divelab/Sys2Bench huggingface dataset:
Question: Martin buys a pencil and a notebook for 80 cents. At the same store, Gloria buys a notebook and an eraser for $1.15 cents, and Zachary buys a pencil and an eraser for 75 cents. How many cents would it cost to buy three pencils, three notebooks, and three erasers? (Assume that there is no volume discount.)
Options:
A)325
B)345
C)365
D)385
E)405
Rationale: pencil + notebook = 80
notebook + eraser = 115
pencil + eraser = 75
Let's add all three equations.
2 pencils + 2 notebooks + 2 erasers = 270 cents
The cost to buy 3 of each would be (3/2)(270) = 405
The answer is E.
Answer: E
Question: A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. If field has a length that is twice its width, find the area of the field in square meters.
Options:
A)70,000 square meters
B)60,000 square meters
C)50,000 square meters
D)20,000 square meters
E)30,000 square meters
Rationale: Let us first find the distance d jogged
distance = rate* time = (12 km / hr) ? 30 minutes
= (12 km/hr) * 0.5 hr = 6 km
The distance of 6 km corresponds to 10 perimeters and therefore 1 perimeter is equal to
6 km / 10 = 0.6 km = 0.6 * 1000 meters = 600 meters
Let L and W be the length and width of the field. The length is twice the width. Hence
L = 2 W
The perimeter is 600 meters and is given by
2 (L + W) = 600
Substitute L by 2 W
2 (2 W + W) = 600
Simplify and solve for W
4 W + 2 W = 600
6 W = 600
W = 100
Find L
L = 2 W = 200
Find the area A of the rectangle
A = L * W = 200 * 100 = 20,000 square meters
correct answer D
Answer: D
Question: How many times are the hands of a clock at right angles in a day?
Options:
A)22
B)44
C)55
D)888
E)11
Rationale: In 12 hours, they are at right angles 22 times.
==> In 24 hours, they are at right angles 44 times.
Answer: Option 'B'
Answer: B
Question: A car gets 20 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 190 kilometers?
Options:
A)3.5 gallons
B)9.5 gallons
C)8.7 gallons
D)4.5 gallons
E)9.2 gallons
Rationale: Each 40 kilometers, 1 gallon is needed. We need to know how many 40 kilometers are there in 180 kilometers?
180 Ã· 40 = 9.5 Ã— 1 gallon = 9.5 gallons
correct answer is B) 9.5 gallons
Answer: B
Question: Two trains are moving in opposite directions with speed of 60 km/hr and 90 km/hr respectively. Their lengths are 1.10 km and 0.9 km respectively. the slower train cross the faster train in --- seconds
Options:
A)56
B)48
C)47
D)26
E)25
Rationale: Explanation:
Relative speed = 60+90 = 150 km/hr (Since both trains are moving in opposite directions)
Total distance = 1.1+.9 = 2km
Time = 2/150 hr = 1//75 hr = 3600/75 seconds = 1200/25 = 240/5 = 48 seconds
Answer: Option B
Answer: B
Question: How many of the following numbers are divisible by 132 ?
264, 396, 462, 792, 968, 2178, 5184, 6336
Options:
A)3
B)4
C)6
D)7
E)8
Rationale: 132 = 4 x 3 x 11
So, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also.
264 11,3,4 (/)
396 11,3,4 (/)
462 11,3 (X)
792 11,3,4 (/)
968 11,4 (X)
2178 11,3 (X)
5184 3,4 (X)
6336 11,3,4 (/)
Therefore the following numbers are divisible by 132 : 264, 396, 792 and 6336.
Required number of number = 4.
B)
Answer: B
Question: If x and y are unique prime integers, which of the following must be even?
Options:
A)x−y
B)x−2y
C)2x−2y
D)2x−y
E)xy^2
Rationale: Any number multiplied by 2 has to be an even number
Answer C
Answer: C
Question: A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
Options:
A)1:2
B)1:6
C)1:9
D)1:3
E)1:1
Rationale: T = 192/32 = 6 h
T = 6 - 3 = 3
Time Ratio = 6:3 = 2:1
Speed Ratio = 1:2.Answer: A
Answer: A
Question: What is the % change in the area of a rectangle when its length increases by 60% and its width decreases by 60%?
Options:
A)0%
B)20% increase
C)36% decrease
D)1% decrease
E)Insufficient data
Rationale: (16/10)*(4/10) = 64/100 of original area
64/100 is a 36% decrease from 100/100 ->C
Answer: C
Question: Which of the following could be the sides of an obtuse angled triangle? all values are in degree only
I. 51, 29, 100
II. 10,110, 60
III. 20, 30, 50
Options:
A)I and III only
B)II only
C)I and II only
D)I
E)I, II and III
Rationale: obtuse angled triangle means one angle more than 90 deg and total 180 deg.. I and II only
HENCE, (C)
Answer: C
Question: When positive integer N is divided by positive integer J, the remainder is 14. If N/J = 213.28, what is value of J?
Options:
A)30
B)35
C)40
D)50
E)60
Rationale: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 213.28
Here 213 is the quotient.
Given that Remainder = 14
So, 213.28 = 213 + 14/J
So, J = 50
Answer: D
Question: Rs.160 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?
Options:
A)120
B)125
C)115
D)110
E)111
Rationale: 4x 5x 6x
100 50 25
400x + 350x + 150x = 16000
x = 20
6x = 120
ANSWER A
Answer: A
Question: 5 men and 12 boys finish a piece of work in 4 days, 7 men and 6 boys do it in 5 days. The ratio between the efficiencies of a man and boy is?
Options:
A)1:5
B)6:5
C)4:5
D)9:5
E)8:5
Rationale: B
6:5
5M + 12B ----- 4 days
7M + 6B ------- 5 days
20M + 48B = 35M + 30B
18B = 15M => 5M = 6B
M: B = 6:5
Answer: B
Question: Ramu and Shamu invested in a shop. The profits were divided in the ratio of 4 : 4 respectively. If Ramu invested Rs. 35,500, the amount invested by Shamu is:
Options:
A)35000
B)40000
C)45000
D)35500
E)None
Rationale: Suppose Shamu invested Rs. y. Then, 35500/y =4/4 or y = [35500 x 4 / 4] = 35500.
Answer D
Answer: D
Question: The principal that amounts to Rs. 4913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?
Options:
A)Rs. 3096
B)Rs. 4076
C)Rs. 4085
D)Rs. 4096
E)Rs. 5023
Rationale: Explanation:
Principal = [4913 / (1 + 25/(4 * 100))3]
= 4913 * 16/17 * 16/17 * 16/17 = Rs. 4096.
ANSWER IS D
Answer: D
Question: If Nancy's income is Rs 17000, calculate his savings given that his income and expenditure are in the ratio 5:3.?
Options:
A)Rs.3800
B)Rs.1800
C)Rs.6800
D)Rs.7800
E)Rs.2800
Rationale: Let the income and the expenditure of the person be Rs.5x and Rs.3x respectively.
Income, 5x = 17000 => x = 3400
Savings = Income - expenditure = 5x - 3x =2x
So, savings = Rs.6800
Answer: C
Answer: C
Question: Kate wanted to buy 2kgs of apples. The vendor kept the 2kg weight on the right side and weighed 4 apples for that. She doubted on the correctness of the balance and placed 2 kg weight on the left side and she could weight 14 apples for 2 kgs. If the balance was correct how many apples she would have got?
Options:
A)6
B)9
C)8
D)4
E)3
Rationale: As she got less apples when the weight put on the right side, the left pan has more weight say w kgs.
Now w + 4a = 2
and w+ 2 = 14a
Solving we get a = 2/9 Kgs.
So she gets, 2/(2/9) = 9 apples
Answer:B
Answer: B
Question: How many seconds will a 900 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)22
B)54
C)99
D)77
E)12
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 900 * 3/50 = 54 sec.
Answer: B
Answer: B
Question: The ratio between the present ages of P and Q is 5:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years?
Options:
A)A)3:4
B)B)8:9
C)C)4:3
D)inadequate
E)of these
Rationale: Let P's age and Q's age be 5x and 7x years respectively.
Then, 7x - 5x = 4 => x = 2
Required ratio = (6x + 4) : (7x + 4)
16 : 18= 8:9
ANSWER:B
Answer: B
Question: If a rectangle length and width are both doubled,by what percent is the rectangle area increase?
Options:
A)100
B)150
C)300
D)200
E)250
Rationale: let length and width are l and b
so area = lb
now after doubling both we will get area = 2l*2b = 4lb
so % increase = 400-100 =300
ANSWER:C
Answer: C
Question: Traders A and B buy two goods for Rs. 1000 and Rs. 2000 respectively. Trader A marks his goods up by x%, while trader B marks his goods up by 2x% and offers a discount of x%. If both make the same non-zero profit, find x.
Options:
A)25%
B)12.5%
C)37.5%
D)40%
E)50%
Rationale: DETAILED SOLUTION
SP of trader A = 1000 (1 + x).
Profit of trader A = 1000 (1 + x) – 1000.
MP of trader B = 2000 (1 + 2x).
SP of trader B = 2000 (1 + 2x) (1 – x).
Profit of trader B = 2000(1 + 2x) (1 – x) – 2000.
Both make the same profit => 1000(1 + x) – 1000 = 2000(1 + 2x) (1 – x) – 2000
1000x = 2000 – 4000x2 + 4000x – 2000x – 2000
4000x2 -1000x = 0
1000x (4x – 1) = 0
=> x = 25%.
Answer choice (A)
Answer: A
Question: The ratio of the present age of Viju to that of Aju is 7:2. Four years from now, the ratio of the ages of Viju to Aju will be 5:2. What was Viju age 2 years ago ? (RBI Assistant 2015)
Options:
A)24
B)19
C)12
D)15
E)13
Rationale: Let the present age of Viju be 7x years and that of Aju be 2x years.
Then, 4 years from now
7x + 4 / 2x + 4 = 5 / 2
or 4x = 12
or x = 3
Viju present age = 7 * 3 = 21 years
Viju age 2 years ago = 21 - 2 = 19 years
answer :B
Answer: B
Question: Speed of boat in water is 12km/hr. and the speed of the stream is 3km/hr. Find the time taken by the boat to go upstream a distance of 45km.
Options:
A)3
B)4
C)5 hrs.
D)6
E)2
Rationale: US =speed of the boat - speed of the stream 12-3 =9km/hr. Time taken to cover 45km =45/9 = 5hrs. Answer : C
Answer: C
Question: An error 6% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
Options:
A)12.36
B)8.36
C)9.36
D)10.36
E)11.36
Rationale: Explanation:
100 cm is read as 106 cm.
A1 =(100 × 100)cm2 = 10000
and A2= (106 × 106)cm2= 11236
(A2 - A1) = 11236-10000 = 1236
=> 1236/10000*100 =12.36
Answer : A
Answer: A
Question: A pharmaceutical company uses 900 gm in place of 1 kg to sell the drug. Find the actual % profit or loss, when the company sells the product on 10% gain on cost price?
Options:
A)20
B)25
C)30
D)35
E)40
Rationale: Selling price of 900gm = 100+10 = $110
Profit = 110-90 = $20
% of profit = 20*100/80 =25 %
Answer is B
Answer: B
Question: A certain cricket team played seven games and scored an average of 180 runs per game. If, in the team’s first five games, it scored 175, 169, 181, 190, and 173 points, what was the average (arithmetic mean) number of points scored over the last two games?
Options:
A)165
B)181
C)182
D)186
E)Cannot be determined from the information given.
Rationale: Avg runs for total of 7 games = 50
So A+B+C+D+E+F+G/7=180
and A+B+C+D+E+F+G = 1260
Given A+B+C+D+E = 888
So F+G = 372
So average (arithmetic mean) number of runs scored over the last two games is 372/2 = 186
Correct answer is D) 186
Answer: D
Question: A train 280 m long, running with a speed of 72 km / hr will pass a tree in
Options:
A)14 sec
B)15 sec
C)16 sec
D)20 sec
E)None
Rationale: Sol.
Speed = (72 x 5/18) m/sec.
= 20 m / sec.
Time taken = (280 x 1/20) sec = 14 sec
Answer A
Answer: A
Question: At what rate of compound interest per annum will a sum of Rs.1200 become Rs.1348.32 in 2 years?
Options:
A)6%
B)6.5%
C)7%
D)7.5%
E)8%
Rationale: Let the rate be R% p.a. (1+ R )2 = 1348.32. Then, 1200* (1+ (R/100))2 = 1348.32
(1+R/100)2 = 134832/120000 = 11236/10000 :. (1 + R/100) 2 = (106/100)2
1 + R/100 = 106/100. So R = 6%
ANSWER:A
Answer: A
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
Options:
A)80 kg
B)85 kg
C)90 kg
D)100 kg
E)110 kg
Rationale: Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.
B)
Answer: B
Question: The sum of a certain number and its reciprocal is equal to 2,9. What is the absolute value of the difference of this number and its reciprocal ?
Options:
A)2,2
B)1,2
C)0,3
D)0,4
E)2,1
Rationale: x + 1/x = 2.9
x-1/x = y
Add two equations
2x = 2.9 + y
So when 2.9 and correct answer choice are added, the final digit should be even
So eliminate A, B and D
Substitute y=0.3
x=1.6
1.6+1/1.6 is not equal to 2.9
Substitute y = 2.1
So x=2.5
2.5+1/2.5 =2.9
ANSWER:E
Answer: E
Question: In what time will a railway train 70 m long moving at the rate of 36 kmph pass a telegraph post on its way?
Options:
A)5 sec
B)4 sec
C)3 sec
D)7 sec
E)1 sec
Rationale: T = 70/36 * 18/5 = 7 sec
Answer: D
Answer: D
Question: In a box of 6 pencils, a total of 2 are defective. If a customer buys 3 pencils selected at random from the box, what is the probability that neither pencils will be defective?
Options:
A)1/2
B)1/5
C)2/3
D)2/5
E)1/7
Rationale: First, there are 4C3 ways you can select 3 good pencils from 4 good ones.
Second, there are 6C3 ways you select 3 pencils from 6 ones in the box.
Then, the probability that neither pen will be defective is: 4C3/6C3=4/20 = 1/5
Answer is B
Answer: B
Question: In a pet shop there are 120 eyes and 172 legs. How many birds are included in these?
Options:
A)33
B)34
C)35
D)36
E)37
Rationale: Let there are x birds and y puppies.
Each bird and puppy has 2 eyes. Each bird has 2 legs and each puppy has 4 legs.
Then 2x+2y = 120 => x+y = 60 (i)
2x+4y = 172 => x+2y = 86 (ii)
Solving (i) and (ii) we get
y = 26 & x = 34
So birds are 34
ANSWER:B
Answer: B
Question: On dividing 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor?
Options:
A)10
B)12
C)14
D)16
E)18
Rationale: d = (D-R)/Q
= (109 - 1)/9
= 108/9 = 12
B)
Answer: B
Question: The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 4 years hence?
Options:
A)22
B)77
C)70
D)68
E)71
Rationale: A + B = 60, A = 2B
2B + B = 60 => B = 20 then A = 40.
4 years, their ages will be 44 and 24.
Sum of their ages = 44 + 24 = 68.
Answer: D
Answer: D
Question: If circles x and y have the same area and circle x has a circumference of 18π, half of the radius of circle y is:
Options:
A)16
B)4.5
C)4
D)2
E)1
Rationale: x be radius of circle x
y be radius of circle y
given:
pi*x^2 = pi*y^2
also,
2*pi*x = 18*pi
x = 9
thus y =9
y/2 = 4.5
Ans: B
Answer: B
Question: . In digging a pond 18 m * 8 m * 6 m the volumes of the soil extracted will be?
Options:
A)889
B)1000
C)864
D)989
E)678
Rationale: 20 * 10 * 5 = 864
Answer: C
Answer: C
Question: The digits of a three-digit number A are written in the reverse order to form another three-digit number B. If B>A and B-A is perfectly divisible by 7, then which of the following is necessarily true?
Options:
A)100<A<299
B)106<A<305
C)112<A<311
D)118<A<317
E)None
Rationale: Explanation:
Let A = abc the B = cba
Given, B – A is exactly divisible by 7.
Therefore, 100c + 10b + a – (100a + 10b + c) = 99c – 99a = 99(c – a)
So 99(c – a) should be divisible by 7.
We know that 99 is not divisible by 7. So (c – a) should be divisible by 7 which implies c – a is 0, 7, 14...
c – a = 0 is not possible as c = a implies A = B but given that B > A
c – a = 14 is not possible as the maximum difference between c and a = 9 – 1 = 8 only.
So c – a = 7.
If c = 9, a = 2
c = 8, a = 1
b can take any value from 0 to 9
Therefore, minimum value of abc = 109, maximum value = 299
From the given options, option B satisfies this.
Correct option: B
Answer: B
Question: A number x is multiplied with itself and then added to the product of 4 and x. If the result of these two operations is -8, what is the value of x?
Options:
A)-4
B)-2
C)2
D)4
E)Cannot be determined.
Rationale: A number x is multiplied with itself --> X^2
added to the product of 4 and x --> X^2+4X
If the result of these two operations is -4 --> X^2+4X=-8
i.e X^2+4X+8=0 is the Quadratic equation which needs to be solved.
no solution
IMO E
Answer: E
Question: Thirty men can do a work in 24 days. In how many days can 20 men can do the work, given that the time spent per day is increased by one-third of the previous time?
Options:
A)27
B)88
C)26
D)55
E)12
Rationale: Let the number of hours working per day initially be x. we have M1 D1 H1= M2 D2 H2
30 * 24 * x = 20 * d2 * (4x)/3 => d2 = (30 * 24 * 3)/(24 * 4) = 27 days.
Answer:A
Answer: A
Question: What is the smallest positive integer K such that the product of 450 x K is a perfect square?
Options:
A)3
B)9
C)15
D)25
E)63
Rationale: A perfect square, is just an integer that can be written as the square of some other integer. For example 16=4^2, is a perfect square.
Now, 450 = 3^2 * 5^2 *3 , so if k=3 then 450k = (3 * 5 * 3)^2, which is a perfect square (basically the least positive value of k must complete only the power of 7 to even power as powers of other primes are already even).
Answer: A.
Answer: A
Question: A train 210 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
A)15 sec
B)16 sec
C)18 sec
D)12 sec
E)25 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 210 * 2/35 = 12 sec
ANSWER: D
Answer: D
Question: The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?
Options:
A)278
B)29
C)12
D)17
E)10
Rationale: x, 2x
(x-2):(2x-2) = 1:3
3x-6 = 2x-2
x = 4
x+2x = 3x
=> 3*4 = 12.Answer:C
Answer: C
Question: What is the area of square field whose side of length 16 m?
Options:
A)225
B)777
C)256
D)288
E)261
Rationale: 16 * 16 = 256 sq m
Answer: C
Answer: C
Question: Einstein walks on an escalator at a rate of 5steps per second and reaches the other end in 10 sec. while coming back, walking at the same speed he reaches the starting point in 40secs. What is the number of steps on the escalator?
Options:
A)40
B)60
C)120
D)80
E)data insufficient
Rationale: Let the speed of escaltor be X steps per sec.
And length of escalator be Y.
Einstein's speed = 5 step/ sec
Then,
During upward movement
5-X=Y/10
During downward movement
5+X=Y/40
By solving equations we get Y=80.
ANSWER:D
Answer: D
Question: In a shop, shirts are usually sold at 40% above the cost price. During a sale, the shopkeeper offers a discount of 10% off the usual selling price. If he manages to sell 72 shirts for Rs 13.608, then his cost price per shirt, in Rs, is
Options:
A)120
B)130
C)140
D)150
E)160
Rationale: suppose cost price is x
so selling price is 14x/10
now after 10% discount selling price is 126x/100
total selling price is 72*126x/100
72*126x/100=13608
x=150
so the cost price per shirt is 150.
ANSWER:D
Answer: D
Question: The speed of a train is 80 kmph. What is the distance covered by it in 6 minutes?
Options:
A)15 kmph
B)11 kmph
C)18 kmph
D)8 kmph
E)12 kmph
Rationale: 80 * 6/60
= 8 kmph
Answer:D
Answer: D
Question: A train consists of 12 boggies, each boggy 15 metres long. The train crosses a telegraph post in 18 seconds. Due to some problem, two boggies were detached. The train now crosses a telegraph post in
Options:
A)18 sec
B)12 sec
C)15 sec
D)20 sec
E)None of these
Rationale: Length of train = 12 × 15 = 180 m.
Then, speed of train = 180⁄18 = 10 m/s
Now, length of train = 10 × 15 = 150m
∴ Required time = 150⁄10 = 15 sec.
Answer C
Answer: C
Question: How many inches are in 2000 millimeters? (round your answer to the nearest hundredth of of an inch).
Options:
A)51.45 inches
B)86.09 inches
C)67.34 inches
D)34.98 inches
E)78.74 inches
Rationale: One inch is the same as 25.4 mm. Let x inches be the same as 1000 mm
x = 1 inch * 2000 mm / 25.4 mm = 78.74 inches
correct answer E
Answer: E
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit ?
Options:
A)13500
B)10500
C)9423
D)8500
E)None of these
Rationale: Explanation:
Simran : Nanda =(50000Ã—36):(80000Ã—30)=(50000Ã—36):(80000Ã—30) =3:4=3:4.
Simran's share = Rs. (24500Ã—37)(24500Ã—37) = Rs. 10500.
ANSWER IS B
Answer: B
Question: A man can do a job in 20 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together?
Options:
A)6.3
B)6.9
C)7.1
D)6.1
E)6.2
Rationale: 1 day work of the three persons = (1/20 + 1/20 + 1/25) = 7/50
So, all three together will complete the work in 300/47 = 7.1 days.
Answer:C
Answer: C
Question: If x is an integer, then x(x – 1)(x – k) must be evenly divisible by five when k is any of the following values EXCEPT
Options:
A)-4
B)-2
C)2
D)-1
E)5
Rationale: We have the product of 3 integers: (x-1)x(x-k).
Note that the product of 3 integers is divisible by 5 if at least one multiple is divisible by 5. Now, to guarantee that at least one integer out of x, (x – 1), and (x – k) is divisible by 5 these numbers must have different remainders upon division by 5, meaning that one of them should have remainder of 1, another reminder of 2 and the last one remainder of 0, so be divisible by 5.
Next, if k=2 then we'll have (x-1)x(x-k)=(x-1)x(x-2) --> which means that (x-1) and (x-2) will have the same remainder upon division by 5. Thus for k=2 we won't be sure whether (x-1)x(x-k) is divisible by 5.
Answer: C.
Answer: C
Question: A hen leaps 3 leaps for every 2 leaps of a duck, but 4 leaps of the duck are equal to 3 leaps of the hen. What is the ratio of the speed of the hen to that of the duck?
Options:
A)2:1
B)3:4
C)4:3
D)1:4
E)5:6
Rationale: Given;
4 duck = 3 hen;
Or, duck/hen = 3/4;
Let hen's 1 leap = 4 meter and ducks 1 leap = 3 meter.
Then, ratio of speed of hen and duck = 4*3/3*2 = 2:1''Answer: 2:1;
Answer: A
Question: What is the fraction in the simplest form of the terminating decimal 0.0325?
Options:
A)31/40
B)41/30
C)13/40
D)1/30
E)1/40
Rationale: The fraction of the decimal 0.0325 is 325/10000. Simplifying by dividing the top and bottom by 25 to get 13/40.
Option C
Answer: C
Question: How many multiples of 4 are there between 12 and 104, inclusive?
Options:
A)21
B)22
C)23
D)24
E)25
Rationale: The multiples of 4 are from 4*3 up to 4*26.
26-3+1 = 24.
The answer is D.
Answer: D
Question: How many integers from 101 to 800, inclusive, remains the value unchanged when the digits were reversed?
Options:
A)50
B)60
C)70
D)80
E)90
Rationale: first digit possibilities - 1 through 7 = 7
8 is not possible here because it would result in a number greater than 8 (i.e 808 , 818..)
second digit possibilities - 0 though 9 = 10
third digit is same as first digit
=>total possible number meeting the given conditions = 7 *10 = 70
Answer is C.
Answer: C
Question: For which of the following functions f is f(a) = f(1-a) for all a?
Options:
A)f (x) = 1 - x
B)f (a) = 1 - a^2
C)f (a) = a^2 - (1 - a)^2
D)f (a) = a^2*(1 - a)^2
E)f (x) = x/(1 - x)
Rationale: I remember seeing this problem in a GMATprep test. I think choice D should be F(a)=(a^2) (1-a)^2. If that is true then substituting (1-a) for will give us the same function back and the answer choice is D, where the function is multiplicative
Answer: D
Question: The ratio of a to b to c is 2 to 3 to 4, and a, b, c are positive integers. If the average (arithmetic mean) of the three numbers is 36, what is the value of a?
Options:
A)21
B)24
C)25
D)27
E)30
Rationale: Let a=2k, b=3k, and c=4k.
a+b+c = 2k+3k+4k = 9k
Since the average is 36:
9k/3 = 36
3k = 36
k=12
Then a=24.
The answer is B.
Answer: B
Question: A student has to obtain 50% of the total marks to pass. He got 200 marks and failed by 20 marks. The maximum marks are?
Options:
A)510
B)520
C)530
D)540
E)440
Rationale: Let the maximum marks be x
Then, 50% of x = 200+20
50x/100 = 220
50x= 220*100= 22000
x = 440
Answer is E
Answer: E
Question: Three medical experts, working together at the same constant rate, can write an anatomy textbook in 18 days. How many additional experts, working together at this same constant rate, are needed to write the textbook in 9 days?
Options:
A)2
B)3
C)5
D)8
E)15
Rationale: Each expert can write 1/54 of the book per day.
To complete the book in 9 days, we need 54/9 = 6 experts, thus 3 more experts are needed.
The answer is B.
Answer: B
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
Options:
A)Rs.1000
B)Rs.1009
C)Rs.1007
D)Rs.1006
E)Rs.1002
Rationale: Explanation:
90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000
Answer:A
Answer: A