday was 3 * (11 and 2/3 pounds), or 35 pounds. The total weight on Tuesday was 7 * (9 and 3/7 pounds), or 66 pounds. The sum of the weights for both days is 66 + 35, or 101 pounds. The average is 101 pounds/10 packages, or 10 and 1/10 pounds per package.
Answer : A
Answer: (A) 0 and 1/10 pounds
Question: Machine A can process 6000 envelopes in 3 hours. Machines B and C working together but independently can process the same number of envelopes in 2.5 hours. If Machines A and C working together but independently process 3000 envelopes in 1 hour, then how many hours would it take Machine B to process 9800 envelopes.
(A) 2
(B) 3
(C) 4
(D) 6
(E) 7
Rationale: You can either take the amount of work done as the same as Karishma has done or take the work done by each in the same time. I will do the latter
1. Work done in 1 hr by A is 2000 envelopes
2. Work done in 1 hr by A and C is 3000 envelopes
3. So work done in 1 hr by C is 1000 envelopes
4. Work done in 1 hr by B and C is 2400 envelopes
5. So work done in 1 hr by B is 1400 envelopes
6. So to process 9800 envelopes B will take 9800/1400 hrs = 7 hrs
So the answer is choice E
Answer: (E) 7
Question: John deposited $10,000 to open a new savings account that earned 10 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in John’s account 6 months after the account was opened?
(A) $10,100.75
(B) $10,101.75
(C) $10,506.25
(D) $10,201.35
(E) $10,404.25
Rationale: 10 percent annual interest compounded quarterly --> 2.5% in 3 moths.
For the first 3 moths interest was 2.5% of $10,000, so $250;
For the next 3 moths interest was 2.5% of $10,000,plus6.25 earned on previous interest of $250, so $250+$6.25=$256.25;
Total interest for 6 months was $250+$256.25=$506.25, hence balance after 6 months was $10,000+ $506.25=$10,506.25.
Answer: C.
Answer: (C) $10,506.25
Question: A committee of four people is to be chosen from five married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?
(A) 16
(B) 48
(C) 64
(D) 80
(E) 96
Rationale: Each couple can send only one representativeto the committee. Let's see in how many ways we can choose 4 couples (as there should be 4 members) out of 4 to send only one representatives to the committee: 5c4=5.
But each of these 5 couples can send two persons (husband or wife): 2*2*2*2=2^4=16.
Total # of ways: 5C4*2^4=80
Answer: E.
Answer: (D) 80
Question: Timothy leaves home for school, riding his bicycle at a rate of 9 miles per hour. Fifteen minutes after he leaves, his mother sees Timothy’s math homework lying on his bed and immediately leaves home to bring it to him. If his mother drives at 27 miles per hour, how far (in terms of miles) must she drive before she reaches Timothy?
I think is a 700 level problem but I tag it as 600/700, let me know. Either way I hope in an explanationThanks
(A) 27/8
(B) 3
(C) 4
(D) 9
(E) 12
Rationale: In 15 mins, Timothy travels=9/4 miles.
Now, let his mother takes x hours to reach him, traveling at 27mph.
So, 27x=9x+9/4
x=1/8 hrs.
Thus, the distance traveled by his mother to reach= 27*1/8=27/8miles. Ans A
Answer: (A) 27/8
Question: Sandy invested a certain sum of money at 12% p.a. simple interest for 'n' years. At the end of 'n' years, Sandy got back 4 times the original investment. What is the value of n?
(A) 20
(B) 25
(C) 30
(D) 35
(E) 40
Rationale: n* 0.12 * principal + principal = 4 * principal
n * 0.12 = 3
n = 25 years
The answer is B.
Answer: (B) 25
Question: A train 550 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
(A) 5 sec
(B) 6 sec
(C) 7 sec
(D) 10 sec
(E) 30 sec
Rationale: Solution
Speed of train relative to man =(60+6) km/hr= 66km/hr
=(66x5/18) m/sec =(55/3) m/sec
∴ Time taken to pass the man = (550 x 3/55)sec = 30 sec
Answer E
Answer: (E) 30 sec
Question: An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
(A) 2%
(B) 2.02%
(C) 4%
(D) 4.04%
(E) 5%
Rationale: Correct value is 100x100.
Measured value is 102x102.
Therefore ERROR Value is (102x102)-(100x100) = 404.
Error% = (error value/ true value)*100.
= (404/100x100)x100 = 4.04.
answer :D
Answer: (D) 4.04%
Question: A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 200 revolutions. How many revolutions does the second wheel make in covering d feet?
(A) 200x/y
(B) 200y - x
(C) 200x - y
(D) 200y/x
(E) 200xy
Rationale: First Wheel with diameter x inches ----> So the circumference = x*pi --------- (1)
Second Wheel with diameter y inches ----> So the circumference = y*pi --------- (2)
Revolutions = distance/circumference
So, from equation (1)
200 = d/(x*pi)
d = 200 * x * pi ---------- (3)
From equation (2)
Revolutions = d/(y*pi) = (100 * x * pi) / (y*pi) = 200x/y
Answer (A)
Answer: (A) 200x/y
Question: A certain barrel, which is a right circular cylinder, is filled to capacity with 300 gallons of oil. The first barrel is poured into a second barrel, also a right circular cylinder, which is empty. The second barrel is twice as tall as the first barrel and has twice the diameter of the first barrel. If all of the oil in the first barrel is poured into the second barrel, how much empty capacity, in gallons, is left in the second barrel?
(A) There is no empty capacity
(B) 2100 gallons
(C) 2300 gallons
(D) 2100 gallons
(E) 2800 gallons
Rationale: Radius of first cylinder=r, diameter=2r, height=h
Radius of second cylinder=2r, diamter=2d and height=2h
Volume of first cylinder=pie (r^2)*h=300
Volume of second cylinder=pie(2r^2)2h
Put the value of pie (r^2)*h=300 in the second cylinder,volume= pie (r^2)*4*2=300*8=2400 gallons
Empty capacity=2100 gallons
Answer D
Answer: (D) 2100 gallons
Question: Tommie spent six lucky days in Las Vegas. On his first day he won a net amount of only $20, but on each of the following days, the daily net amount he won grew by d dollars. If Tommie won a total net amount of $1620 during his stay in Las Vegas, how much did he win on the last day?
(A) 330
(B) 500
(C) 520
(D) 540
(E) 620
Rationale: I drew a diagram:
1 - $20
2 -
3 -
4 - $320
5 -
6 -
Total: $1,620
Between 1 and 6 are 5 days where he won $1,600. This means he averaged $320 per day (1600/5). You can put $320 by 4 because it's the middle number. Now you just find the two points betwenn $20 and $320 (320-20 = 300 / 3 = 100). So each day, he earned $100 more. This means on day 6, tommie earned$520. Answer choice C.
Answer: (C) 520
Question: If the line L passes through the point (3,n) and (n,3), where n is not equal to 3, which of the following must be true?
1. Line L must passes through the first quadrant.
2. Line L does pass the origin.
3.The slope of L is negative
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
Rationale: Slope of the given line= 3-n/n-3
Given information is that n is not equal to 3, that means n <3 or n>3. In both these conditions the slope will be negative.
1) n<3 (n=2)
3-2/2-3= -1
2) n<3 (n= 0)
3-0/0-3= -1
3) n<3 (n=-3)
3+3/ -3-3= -2/3
4) n>3
3-4/4-3= -1
Answer C
Answer: (C) III only
Question: In an examination, 35% of total students failed in Hindi, 45% failed in English and 20% in both. The percentage of these who passed in both the subjects is :
(A) 23
(B) 37
(C) 28
(D) 40
(E) 81
Rationale: Explanation:
Formula n(a∪b) = n(a) + n(b) − n(a∩b)
Fail in Hindi or English = 35 + 45 – 20 = 60
Therefore students who passed = 100 – 60 = 40.
Answer: D
Answer: (D) 40
Question: A can do a piece of work n 7 days of 9 hours each and B alone can do it in 6 days of 7 hours each. How long will they take to do it working together 8 2/5 hours a day?
(A) 3 days
(B) 6 days
(C) 2 days
(D) 8 days
(E) 4 days
Rationale: A can complete the work in (7*9) = 63 days
B can complete the work in (6*7) = 42 days
--> A’s one hour’s work = 1/63 and B’s one hour work = 1/42.
(A+B)’s one hour work = 1/63+1/42 = 5/126
Therefore, Both can finish the work in 126/5 hours.
Number of days of 8 2/5 hours each = (126*5/(5*42)) = 3 days
Answer : A
Answer: (A) 3 days
Question: What is the probability that in the rearrangements of the word AMAZED, the letter ’E’ is positioned in between the 2 ’A’s (Not necessarily flanked)?
(A) 1/6
(B) 1/4
(C) 1/3
(D) 1/5
(E) 1/8
Rationale: In any rearrangement of the word, consider only the positions of the letters A, A and E.
These can be as A A E, A E A or E A A.
Therefore, effectively one-third of all words will have ’E’ in between the two ’A’s.
ANSWER:C
Answer: (C) 1/3
Question: If b does not equal zero, and ab = b/6, what is the value of a?
(A) A)1/6
(B) B)1/4
(C) C)1/3
(D) D)1/2
(E) of the above
Rationale: Explanation:
To solve for a, divide both sides of the equation by b: ab = b/6
(ab)/b = (b/6)/b
a = (b/6)*1/b
a = 1/6
Answer: (A).
Answer: (A) A)1/6
Question: How many ways are there to split a group of 8 boys into two groups of 4 boys each? (The order of the groups does not matter)
(A) 35
(B) 40
(C) 42
(D) 44
(E) 46
Rationale: the combination is 8C4 /2
= 8!/4!*4! *2 = 35
A
Answer: (A) 35
Question: If A is thrice as fast as B and together can do a work in 12 days. In how many days A alone can do the work?
(A) 16
(B) 42
(C) 28
(D) 54
(E) 45
Rationale: A’s one day’s work= 1/X
B’s one day’s work= 1/3x
A + B’s one day’s work= 1/x + 1/3x = 1/12
= 3+1/3x = 4/3x = 1/12
x = 12*4/3 = 16
ANSWER:A
Answer: (A) 16
Question: Length of a rectangular plot is 28 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
(A) 54 m
(B) 64 m
(C) 74 m
(D) 84 m
(E) 94 m
Rationale: Let breadth = x metres.
Then, length = (x + 28) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 28) + x] = 200
2x + 28 = 100
2x = 72
x = 36.
Hence, length = x + 28 = 64 m
B
Answer: (B) 64 m
Question: The sum of two number is 25 and their difference is 13. Find their product.
(A) 104
(B) 114
(C) 315
(D) 325
(E) 271
Rationale: Let the numbers be x and y.
Then, x + y = 25 and x - y = 13.
4xy = (x + y)2 - (x- y)2
= (25)2 - (13)2
= (625 - 169)
= 456
xy = 114.
Answer: B
Answer: (B) 114
Question: Two dice are tossed. The probability that the total score is a prime number is
(A) 2/13
(B) 5/7
(C) 31/7
(D) 6/7
(E) 5/12
Rationale: n(S)=36
E= {(1,1),(1,2), (1,4),….(6,5)}
n(E)=15
P(E)=15/36
=5/12
Ans: E
Answer: (E) 5/12
Question: A certain elevator has a safe weight limit of 2,500 pounds. What is the greatest possible number of people who can safely ride on the elevator at one time with the average (arithmetic mean) weight of half the riders being 200 pounds and the average weight of the others being 230 pounds?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: Lets assume there are 2X people.
Half of them have average weight of 200 and other half has 230.
Maximum Weight is = 2500
So 200*X + 230*X = 2500
=> 430X = 2500
=> X is approximately equal to 6.
So total people is 2*6 = 12
We are not taking 12 as answer because say 11th person has minimum of 180 weight then
200*6 + 230*6 = 2580 (Which is more than 2500)
Answer E.
Answer: (E) 11
Question: The Royals softball team played 75 games and won 55 of them. What percent of the games did they lose? (round to the nearest tenth)
(A) 26.7% games lost
(B) 27.7% games lost
(C) 25.7% games lost
(D) 20.7% games lost
(E) 22.7% games lost
Rationale: Total 100%=75
Won=55
Lost=20
75-55
=20
x/100=20/75
Multiply the opposites:
100 x 20 = 2000
Divide by the remaining number:
26.667/2000.000
75
26.7% games lost (rounded to tenth)
correct answer A
Answer: (A) 26.7% games lost