divelab/Sys2Bench huggingface dataset:
Question: A crate measures 3 feet by 8 feet by 12 feet on the inside. A stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides. What is the radius, in feet, of the pillar with the largest volume that could still fit in the crate?
Options:
A)27
B)3
C)6
D)8
E)12
Rationale: We can find the radius of all the three cases of cylinders.
The only crux to find the answer faster is that:
Voulme is pi*r^2*h. The volume is a function of r^2. so r has to be the highest to find the largest volume.
So r=3 for the surface 8*12 face.
Volume = 27pi
Answer B
Answer: B
Question: A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?
Options:
A)2 2 ½ kmph
B)6 2 ½ kmph
C)5 2 ½ kmph
D)2 8 ½ kmph
E)6 5 ½ kmph
Rationale: 100 --- 10 DS = 10
? ---- 1
75 ---- 15 US = 5
? ----- 1 S = (10 - 5)/2
= 2 2 ½ kmph
Answer:A
Answer: A
Question: 31 of the scientists that attended a certain workshop were Wolf Prize laureates, and 18 of these 31 were also Nobel Prize laureates. Of the scientists that attended that workshop and had not received the Wolf prize, the number of scientists that had received the Nobel Prize was 3 greater than the number of scientists that had not received the Nobel Prize. If 50 of the scientists attended that workshop, how many of them were Nobel Prize laureates?
Options:
A)A)11
B)B)18
C)C)24
D)D)29
E)D)36
Rationale: lets solve by creating equation..
W = 31..
Total = 50..
Not W = 50 -31= 19..
Now let people who were neither be x, so out of 19 who won Nobel = x+3..
so x+x+3=19 or x=8..
so who won Nobel but not Wolf = x+3 = 11..
But people who won BOTH W and N = 13..
so total who won N = 11+18 = 29..
D
Answer: D
Question: A person walks from one end to the other of a 90-meter long moving walkway at a constant rate in 30 seconds, assisted by the walkway. When this person reaches the end, they reverse direction and continue walking with the same speed, but this time it takes 120 seconds because the person is traveling against the direction of the moving walkway. If the walkway were to stop moving, how many seconds would it take this person to walk from one end of the walkway to the other?
Options:
A)36
B)42
C)48
D)54
E)60
Rationale: Let v be the speed of the person and let x be the speed of the walkway.
30(v+x)=90 then 120(v+x)=360
120(v-x)=90
When we add the two equations:
240v=450
v=15/8
time = 90 / (15/8) = 48 seconds
The answer is C.
Answer: C
Question: The ratio of the present ages of P and Q is 3:4. 5 years ago, the ratio of their ages was 5:7. Find the their present ages?
Options:
A)30, 40
B)30, 47
C)30, 46
D)30, 498
E)30, 41
Rationale: Their present ages be 3X and 4X.
5 years age, the ratio of their ages was 5:7, then (3X - 5):(4X - 5) = 5:7
X = 35 - 25 => X = 10.
Their present ages are: 30, 40.
Answer: A
Answer: A
Question: A and b make a business together, and make a profit of Rs 84000. If A get Rs 48000, what was the ratio of investment between them?
Options:
A)4 : 3
B)3 : 2
C)5 : 2
D)4 : 5
E)6 : 5
Rationale: A get 48000
Then B get = (84000-48000) = 36000
Ratio between A and B is = 48000 : 36000 = 4 : 3
Answer : Option A
Answer: A
Question: Solve the following quadratic equation by factoring.
u2+15u=-50
Options:
A)-5,-10
B)5,10
C)4,3
D)-4,3
E)2,5
Rationale: u+5=0=>u=-5
u+10=0=>u=-10
ANSWER A
Answer: A
Question: A certain sum earns simple interest of Rs. 800 in 2 years at a certain rate of interest. If the same sum earns compound interest of Rs.900in the same period of 2 years, What must be the rate of interest?
Options:
A)25%
B)10%
C)15%
D)20%
E)30%
Rationale: Explanation:
Given: 800 = (P * R * 2) / 100
S.I. For 1 year = Rs. 400
Thus, (900 – 800) = S.I. on Rs. 400 for 1 year
100 = (400 * R * 1) / 100
R = 25% p.a.
ANSWER: A
Answer: A
Question: In a consumer survey, 66% of those surveyed liked at least one of three products: 1, 2, and 3. 35% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 8% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?
Options:
A)9
B)10
C)11
D)12
E)13
Rationale: 35 + 30 + 20 = 85
This number includes some people counted twice and some people counted three times.
85 - 66 = 19, and this number represents people counted twice or three times.
8% of the people are counted two extra times.
The percentage of people counted one extra time is 19 - 8(2) = 3.
The percentage of people who liked more than one product is 8% + 3% = 11%.
The answer is C.
Answer: C
Question: Which of the following is true about 0<|x|-2x<5?
Options:
A)-1<x<0
B)0<x<1
C)1<x<2
D)2<x<3
E)3<x<4
Rationale: when can be |x|-2x be greater than 0..
NEVER when x is positive..
ONLY A is left..
you can also substitute any value within the given range to check for answer
Example - put x as -0.5 for A. -1<x<0..
so |x|-2x = |-0.5|- 2*(-0.5) = 0.5+1 = 1.5 and it satisfies 0<|x|-4x<5
A
Answer: A
Question: A trader marked the selling price of an article at 12% above the cost price. At the time of selling, he allows certain discount and suffers a loss of 1%. He allowed a discount of :
Options:
A)10 %
B)10.5 %
C)11 %
D)12.5 %
E)9.8
Rationale: Sol.
Let C.P. = Rs. 100. Then, Marked Price = Rs. 110, S.P. = Rs. 99.
∴ Discount % = [11/112 * 100] % = 9.8%
Answer E
Answer: E
Question: In how many ways can 3 hats be formed out of 3 blue hats and 10 red hats?
Options:
A)12
B)302
C)1
D)250
E)286
Rationale: Total number of hats = 13Possible number of formations = 13C3 = 286Correct answer is E
Answer: E
Question: Two numbers when divided by a divisor leave remainders of 208 and 332 respectively. The remainder obtained when the sum of the numbers is divided by the same divisor is 68. Find the divisor.
Options:
A)335
B)365
C)387
D)472
E)516
Rationale: Let x be the divisor.
N1 = xa + 208
N2 = xb + 332
N1 + N2 = x(a+b) + 540 = xc + 68
x(c-a-b) = 472 but we know that x > 332, thus (c-a-b) must equal 1.
The answer is D.
Answer: D
Question: When Greenville State University decided to move its fine arts collection to a new library, it had to package the collection in 20-inch by 20-inch by 12-inch boxes. If the university pays $0.40 for every box, and if the university needs 2.4 million cubic inches to package the collection, what is the minimum amount the university must spend on boxes?
Options:
A)$200
B)$275
C)$510
D)$1,250
E)$2,550
Rationale: The volume of each box is 20*20*12 = 4800 cubic inches.
Number of boxes = 2,400,000/4800 = 500 boxes
Total cost = 500×$0.4=$200
The answer is A.
Answer: A
Question: A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.3 per sq m?
Options:
A)1350
B)1357
C)2025
D)2052
E)2122
Rationale: Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 3 = Rs.2025
Answer:C
Answer: C
Question: A sum of money is to be divided among Ann, Bob and Chloe. First, Ann receives $4 plus one-half of what remains. Next, Bob receives $4 plus one-third of what remains. Finally, Chloe receives the remaining $32. How much money J did Bob receive?
Options:
A)20
B)22
C)24
D)26
E)52
Rationale: Notice that we need not consider Ann's portion in the solution. We can just let K = the money REMAINING after Ann has received her portion and go from there.
Our equation will use the fact that, once we remove Bob's portion, we have $32 for Chloe.
So, we getK - Bob's $ = 32
Bob received 4 dollars plus one-third of what remained
Once Bob receives $4, the amount remaining is K-4 dollars. So, Bob gets a 1/3 of that as well.
1/3 of K-4 is (K-4)/3
So ALTOGETHER, Bob receives4 + (K-4)/3
So, our equation becomes:K -[4 + (K-4)/3 ]= 32
Simplify to get: K - 4 - (K-4)/3 = 32
Multiply both sides by 3 to get: 3K - 12 - K + 4 = 96
Simplify: 2K - 8 = 96
Solve: K = 52
Plug this K-value intoK - Bob's $ = 32to get: 52 - Bob's $ = 32
So, Bob's $ J= 20
Answer:
B
Answer: B
Question: A horse is tied to one corner of a square playground of side 20m by a rope 3.5m long. Find the area it can move in that playground?
Options:
A)9.625
B)10.5
C)11.125
D)12.5
E)14.45
Rationale: Area covered by horse = Pi*r^2/4 ( here we divide by 4 because rope is tied at the corner of the playground and only 1/4 part , the horse can move in that playground.)
where r= 3.5 m = length of rope
So area = (22/7)*3.5*3.5/4 = 9.625 sq m
answer :A
Answer: A
Question: In a triangle, one side is 5 Cm and another side is 9 Cm. which of the following can be the perimeter of the triangle?
Options:
A)18.
B)25.
C)30.
D)32.
E)23.
Rationale: Given : one side is 5 Cm and another side is 9 Cm. So the 3rd side will be > 3 and < 15. Thus the perimeter will be : 18 < perimeter < 30. Only option satisfying this condition is 23. Hence E.
Answer: E
Question: Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $9 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 50 percent, what is the discount rate on Pony jeans?
Options:
A)9%
B)10%
C)110%
D)120%
E)150%
Rationale: x discount on Pony jeans, (0.5-x) discount on Fox jeans.
Set the equation: 3*15(0.5-x)+2*18x=9 --> x=1.5=150%
Answer: E.
Answer: E
Question: What is the unit digit of 3^58?
Options:
A)0
B)5
C)7
D)1
E)9
Rationale: Unit digit in 3^58 = unit digit in [(3^4)^14]*3^2 = 1*9 = 9
Answer is E
Answer: E
Question: By mixing two qualities of pulses in the ratio 2: 3 and selling the mixture at the rate of Rs 22 per kilogram, a shopkeeper makes a profit of 10 %. If the cost of the smaller quantity be Rs 14 per kg, the cost per kg of the larger quantity is:
Options:
A)Rs 23
B)Rs 25
C)Rs 24
D)None of these
E)Cannot be determined
Rationale: Explanation:
Cost Price of 5 kg = Rs.(14*2 + x*3) = (28 + 3x).
Sell price of 5 kg = Rs. (22x5) = Rs. 110.
[{110 - (28 + 3x)}/(28 + 3x) ]* 100 =10
[82-3x/28 + 3x]= 1 / 10
820 - 30x = 28 +3x
33x = 792
x = 24
Answer: C
Answer: C
Question: If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area?
Options:
A)120 cm2
B)176 cm2
C)112 cm2
D)166 cm2
E)167 cm2
Rationale: The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle
= 1/2 * 24 * 10
= 120 cm2
Answer:A
Answer: A
Question: Two trains of length 160 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
Options:
A)28
B)266
C)990
D)20
E)22
Rationale: Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.
Distance covered in passing each other = 160 + 280 = 440 m.
The time required = d/s = 440/20 = 22 sec.
Answer: E
Answer: E
Question: A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
Options:
A)288
B)277
C)284
D)108
E)133
Rationale: The boy can select one trouser in nine ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 12
= 108 ways.
Answer: D
Answer: D
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
Options:
A)2.5 sec
B)2.8 sec
C)8.5 sec
D)2.7 sec
E)8.5 sec
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 100/40 = 2.5 sec.
Answer:A
Answer: A
Question: If the average of 365, 409, 187, 420, 451, and x is 314, then what is x?
Options:
A)190
B)52
C)232
D)114
E)400
Rationale: x = 52 because:
(365+409+187+420+451+x)/6=314
(365+409+187+420+451+x)/6*6=314*6
(365+409+187+420+451+x)=1884
(365+409+187+420+451+x)-1832=1884-1832
x=52
Therefore, the answer is B, 52.
Answer: B
Question: If a certain toy store's revenue in November was 2/5 of its revenue in December and its revenue in January was 1/5 of its revenue in November, then the store's revenue in December was how many times the average (arithmetic mean) of its revenues in November and January?
Options:
A)5/2
B)10/3
C)15/4
D)25/3
E)25/6
Rationale: N = 2D/5
J = N/5 = 2D/25
The average of November and January is (N+J)/2 = 12D/25 / 2 = 6D/25
D is 25/6 times the average of November and January.
The answer is E.
Answer: E
Question: A committee is composed of w women and m men. If 3 women and 4 men are added to the committee, and if one person is selected at random from the enlarged committee, then the probability that a woman is selected can be represented by
Options:
A)w/m
B)w/(w+m)
C)(w+3)/(m+4)
D)(w+3)/(w+m+3)
E)(w+3)/(w+m+7)
Rationale: The number of women is w+3.
The total number of people is w+m+7.
P(a woman is selected) = (w+3) / (w+m+7)
The answer is E.
Answer: E
Question: The duplicate ratio of 3:4 is?
Options:
A)9:19
B)9:11
C)9:16
D)9:109
E)9:12
Rationale: 32: 42 = 9:16
Answer: C
Answer: C
Question: Darcy lives 1.5 miles from work. She can walk to work at a constant rate of 3 miles per hour, or she can ride the train to work at a constant rate of 20 miles per hour. If she rides the train, there is an additional x minutes spent walking to the nearest train station, waiting for the train, and walking from the final train station to her work. If it takes Darcy a total of 2 more minutes to commute to work by walking than it takes her to commute to work by riding the train, what is the value of x?
Options:
A)10.5
B)15
C)25.5
D)30
E)23.5
Rationale: The time it takes Darcy to walk to work is (1.5/3)*60 = 30 minutes
The time it takes Darcy to take the train is (1.5/20)*60 + x = 4.5 + x minutes
It takes 15 minutes longer to walk, so 30 = 4.5 + x + 2
x=23.5 minutes
Answer: E
Answer: E
Question: What is the least possible product of 4 different integers, each of which has a value between –3 and 10, inclusive?
Options:
A)–5040
B)–3600
C)–2160
D)–600
E)–120
Rationale: Maximize the total product with a -ve sign
so -3 * 10 * 9 * 8 = 720 * -3 = -2160
Answer is C.
Answer: C
Question: P is a prime number. If 6p is between 15 and 95, which of the following can be a value of 7p + 2?
Options:
A)15
B)79
C)121
D)65
E)21
Rationale: We see that the format we are looking for is 7p + 2.
When you subtract 2 from option A, you get 13 - not a multiple of 7. Ignore.
When you subtract 2 from option B, you get 77. It is a multiple of 7. Let's check it. p = 11 which is prime. Good. 6p = 66 which is between 15 and 95. Very good.
ANSWER:D
Answer: D
Question: Shekhar started a business investing Rs.25,000 in 1999.In 2000,he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000.In 2001,Shekhar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000.What will be Rajeev’s share in the profit of Rs.2,70,000 earned at the end of 3 years from the start of the business in 1999 ?
Options:
A)Rs.45,000
B)Rs.50,000
C)Rs.90,000
D)Rs.75,000
E)None of these
Rationale: Solution
Shekhar : Rajeev : Jatin
= (25000x12+35000x12+45000x12) :(35000x24) : (35000x12)
= 1260000 : 840000 : 420000 = 3 : 2 : 1.
∴ Rajeev’s share = Rs.(27000x2/6) = Rs. 90,000. Answer C
Answer: C
Question: The speed of a boat in upstream is 90 kmph and the speed of the boat downstream is 190 kmph. Find the speed of the boat in still water and the speed of the stream?
Options:
A)10 kmph
B)76 kmph
C)12 kmph
D)97 kmph
E)50 kmph
Rationale: Speed of the boat in still water
= (90+190)/2
= 140 kmph. Speed of the stream
= (190-90)/2
= 50 kmph.
Answer:E
Answer: E
Question: Arun purchased 30 kg of wheat at the rate of Rs. 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg. He mixed the two and sold the mixture. Approximately what price per kg should be sell the mixture to make 15% profit?
Options:
A)14.49
B)16.33
C)16.35
D)16.3
E)16.32
Rationale: C.P. of 50 kg wheat = (30 * 11.50 + 20 * 14.25) = Rs. 630.
S.P. of 50 kg wheat = 115% of Rs. 630 = 115/100 * 630 = Rs. 724.5
S.P. per kg = 724.5/50 = 14.49
A
Answer: A
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
Options:
A)3/9
B)3/2
C)3/1
D)3/7
E)3/4
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train
= 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23
==> 27 x + 17 y = 23 x + 23 y ==> 4 x
= 6 y ==> x/y = 3/2.
Answer:B
Answer: B
Question: (5)1.25 × (12)0.25 × (60)0.75 = ?
Options:
A)420
B)260
C)200
D)300
E)400
Rationale: Explanation :
(5)1.25 × (12)0.25 × (60)0.75
=(5)1.25 × (12)0.25 × (12 × 5)0.75
= (5)1.25 × (12)0.25 × (12)0.75 × (5)0.75
= (5)(1.25 + 0.75) × (12)(0.25 + 0.75)
= (5)2 × (12)1
= 25 × 12
= 300
Answer : Option D
Answer: D
Question: The probability of picking 2 red balls one after another without replacement from a bag containing only red and white balls is 14/33. What will be the probability of picking 2 white balls one after another w/o replacement from that bag, given that it can hold at the most 20 balls?
Options:
A)1/33
B)3/33
C)5/33
D)9/33
E)19/33
Rationale: Probability of picking 2 red balls = 14/33
(R/R+W)*(R-1)/(R+W-1) = 14/33 = (2*7)/(3*11) = (2/3)*(7/11) --> Once the value is reduced to this level, it should be easy to find out the number of red balls.
1) Considering the above expression, both numerator and denominator must be consecutive.
2) Lets multiply both numerator and denominator with the same integer so that the value remains unaffected.
3) We can't multiply 7/11 as we need a consecutive term in both numerator and denominator. So lets multiply (2/3) to make the numerator and denominator consecutive.
(2/3)*(2/2) = 4/6 --> 4*7/6*11 --> Numerator and denominator not consecutive
(2/3)*(3/3) = 6/9 --> 6*7/9*11 --> Only numerator is consecutive
(2/3)*(4/4) = 8/12 --> 8*7/12*11 --> Numerator and denominator are consecutive here
Number of red balls, R = 8.
Total number of balls, R + W = 12 (This value is < 20, satisfying the condition)
Number of white balls, W = 12 - 8 = 4
Probability of picking 2 white balls w/o replacement = (W/R+W)*(W-1)/(R+W-1) = (4/12)*(3/11) = 3/33
Answer: B
Answer: B
Question: Worker W produces n units in 5 hours. Workers V and W, workers independently but at thesame time, produce n units in 2 hours.how long would it take V alone to produce n units?
Options:
A)1 hr 26 min
B)1 hr 53 min
C)2 hr 30 min
D)3 hr 30 min
E)3 hr 20 min
Rationale: V and W produce n units in 2 hours. So they produce n/2 units in 1 hour.
W produces n units in 5 hrs. So he alone produce n/5 units in 1 hr.
So V produces in 1 hr. = n/2 - n/5 = 3 n/10 units.
V produces n units in 10/3 hrs. which is 3 hrs 20 min.
ANSWER:E
Answer: E
Question: The average of 11 results is 50, if the average of first five results is 49 and that of the last seven is 52. Find the fifth result?
Options:
A)55
B)56
C)57
D)58
E)59
Rationale: 1 to 11 = 11 * 50 = 550
1 to 5 = 5 * 49 = 245
5 to 11 = 7 * 52 = 364
5th = 245 + 364 – 550 = 59
ANSWER:E
Answer: E
Question: Find the rank of the word GOOGLE if all the words which can be formed by permuting letters of this word without repitition are arranged in dictionary in alphabetical order???
Options:
A)86
B)67
C)88
D)89
E)69
Rationale: EGGLOO arranging in alphabetiaccal order
E - - - - - 5!/(2!*2!)=30
GE- - - - 4!/2!=12 30+12=42
GG- - - - 4!/2!=12 42+12=54
GL- - - - 4!/2!=12 54+12=66
GOE - - - 3!=6 66+6=72
GOG- - - 3!=6 72+6=78
GOL- - - 3!=6 78+6=84
GOOE- - 2!=2 84+2=86
GOOGE - 1!=1 86+1=87
GOOGLE 1!=1 87+1=88
So, 88 th no, is GOOGLE
ANSWER:C
Answer: C
Question: The surface of a cube is 54sq cm. Find its volume?
Options:
A)8cc
B)27cc
C)2cc
D)4cc
E)6cc
Rationale: 6a2 = 54 = 6*9
a = 3 => a3 = 27cc
Answer: B
Answer: B
Question: A firm has 3 senior partners and 5 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner? (Note that two groups are considered different if at least one group member is different.)
Options:
A)42
B)46
C)50
D)54
E)58
Rationale: The number of ways to form a group of 3 is 8C3 = 56
The number of groups with no senior partner is 5C3 = 10
The number of groups with at least one senior partner is 56-10 = 46
The answer is B.
Answer: B
Question: Fresh grapes contain 75% by weight while dried grapes contain 25% water by weight. What is the weight of dry grapes available from 200 kg of fresh grapes?
Options:
A)40.00 kg
B)45.50 kg
C)66.67 kg
D)80.56 kg
E)90.00 kg
Rationale: From the question we know: 200kg * 75% = 150kg of water in the fresh grapes
200kg - 150kg of water = 50kg of non-water mass
We are looking for the weight of the dry grapes (X).
Since the question tells us that 25% of the weight of the dry graps is water and we know that 50kg is non-water mass we can set up the following equation:
X = 1/4(X) + 50kg
3/4(X) = 50kg
X = 66.67 kg
Answer- C
Answer: C
Question: A woman has five blouses of different colors, three skirts of different colors, and two different pairs of shoes. She refuses to wear her pink blouse with her green skirt. How many different blouseskirt-shoe combinations could she wear?
Options:
A)8
B)12
C)28
D)17
E)18
Rationale: total ways = 5*3*2=30..
now its better to find the ways in which the pink blouse and green skirt are together and subtract from total to get the answer..
the ways in which the pink blouse and green skirt are together=1*1*2=2..
total ways =30-2=28..
ANSWER:C
Answer: C
Question: The value of 0.1 x 0.1 x 0.1 + 0.02 x 0.02 x 0.02/ 0.2 x 0.2 x 0.2 + 0.04 x 0.04 x 0.04	is:
Options:
A)0.125
B)0.135
C)0.145
D)0.155
E)0.165
Rationale: Given expression
=(0.1)(power 3) + (0.02)(power 3) /2(power 3) [(0.1)(power 3) + (0.02)(power 3)]
=1/8
= 0.125
Answer is A
Answer: A
Question: A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30° with the man’s eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60°. What is the distance between the base of the tower and the point P?
Options:
A)4 units
B)8 units
C)12 units
D)Data inadequate
E)None of these
Rationale: Explanation:
One of AB, AD and CD must have been given.So, the data is inadequate.
Answer: D
Answer: D
Question: The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 10 terms of the arithmetic progression?
Options:
A)300
B)100
C)150
D)170
E)270
Rationale: n th term of A.P. is given by a+(n-1)d
4 th term = a+3d
12 th term = a+11d
Given a+3d+a+11d=20 --> 2a+14d=20 --> a+7d = 10
Sum of n term of A.P = n/2[2a+(n-1)d]
subsitiuing n = 10 ...we get 10/2[ 2a + 14d] = 10 [a+7d] = 10*10 = 100...
Answer is B...
Answer: B
Question: In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 46, the divident is
Options:
A)4236
B)4306
C)4336
D)5336
E)None
Rationale: Solution
Divisor	= (5×46)
= 230.
Also. 10×Q	= 230
‹=› Q=23.
And, R= 46.
Dividend	= (230×23+46)
= 5336.
Answer D
Answer: D
Question: A line that passes through (–1, –4) and (3, k) has a slope = k. What is the value of k?
Options:
A)3/4
B)1
C)4/3
D)2
E)7/2
Rationale: This is a considerably more difficult one, which will involve some algebra. Let’s say that the “first” point is (–1, –4) and the “second,” (3, k). The rise = k + 4, which involves a variable. The run = 3 – (–1) = 4. There the slope is (k + 4)/4, and we can set this equal to k and solve for k.
{{k + 4}/4} = k
k + 4 = 4k
4 = 3k
k = 4/3
Answer = C
Answer: C
Question: If the function f(x) is defined for all real numbers x as the maximum value of 4x + 4 and 12 + 3x, then for which one of the following values of x will f(x) actually equal 4x + 4 ?
Options:
A)4
B)5
C)6
D)7
E)9
Rationale: Since f(x) defines maximum of 4x + 4 and 12 + 3x,
to find those x when 4x+4 has greater value,
4x + 4 > 12 + 3x
or x < 8
Only value that satisfy this is 7.
Answer is (D),
Answer: D
Question: A train 250 m long is running at a speed of 58 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train?
Options:
A)5 sec
B)9 sec
C)12 sec
D)18 sec
E)15 sec
Rationale: Answer : D.
Speed of the train relative to man = (58 - 8) kmph
= (50* 5/18) m/sec = (125/9)m/sec
Time taken by the train to cross the man
= Time taken by It to cover 250 m at 125/9 m / sec = 250 *9/ 125 sec = 18sec
Answer: D