divelab/Sys2Bench huggingface dataset:
Question: In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/6.
The probability of drawing a red ball is 1/5.
The probability of drawing a green ball is 1/10.
If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar?
Options:
A)25.
B)24.
C)23.
D)20.
E)16.
Rationale: We need to get some number which is less than 50 and exactly divisible by 6,5 and 10
Lets take LCM of three balls 6,5 and 10 = 30.
The probability of drawing a blue ball is 1/6...For every 8 balls we get 1 BLUE ball then out of 30 balls we get 5 BLUE balls.
The probability of drawing a red ball is 1/5...For every 5 balls we get 1 RED ball then out of 30 balls we get 6 REB balls.
The probability of drawing a green ball is 1/10. For every 10 balls we get 1 GREEN ball then out of 30 balls we get 3 GREEN BALLS.
Then out of 30 - ( 5 + 6 + 3 ) = 16 YELLOW balls.
IMO option E is correct.
Answer: E
Question: P, Q, R, S, T and U are six cities which are in a row in the same order. A bus, b1 travels from P to U and another bus b2 travel from U to P. The bus b1 reaches S at 10:40 and bus b2 reaches Q at 10:35 if the travel time between any two adjacent cities is 40 minutes and the stoppage time at each city is 15 minutes, then at what time do they start at their respective destinations?
Options:
A)8:00, 7:00
B)8:00, 7:10
C)8:10, 7:10
D)8:15, 7:25
E)8:10, 7:00
Rationale: Explanation:
The bus b1, which started at P, reached S at 10:40, passing through the intermediary cities Q and R.
The time taken to travel from P to S
= 3 * 40 + 2 * 15 = 150minute
(journey)+(stoppage) = 2 hrs 30 minutes.
Hence, b1 started at 10:40 - 2:30 = 8:10 at P.
b2 reached Q, starting at U, through the city T, S and R.
The time taken by it to reach S = 4 * 40 + 3 * 15 = 205 minutes = 3 hr 25 minutes.
Hence, b2 started at, 10:35 - 3:25 = 7:10, at U.
ANSWER IS C
Answer: C
Question: X and Y are two towns. Ganesh covers the distance from X to Y at an average speed of 54 Km/hr. However, he covers the distance from Y to X at an average speed of 36 Km/hr. His average speed during the whole journey in km/hr. is :
Options:
A)34
B)43.2
C)40
D)38
E)29
Rationale: Solution: Average speed = 2XY / X+Y
= 2*54*36 / 54+36
= 43.2
Answer : B
Answer: B
Question: The population of a village is 14300. It increases annually at the rate of 15% p.a. What will be its population after 2 years?
Options:
A)18911
B)18788
C)19898
D)14000
E)14400
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
14300 × 115/100 × 115/100 = 18911
A
Answer: A
Question: Solve for x: 2x – y = (3/4)x + 6.
Options:
A)(y + 6)/5
B)4(y + 6)/5
C)(y + 6)
D)4(y - 6)/5
E)6(y-4)/5
Rationale: 2x – y = (3/4)x + 6.
or, 2x - (3/4)x = y + 6.
or, (8x -3x)/4 = y + 6.
or, 5x/4 = y + 6.
or, 5x = 4(y + 6).
or, 5x = 4y + 24.
or, x = (4y + 24)/5.
Therefore, x = 4(y + 6)/5
correct answer B
Answer: B
Question: On dividing a number by 357, we get 38 as remainder.On dividing the same number by 17, what will be the remainder ?
Options:
A)4
B)5
C)8
D)7
E)2
Rationale: Let x be the number and y be the quotient.Then,
x=357*y+38
=(17*21*y)+(17*2)+4
=17*(21y+2)+4.
Required number =4.
Answer is A
Answer: A
Question: If 3^x*4^y = 1,594,323 and x – y = 13, then x = ?
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: Since 1,594,323 is an odd number, it is not a multiple of 4.
This means that y must equal zero.
Since x - y = 13 and y = 0, then x = 13.
The answer is D.
Answer: D
Question: The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is?
Options:
A)8
B)9
C)7
D)6
E)4
Rationale: 2x * x = 128 => x= 8
Answer: A
Answer: A
Question: Lines y=√2·x+2 and y=3√2·x−1 intersect at what height above the x axis?
Options:
A)(13√2)/2
B)13/2
C)13
D)2
E)0
Rationale: Solve two equations for y
y=√2·x+2
y=3√2·x−1
Set the two equations equal to each other and solve for x
√2·x+2 = 3√2·x−1
3 = 2√2·x
3/(2√2) = x
Plug x = 3/(2√2) into any one of the original equations to find the y value (height above x axis) where the two lines intersect
y=√2·x+2
y=√2·(3/(2√2))+2
y = 3/2 + 5
y = 3/2 + 10/2
y = 13/2
Final answer:
B) 13/2
Answer: B
Question: Calculate how many men are needed to finish a specific task in 35 days if it will take 20 men to complete the same task in 70 days. ?
Options:
A)40
B)20
C)10
D)30
E)60
Rationale: men required to finish the work in 35 days = 20*70/35 = 40
Answer is A
Answer: A
Question: The length W of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent?
Options:
A)Decreases by 19%
B)Decreases by 25%
C)Increases by 6%
D)Increases by 19%
E)Increases by 25%
Rationale: Let the length W of the rectangle be 100x, and width be 100y. Area = 100x * 100y = 10000xy
Now after the change Length = 85x, and width = 140 y. Area = 11900xy
% Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence D.
Answer: D
Question: The ratio between the speeds of two Bullet trains is 7: 8. If the second Bullet train runs 440 kms in 4 hours, then the speed of the first train is:
Options:
A)89.25 km/hr.
B)37.25 km/hr.
C)90.25 km/hr.
D)94.25 km/hr.
E)96.25 km/hr.
Rationale: E
96.25 km/hr.
Let the speed of two bullet trains be 7x and 8x km/hr.
Then, 8x = (440/4) = 110
x = (110/8) = 13.75
Hence, speed of first bullet train = (7 x 13.75) km/hr = 96.25 km/hr.
Answer: E
Question: In a village of 120 families, 93 families use firewood for cooking, 63 families use kerosene, 45 families use cooking gas, 45 families use firewood and kerosene, 24 families use kerosene and cooking gas, 27 families use cooking gas and firewood. Find how many useall?
Options:
A)120
B)93
C)150
D)15
E)45
Rationale: Let F,K and G represent the sets of students who liked rock music, folk music and classical music respectively.
F=93, K=63, G=45
F and K=45
F and G=27
K and G=24
All= 120-93-63-45+45+27+24=15
ANSWER D
Answer: D
Question: X’s income is 3/4 of Y’s income, and X’s expenditure is 4/5 of Y’s expenditure. If X’s income is 9/10 of Y’s expenditure, find the ratio of X’s savings to Y’s savings ?
Options:
A)1 : 2
B)2 : 1
C)1 : 4
D)2 : 3
E)3 : 2
Rationale: Let X’s income be 3k then Y’s income is 4k.
Let X’s expenditure be 4g then Y’s expenditure is 5g.
But 3k = 9/10 (5g) or k = 3/2g
X’s saving/Y’s saving = (3k - 4g)/(4k - 5g)
[3 (3 / 2g) - 4g]/[ 4(3 / 2g) - 5g] = 1/2
X’s saving : Y’s saving = 1 : 2
ANSWER:A
Answer: A
Question: If 31% of a number is 46.5,the number is ?
Options:
A)150
B)155
C)160
D)165
E)None
Rationale: Answer
Let 31% of A = 46.5
⇒ (31 x A)/100 = 46.5
∴ A = (46.5 x 100) / 31 = 150
Correct Option: A
Answer: A
Question: On five consecutive flips of a coin, what is the probability that all five produce the same result?
Options:
A)1/16
B)1/8
C)1/4
D)3/8
E)1/2
Rationale: TTTTT case --> P = (1/2)^5 = 1/32
HHHHH case --> P = (1/2)^5 = 1/32
P(TTTTT or HHHHH) = 1/32 + 1/32 = 1/16
Answer: A
Answer: A
Question: Two trains of length 100 meters and 200 meters are 450 meters apart. They are moving towards each other on parallel tracks, at speeds of 90 km/h and 72 km/h. After how many seconds will the trains meet?
Options:
A)6
B)8
C)10
D)12
E)14
Rationale: The speeds are 90000/3600 = 25 m/s and 72000/3600 = 20 m/s
The relative speed is 45 m/s.
time = 450 / 45 = 10 seconds
The answer is C.
Answer: C
Question: In a class of students, the ratio of girls to boys is 2:3. If 3 more girls joined the class, the ratio would be 3:4. How many students are in the class?
Options:
A)50
B)55
C)60
D)65
E)70
Rationale: Let x be the number of students in the class.
(2/5)*x=(3/7)(x+3)-3
14x=15x+45-105
x=60
The answer is C.
Answer: C
Question: A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast?
Options:
A)7500
B)7508
C)7528
D)7527
E)7232
Rationale: 35%-----------L
65%-----------W
------------------
30%----------2250
100%---------? => 7500
Answer:A
Answer: A
Question: The ratio between the sale price and the cost price of an article is 7:5. What is the ratio between the profit and the cost price of that article?
Options:
A)2:9
B)2:5
C)3:6
D)2:0
E)2:1
Rationale: Let C.P. = Rs. 5x and S.P. = Rs. 7x.
Then, Gain = Rs. 2x
Required ratio = 2x : 5x = 2:5
Answer:B
Answer: B
Question: A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is?
Options:
A)281
B)278
C)698
D)277
E)1911
Rationale: S.I. for 1 year = (854 - 815) = Rs. 39
S.I. for 3 years = 39 * 3 = Rs. 117
Principal = (815 - 117) = Rs. 698.
Answer:C
Answer: C
Question: Of the 5 numbers, whose average is 150, the first is one-fourth of the sum of the last 4. The first number is?
Options:
A)100
B)80
C)70
D)150
E)60
Rationale: Total of 5 numbers = 5 * 150 = 750
Let total of last 4 numbers = x
1st number = x/4
x+ x/4 = 750
5x = 3000 => x =600
1st number = 600/ 4 = 150
Answer : D
Answer: D
Question: In a rectangular coordinate system, if a line passes through the points (-14,-18), (16,22) and (x,2) then what is the value of x?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: The slope of the line m is rise/run = 22-(-18) / 16-(-14) = 4/3
4/3 = 22-2 / 16-x
64-4x = 66-6
x = 1
The answer is B.
Answer: B
Question: How many 3 digit number contain number 4 ?
Options:
A)352
B)268
C)236
D)252
E)354
Rationale: total 3 digit no. = 9*10*10 = 900
not containing 4 = 8*9*9 = 648
total 3 digit number contain 4 = 900 - 648 = 252
ANSWER:D
Answer: D
Question: A train speeds past a pole in 15 sec and a platform 130 m long in 25 sec, its length is?
Options:
A)238
B)150
C)195
D)177
E)171
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 130)/25 = x/15 => x = 195 m.
Answer: C
Answer: C
Question: A, B and C can do a work in 90, 45 and 6 days respectively. If they work together, in how many days will they complete the work?
Options:
A)5
B)6
C)7
D)8
E)11
Rationale: One days's work of A, B and C = 1/90 + 1/45 + 1/6
= (1 + 2 + 15)/90 = 1/5
A, B and C together can do the work in 5 days.
Answer:A
Answer: A
Question: The list price of an article is Rs.70. A customer pays Rs.59.85 for it. He was given two successive discounts, one of them being 10%. The other discount is?
Options:
A)8%
B)7%
C)10%
D)6%
E)5%
Rationale: Option E
Explanation:
70*(90/100)*((100-x)/100) = 59.85
x = 5%
Answer: E
Question: A rectangle the length of which is 8 inches and the width of which is 6 inches is made up 48 1 inch by 1 inch squares. Through how many of the squares does a diagonal of the rectangle pass?
Options:
A)6
B)8
C)10
D)12
E)16
Rationale: 1)If the two sides are co-prime, SUM of sides -1..
2)and if not co-prime , Sum of sides - HCF of sides..
the difference is related to the diagonal passing through a vertex of squares at some place..
here 6 and 8 are NOT co-primes, so ans =6+8−HCF(6,8)=14−2=12
ANSWER:D
Answer: D
Question: A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.340 less than the sum lent. What was the sum lent?
Options:
A)287
B)278
C)296
D)500
E)297
Rationale: P - 340 = (P*4*8)/100
P = 500
Answer:D
Answer: D
Question: A team bought a total of 450 balls. If each player on the team bought at least 12 balls, then what is the greatest possible number of players on the team?
Options:
A)37
B)22
C)23
D)24
E)25
Rationale: 450/12=37 plus remainder.
The answer is A.
Answer: A
Question: What is the square root of 168,921?
Options:
A)476
B)389
C)497
D)411
E)524
Rationale: 1) Checking the last digits in the answer options A, C, E are out since last digit of the square is known to be 1.
2) B = 389^2 and D = 411^2
B = (400-11)^2 and D = (400 + 11)^2
Since we need the answer less than 160000 => B is out.
Thus we have D as the ans.
Answer: D
Question: The sum of the squares of three numbers is 138,while the sum of their products take two at a time is 131.Find the sum?
Options:
A)10
B)30
C)20
D)50
E)40
Rationale: Formula is (a+b+c)^2=(a^2)+(b^2)+(c^2)+2(ab+bc+ca)
=138+(2*131)
The sum of the three numbers a+b+c=√400=20
Answer is option C
Answer: C
Question: At the beginning of year 1, an investor puts pp dollars into an investment whose value increases at a variable rate of xnxn per year, where nn is an integer ranging from 1 to 3 indicating the year. If 85<xn<11085<xn<110 for all nn between 1 and 3, inclusive, then at the end of 3 years, the value of the investment must be between?
Options:
A)$p and $2p
B)$2pand $5p
C)$5p and $10p
D)$10p and $ 25p
E)$25p and $75p
Rationale: Since the min rate of interest is 86% the min value of investment will be (1+0.86)^3*p = (1.86^3)*p. Similarly max value will be (2.1)^3*p.
2.1^3 is 9.5 or you can guess little over 8 so 10p may be good estimate.
1.86^3 is trickier to estimate. I knew root(3) = 1.73. So 1.86^2 is close to 3 and 3*1.8 is 5.4. So 5p is a close lower bound.
So range is 5p to 10p.
Answer C.
Answer: C
Question: There are 15 balls in a jar. You take out 3 blue balls without putting them back inside, and now the probability of pulling out a blue ball is 1/3. How many blue balls were there in the beginning?
Options:
A)12.
B)9.
C)8.
D)7.
E)6.
Rationale: 7 = 3 blue balls + 12 / 3
Answer:D
Answer: D
Question: If + means * and * means / and / means %. What is the value of 2+3*5/7 = ?
Options:
A)1.8
B)1.6
C)1.4
D)1.2
E)1.0
Rationale: 5%7=5
2*3/5=6/5=1.2
ANSWER:D
Answer: D
Question: The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is :
Options:
A)Rs. 120.41
B)Rs. 134.51
C)Rs. 124.75
D)Rs. 145.89
E)Rs. 155.89
Rationale: For an income of Rs.756, investment = Rs.9000
For an income of Rs., investment = = Rs.125
For a Rs.100 stock, investment = Rs.125.
Market value of Rs. 100 stock = = Rs. 124.75
C
Answer: C
Question: Ajay spends 10 per cent of his salary on house rent, 5 percent on food, 15 percent travel, 10 percent on clothes and the remaining amount of Rs.27000 is saved. What is Ajayâ€™s income?
Options:
A)Rs.60000
B)Rs.80500
C)Rs.60700
D)Rs.45000
E)None of these
Rationale: Explanation:
Savings = Income â€“ expenditure
100 â€“ (10+5+15+10) = 60%
60% of income = Rs.27000
:. Income = 27000 x 100/60 = Rs. 45000.
Answer: Option D
Answer: D
Question: By selling 33 meters of cloth , one gains the selling price of 11 metres . Find the gain percent .
Options:
A)50
B)45
C)40
D)60
E)55
Rationale: (Selling Price of 33m)-(Cost Price of 33m)=Gain=Selling Price of 11m
Selling Price of 22m = Cost Price of 33m Let Cost Price of each meter be $1 , Then, Cost Price of 22m= $22, Selling Price of 22m=$33.
Gain%=[(11/22)*100]%=50%
Answer A) 50.
Answer: A
Question: A driver of auto rickshaw makes a profit of 20% on every trip when he carries 3 passengers and the price of petrol is Rs. 30 a litre. Find the % profit for the same journey if he goes for 4 passengers per trip and the price of petrol reduces to Rs. 24 litres?
Options:
A)40%.
B)60%.
C)80%.
D)100%.
E)120%.
Rationale: 20% of 30 = 6 rupee profit
36/3 = 12 rupee per passenger
12*4 = 48
48 - 24 = 24.
so profit = 100%.
ANSWER:D
Answer: D
Question: A basket of 1430 apples is divided equally among a group of apple lovers. If 45 people join the group, each apple lover would receive 9 apples less. How many W apples did each person get before 45 people joined the feast?
Options:
A)20.
B)21.
C)22.
D)23.
E)24.
Rationale: Before solving it algebraically, let us prime factorize 1430 = 2*5*11*13.
Since number of apples per person * total persons W= 1430, the answer should be a factor of 1430. Only C is. And that's your answer.C
Answer: C
Question: Find the time between 7 and 8 o'clock when two hands are at right angles?
Options:
A)2 2/11 minutes past 7 o'clock
B)3 2/11 minutes past 7 o'clock
C)21 9/11 minutes past 7 o'clock
D)7 10/11 minutes past 7 o'clock
E)8 10/11 minutes past 7 o'clock
Rationale: angle=90 deg
so,
angle=30(h)-11/2(min)
=> 90=30(7)-11/2(min)
=>210-90=11/2(min)
=> (120*2)/11=min
=> min=21 9/11 min
ANSWER:C
Answer: C
Question: A boy bought a pen at 40% discount on its original price. He sold it at a 70% increase on the price he bought it. What percent of profit did he make on the original price?
Options:
A)10%
B)8%
C)6%
D)2%
E)4%
Rationale: Original price = 100
CP = 60
S = 60*(170/100) = 102
100 - 102 = 2%
Answer: D
Answer: D
Question: A can do a piece of work in 4 days. B can do it in 8 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
Options:
A)8 days
B)2 days
C)6 days
D)7 days
E)4 days
Rationale: C = 1/2 - 1/4 - 1/8 = 1/8
=> 8 days
Answer: A
Answer: A
Question: A circular mat with diameter 40 inches is placed on a square tabletop, each of whose sides is 30 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?
Options:
A)5/12
B)2/5
C)1/2
D)1.395
E)5/6
Rationale: C.
It is a circle inscribed in a square.
Square side=24---> square(table) area=24^2
Circle diameter=40---> Circle area=PiR^2=4*100Pi (where Pi=~3.14)
covered fraction=4*100*3.14/30*30=4*314/900=1.395
D
Answer: D
Question: Three numbers are in the ratio 3:5:7. The largest number value is 42. Find difference between Smallest & largest number is?
Options:
A)24
B)26
C)27
D)28
E)32
Rationale: == 3:5:7
Total parts = 15
= The largest number value is 42
= The largest number is = 7
= Then 7 parts -----> 42 ( 7 * 6 = 42 )
= smallest number = 3 & Largest number = 7
= Difference between smallest number & largest number is = 7 - 3 = 4
= Then 4 parts -----> 24 (4 * 6 = 24)
A)
Answer: A
Question: A four-digit code can consist of the digits 0 ~ 9 except that it does not contain the digits 1, 3, 4, and 5 at all. If repeated digits are allowed, what is the probability that it has at least one even digit?
Options:
A)35/36
B)49/50
C)80/81
D)100/101
E)120/121
Rationale: P(no even digits) = 1/3*1/3*1/3*1/3 = 1/81
P(at least one even digit) = 1 - 1/81 = 80/81
The answer is C.
Answer: C
Question: Walking at 4/5 of her normal speed, a worker is 15 minutes later than usual in reaching her office. The usual time (in minutes) taken by her to cover the distance between her home and her office is
Options:
A)45
B)50
C)55
D)60
E)65
Rationale: Let V be her normal speed and let T be her normal time.
D = (4/5)V * (T+15)
Since the distance is the same we can equate this to a regular day which is D = V*T
V*T = (4/5)V * (T+15)
T/5 = 12
T=60
The answer is D.
Answer: D
Question: In the xy-plane, line e passes through point (3,-2) and intersect perpendicularly with line n that passes through points (0,3) and (3,5). What is the equation of line e?
Options:
A)3x+2y-5=0
B)3x+2y+5=0
C)2x-3y-12=0
D)2x+3y=0
E)4x+3y-6=0
Rationale: If two lines intersect perpendicularly, we get -1 when we multiply two slopes together. The slope of a line n is (5-3)/(3-0)=2/3. Hence, the slope of a line e should be -3/2. Since it crosses (3,-2), if we calculate we get 3x+2y=5. Hence, the correct answer is A.
Answer: A
Question: Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made?
Options:
A)13.5
B)14.50
C)15.50
D)32:19
E)16.50
Rationale: Explanation:
Let the quantities of A and B mixed be 3x kg and 7x kg.
Cost of 3x kg of A = 9(3x) = Rs. 27x
Cost of 7x kg of B = 15(7x) = Rs. 105x
Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x
Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66
Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50
Answer: Option E
Answer: E
Question: Average of 9 numbers is zero. At most how many numbers may be greater than zero
Options:
A)0
B)1
C)8
D)9
E)10
Rationale: Answer: Option C
Answer: C
Question: The Price of 357 apples is Rs.2499. What will be the price of 49 dozens of such apples?
Options:
A)Rs.3800
B)Rs.2816
C)Rs.4116
D)Rs.3116
E)Rs.5116
Rationale: More apples, more cost(Direct)
357 *588 : : 2499 : x
x = (588*2499)/357 = 4116
ANSWER:C
Answer: C
Question: When ticket sales began, Pat was the pth customer in line for a ticket, and customers purchased their tickets at the rate of x customers per minute. Of the following, which best approximates the time, in minutes, that Pat had to wait in line from the moment ticket sales began?
Options:
A)(p - 1) x
B)p + x –1
C)(p-1)/x
D)x/(p-1)
E)p/(x-1)
Rationale: C. (p - 1) / x
Answer: C
Question: If the average (arithmetic mean) of x, x + 2, and x + 4 is 33, what is the value of x?
Options:
A)30
B)31
C)32
D)32
E)37
Rationale: AM of x, x + 2, and x + 4 = x + (x + 2) + (x + 4) / 3 = 3x + 6 /3 = x + 2
Given that x + 2 = 33
x = 31
Correct Option: B
Answer: B
Question: A fair coin is tossed 3 times. What is the probability of getting at least 2 tails?
Options:
A)3/4
B)3/2
C)1/2
D)3/4
E)1/4
Rationale: Let's find the probability of 2 tails , 3 tails
P(TTT)=((1/2)^3=1/8.
P(HTT)=(3!/2!)*(1/2)^3=3/8
Total Probablity = 1/8 + 3/8
=1/2
Answer(C)
Answer: C
Question: If M:N is 3:9 and N:P is 9:12 then M:P is equal to
Options:
A)1:5
B)1:4
C)1:6
D)1:8
E)1:7
Rationale: The two ratios given are having the same number 9 for N in both the ratios.
Hence- M:N = 3:9 N:P = 9:12
=> M:P = 3:12 = > 1:4
Answer B
Answer: B
Question: A retailer buys a radio for Rs 225. His overhead expenses are Rs 15. He sellis the radio for Rs 300. The profit percent of the retailer is
Options:
A)10%
B)50%
C)25%
D)52%
E)None of these
Rationale: Explanation:
cost price = (225 + 15) = 240 sell price = 300
gain = (60/240)*100 = 25%. Answer: C
Answer: C
Question: Mudit's age 18 years hence will be thrice his age four years ago. Find Mudit's present age?
Options:
A)12 years
B)21 years
C)18 years
D)9 years
E)None of these
Rationale: Let Mudit's present age be 'm' years.
m + 18 = 3(m - 4)
=> 2m = 30 => m = 15 years.
ANSWER:E
Answer: E
Question: A group consists of 4 men, 6 women and 5 children. In how many ways can 3 men, 2 women and 3 children selected from the given group?
Options:
A)987 ways
B)346 ways
C)600 ways
D)157 ways
E)134 ways
Rationale: The number of ways of selecting three men, two women and three children is:
= ⁴C₃ * ⁶C₂ * ⁵C₃
= (4 * 3 * 2)/(3 * 2 * 1) * (6 * 5)/(2 * 1) * (5 * 4 * 3)/(3 * 2 * 1)
= 4 * 15 * 10
= 600 ways.
Answer: C
Answer: C
Question: A train passes a station platform in 36 sec and a man standing on the platform in 25 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
Options:
A)767 m
B)240 m
C)187 m
D)176 m
E)165 m
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 25 = 375 m.
Let the length of the platform be x m . Then,
(x + 375)/36 = 15 => x = 165 m.
Answer:E
Answer: E
Question: The variable x is inversely proportional to the square of the variable y. If y is divided by 4a, then x is multiplied by which of the following?
Options:
A)1/16a
B)1/16a^2
C)1/4a
D)16a
E)16a^2
Rationale: initially - did x= 1/y^2
But this yielded the wrong answer,
I then re examined the question and tried y^2/x =1
Which I then got y = SQR(X)
subbing into y/4a I got answer E)
Answer: E
Question: Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
Options:
A)2000
B)6657
C)2776
D)2679
E)2551
Rationale: (10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
Answer: A
Answer: A
Question: What is the prime factors’ number of 28?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: prime factors’ number, as I assume, for a number X=a^n*b^m*c^o*d^p... is = n+m+o+p...
So, 28 = 2^2*7^1
prime factors’ number will be 2+1 = 3.
Hence, answer is B.
Answer: B
Question: A began business with Rs.45000 and was joined afterwards by B with Rs.5400. When did B join if the profits at the end of the year were divided in the ratio of 2:1?
Options:
A)1
B)6
C)7
D)8
E)2
Rationale: 45*12 : 54*x = 2: 1
x = 5
12 -5 = 7
Answer: C
Answer: C
Question: When the number 209y913 is exactly divisible by 11, then the smallest whole number that can replace y?
Options:
A)0
B)1
C)2
D)5
E)9
Rationale: The given number =209y913
Sum of the odd places =3+9+9+2=23
Sum of the even places = 1+y+0
(Sum of the odd places)- (Sum of even places) = Number (exactly divisible by 11)
23-(1+y) = divisible by 11
22 � y = divisible by 11.
Y must be 0, to make given number divisible by 11.
A
Answer: A