mathewhe/aqua_rat huggingface dataset:
Question: A wooden cube whose edge length is 9 inches is composed of smaller cubes with edge lengths of one inch. The outside surface of the large cube is painted red and then it is split up into its smaller cubes. If one cube is randomly selected from the small cubes, what is the probability that the cube will have at least one red face?
(A) 52.9%
(B) 55.4%
(C) 58.3%
(D) 61.7%
(E) 64.5%
Rationale: There are a total of 9*9*9 = 729 cubes.
All the exterior cubes will have at least one face painted red.
The interior is formed by 7*7*7 = 343 cubes.
The number of cubes with at least one side painted red is 729 - 343 = 386 cubes
The probability that a cube has at least one side painted red is 386/729 which is about 52.9%
The answer is A.
Answer: (A) 52.9%
Question: If two of the four expressions a+b, 3a+b, a-b, and a-3b are chosen at random, what is the probability that their product will be of the form of a^2 + kb^2, where k is a positive integer?
(A) 1/2
(B) 1/6
(C) 1/4
(D) 1/3
(E) 1/2
Rationale: *3=12 --> total number of outcomes
but only two of the expressions will result in desired form -->so the probability of choosing the right pair is 2/12=1/6
ANS:B
Answer: (B) 1/6
Question: The perimeter of a triangle is 44 cm and the in radius of the triangle is 2.5 cm. What is the area of the triangle?
(A) 76
(B) 88
(C) 66
(D) 55
(E) 35
Rationale: Area of a triangle = r * s
Where r is the in radius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 44/2 = 55 cm2
Answer:D
Answer: (D) 55
Question: If a and b are Positive Integers and a<b, b is not equal to zero, which of the following can give NEGATIVE answer?
(A) a+b
(B) ab
(C) a/2+b/2
(D) a-b
(E) a^2+b^2
Rationale: (A)a+b
This cannot be answer. Because a and b are positive integers
All the following options (Except D) should not be an answer.
(D) a-b
If a>0,a-b gives a negative answer.
So the option D is answer
Answer: (D) a-b
Question: John was thrice as old as Tom 6 yrs back. He will be 5/3 times as old as Tom 6 years hence. How old is Tom today?
(A) 10
(B) 11
(C) 12
(D) 15
(E) 16
Rationale: Sol. RMBflSk -6 = 3 (Ravi - 6) ...(j)
and Rupesh + 6 = | (Ravi + 6) ...(ii)
Solving both the equations we get,
Ravi = 12 years.
C
Answer: (C) 12
Question: A single discount equivalent to the discount series of 20%, 12% and 5% is?
(A) 31.6
(B) 31.0
(C) 31.6
(D) 33.12
(E) 31.5
Rationale: 100*(80/100)*(88/100)*(95/100)
= 68.4
100 - 66.88 = 33.12
Answer: D
Answer: (D) 33.12
Question: Calculate how long it will take a swimmer to swim a distance of 3km against the current of a river which flows at 1.7km/hr, given that he can swim in still water at 3km/h
(A) 2.31
(B) 9.31
(C) 1.31
(D) 4.31
(E) 3.31
Rationale: swim in still water at = 3
speed of river= 1.7
US = 3 - 1.7= 1.3
Distance = 3
T = 3/1.3 = 2.31
Answer: A
Answer: (A) 2.31
Question: Find the odd man out. 3, 5, 15, 75, 1120, 84375
(A) 84375
(B) 1120
(C) 15
(D) 3
(E) 75
Rationale: Explanation :
Pattern : 1st * 2nd = 3rd, 2nd * 3rd = 4th, etc.
3
5
3 × 5 = 15
5 × 15 = 75
15 × 75 = 1125
75 × 1125 = 84375
Hence, 1120 is wrong. 1125 should have come in place of 1120
Answer : Option B
Answer: (B) 1120
Question: A company, Chauncy Co., has an annual travel budget of $53,000. The accounting department estimates that transportation expenses will increase 5 percent in the coming year, and nontransportation travel expenses will increase by 15 percent in the coming year. Last year, Chauncy Co. spent $19,500 on transportation-related expenses, and $35,000 on nontransportation travel expenses. If the annual travel budget does not increase this year, and if the accounting department’s estimates are correct, how far over the annual travel budget will expenses be this year?
(A) Expenses will not go over the budget.
(B) $500
(C) $4,225
(D) $7,725
(E) $60,725
Rationale: annual travel budget of $53,000
Let, Transportation expenses = T = 19500
and Non-Transportation expenses = N=35000
i.e. Increased Transportation expenses = 1.05T = 20475
and Increased Non-Transportation expenses = 1.15N = 40250
Total Expense = 20475+40250 = 60725
Expense over Budget = Budget - expense = 53000-60725 = 7725
Answer: Option D
Answer: (D) $7,725
Question: The forth proportional to 10,20,30 is?
(A) 20
(B) 60
(C) 45
(D) 75
(E) 100
Rationale: Let the fourth proportional to 10,20,30 be x
then 10:20::30:x
10x = 20*30
x = 60
Answer is B
Answer: (B) 60
Question: If â€œ*â€ is called â€œ+â€, â€œ/â€ is called â€œ*â€, â€œ-â€ is called â€œ/â€, â€œ+â€ is called â€œ-â€. 120/40 â€“ 30 * 20 - 5 = ?
(A) 178.5
(B) 156.6
(C) 160.4
(D) 163.6
(E) 164.1
Rationale: Explanation:
Given : 120/40 â€“ 30 * 20 - 5 = ?
Substituting the coded symbols for mathematical operations, we get,
120 * 40/30 +20 / 5 = ?
120 * 1.33 + 4 = ?
159.6 + 4 = 163.6
ANSWER : D
Answer: (D) 163.6
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?
(A) 10
(B) 18
(C) 36
(D) 72
(E) 64
Rationale: Explanation:
Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12 => x = 10
Speed of each train = 10 m/sec.
= 10 * 18/5 =- 36 km/hr.
ANSWER IS C
Answer: (C) 36
Question: .003/?= .01
(A) .3
(B) .09
(C) .009
(D) .0009
(E) None of them
Rationale: Let .003/x = .01;
Then x = .003/.01
= .3/1
= .3
Answer is A
Answer: (A) .3
Question: Find the fourth proportion to 2,4,6
(A) 18
(B) 12
(C) 9
(D) 6
(E) 8
Rationale: Explanation:
2:4 :: 6:x
=> 2/4= 6/x
=> x = 24/2
=> x = 12
Answer:B
Answer: (B) 12
Question: A man takes 6 hours 15 minutes in walking a distance and riding back to the starting place. He could walk both ways in 7 hours 45 minutes. The time taken by him to ride both ways, is
(A) 4 hours
(B) 4 hours 30 minutes
(C) 4 hours 45 minutes
(D) 5 hours
(E) 6 hours
Rationale: Explanation:
Time taken in walking both ways = 7 hours 45 minutes --------(i)
Time taken in walking one way and riding back= 6 hours 15 minutes-------(ii)
By equation (ii)*2 -(i), we have
Time taken to man ride both ways, = 12 hours 30 minutes - 7 hours 45 minutes
= 4 hours 45 minutes
ANSWER IS C
Answer: (C) 4 hours 45 minutes
Question: In a psychology school the grade of the students is determined by the following method: At the end of the first year the grade equals to twice the age of the student. From then on, the grade is determined by twice the age of the student plus half of his grade from the previous year. If Joey's grade at the end of the first year is 40, what will be his grade at the end of the third year?
(A) 74
(B) 75
(C) 76
(D) 77
(E) 78
Rationale: let the age is 'x' so after 1st yr 2x=40 and x=20
after 2nd year (now age become 21)
2*21+ 20=62 grades
after 3rd year(now age becomes 22)
2*22+31=75
ANSWER:B
Answer: (B) 75
Question: Find smallest prime number is:
(A) 13
(B) 21
(C) 14
(D) 18
(E) 42
Rationale: A
13
Answer: (A) 13
Question: The radius of a cylindrical vessel is 7cm and height is 2cm. Find the whole surface of the cylinder?
(A) 281
(B) 396
(C) 440
(D) 767
(E) 1981
Rationale: r = 7 h = 2
2πr(h + r) = 2 * 22/7 * 7(9) = 396
Answer:B
Answer: (B) 396
Question: What is the median from the below series 90, 92, 93, 88, 95, 88, 97, 87, and 98
(A) 76
(B) 79
(C) 92
(D) 94
(E) 95
Rationale: Ordering the data from least to greatest, we get:
87, 88, 88, 90, 92, 93, 95, 96, 98
The median quiz score was 92. (Four quiz scores were higher than 92 and four were lower.)
C
Answer: (C) 92
Question: A rectangle having length 140 cm and width 40 cm. If the length of the rectangle is increased by thirty percent then how much percent the breadth should be decreased so as to maintain the same area.
(A) 17.64%
(B) 33.33%
(C) 40%
(D) 75%
(E) None of these
Rationale: Explanation :
Solution: (30/(140+30) * 100)% = 17.64%
Answer : A
Answer: (A) 17.64%
Question: A number increased by 30% gives 650. The number is?
(A) 200
(B) 300
(C) 400
(D) 500
(E) 600
Rationale: Formula = TOTAL=100% ,INCREASE = "+" DECREASE= "-"
A number means = 100 %
That same number increased by 30 % = 130 %
130 % -------> 650 (130 Ã— 5 = 650)
100 % -------> 400 (100 Ã— 5 = 500)
Option 'D'
Answer: (D) 500
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train?
(A) 23 m
(B) 23 2/9 m
(C) 27 m
(D) 27 7/9 m
(E) 28 m
Rationale: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m.
ANSWER:D
Answer: (D) 27 7/9 m
Question: In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Abhay speed =x
sameer speed=y
(30/x)- (30/y)= 2 ....1
-(30/2x)+(30/y)= 1 ...-2
Solving 1 and 2 we get
6x=30
x=5
ANSWER E
Answer: (E) 5
Question: There are two inlets and one outlet to a cistern. One of the inlets takes 5/2hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern. Both of the inlets are turned on at 9:00 AM with the cistern completely empty, and at 10:30AM, the outlet is turned on and it takes 1 more hour to fill the cistern completely. How much time does the outlet working alone takes to empty the cistern when the cistern is full?
(A) 2 hours
(B) 2.5 hours
(C) 3 hours
(D) 3.5 hours
(E) 4 hours
Rationale: The combined inflow rate of the two inlets is 2/5 + 1/5 = 3/5 cistern/hour. Thus, working together, it takes 5/3 hours (time is reciprocal of rate) to fill the cistern.
From 9:00 AM to 10:30 AM, so in 1.5=3/2 hours, the inlet pipes will fill (time)*(rate) = 3/2*3/5 = 9/10 th of the cistern .
Then the outlet is turned on and the remaining 1/10 th of the cistern is filled in 1 hour.
Letting x to be the rate of the outlet, we would have: 3/5 - x = 1/10 --> x = 1/2 cistern/hour, which means that it takes 2 hours the outlet working alone to empty the cistern.
Answer: A.
Answer: (A) 2 hours
Question: What is the next number: 3, 27, 627, __
(A) 8847
(B) 9837
(C) 11,497
(D) 15,627
(E) 19,307
Rationale: 5^0 + 2 = 3
5^2 + 2 = 27
5^4 + 2 = 627
5^6 + 2 = 15,627
The answer is D.
Answer: (D) 15,627
Question: There are 6561 balls out of them 1 is heavy.Find the min. no. of times the balls have to be
weighed for finding out the haevy ball.
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: 1))6561/3=2187->2187,2187,2187
2)2187/3=729->729,729,729
3)729/3=243->243,243,243
4)243/3=81->81,81,81
5)81/3=27->27,27,27
6)27/3=9->9,9,9
7)9/3=3->3,3,3
8)3/3=1->1,1,1
8 times required
ANSWER:B
Answer: (B) 8
Question: A rectangular ground is to be filled with square tiles of unit area. The border of the ground should be of red coloured tiles and inside white. If the number of red and white tiles are the same, find the minimum dimensions of the ground.
(A) 44
(B) 45
(C) 46
(D) 47
(E) 48
Rationale: Let us consider R for RED & W for WHITE
[R01][R02][R03][R04][R05][R06][R07][R08]
[R24][W01][W02][W03][W04][W05][W06][R09]
[R23][W07][W08][W09][W10][W11][W12][R10]
[R22][W13][W14][W15][W16][W17][W18][R11]
[R21][W19][W20][W21][W22][W23][W24][R12]
[R20][R19][R18][R17][R16][R15][R14][R13]
In this rectangle there are 24 RED & 24 WHITE.
So the dimension is (6*8) or (8*6).
Total number of tiles is 48.
ANSWER:E
Answer: (E) 48
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
(A) 1/455
(B) 1/458
(C) 1/457
(D) 1/454
(E) 1/451
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that all the three marbles picked at random are blue
= ³C₃/¹⁵C₃
= (1 * 3 * 2 * 1)/(15 * 14 * 13)
= 1/455
Answer: A
Answer: (A) 1/455
Question: Carmen made a sculpture from small pieces of wood. The sculpture is 2 feet 6 inches tall.Carmen places her sculpture on a base that is 12 inches tall. How tall are the sculpture andbase together?
(A) 3.1 feet
(B) 3.2 feet
(C) 3.3 feet
(D) 3.4 feet
(E) 3.83 feet
Rationale: we know 1 feet =12 inch then
2 feet =24 inch
24+10=34 then
34+12=44
46/12=3.83 feet
ANSWER:E
Answer: (E) 3.83 feet
Question: One train is travelling 45 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is?
(A) 3:3
(B) 5:7
(C) 5:4
(D) 7:2
(E) 8:5
Rationale: C
5:4
45 * 5/18 = 10
25:20 => 5:4
Answer: (C) 5:4
Question: A person walking 5/6 of his usual rate is 40 minutes late. What is
his usual time?
(A) 3 hrs 20 min
(B) 4 hrs 20 min
(C) 5 hrs 20 min
(D) 6 hrs 20 min
(E) 3 hrs 30 min
Rationale: Let t be the usual time. If the usual rate is 1 unit, then the unusual rate is 5/6.
Balance by the distance,
1*t = (5/6)(t+40)
6t = 5(t+40)
Solve for t,
t = 200 minutes = 3 hrs 20 min
ANSWER:A
Answer: (A) 3 hrs 20 min
Question: The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
(A) 12 cm
(B) 14 cm
(C) 18 cm
(D) 20 cm
(E) 15 cm
Rationale: 2(l+b)/b=5/1
2l+2b=5b
3b=2l
b=2/3l
Then, Area = 216 cm2
lx b=216
lx 2/3l=216
l2=324
l=18 cm
ANSWER:C
Answer: (C) 18 cm
Question: 217 * 217 + 183 * 183
(A) 70578
(B) 82578
(C) 80578
(D) 80568
(E) 89045
Rationale: Explanation:
1/2×2(a2+b2)=1/2×[(a+b)2+(a−b)2]
=1/2×[(217+183)2+(217−183)2]=80578
Option C
Answer: (C) 80578
Question: In how many ways Chief Minister and Minister be elected from a team of 13 members?
(A) 124
(B) 131
(C) 132
(D) 145
(E) 156
Rationale: To do this, if captain is elected first, then we have 13 ways of doing this.
For election of vice-captain, we have only 12 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 13*12 = 156 ways.
E
Answer: (E) 156
Question: Which of the following is closest in value to (9^11)-(9^2)?
(A) 9^9
(B) 9^8
(C) 9^7
(D) 9^6
(E) 9^11
Rationale: 9^11 is much larger number than 9^2 and as we need approximate value then it's pretty much negligible in this case, so: (9^11)-(9^2) = ~9^11.
Answer: E.
Similar questions to practice:
Hope it helps.
Answer: (E) 9^11
Question: Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?
(A) 4
(B) 10
(C) 15
(D) 16
(E) 17
Rationale: Explanation:
L.C.M. of 2, 4, 6, 8, 10, 12 is 120.
So, the bells will toll together after every 120 seconds(2 minutes).
In 30 minutes, they will toll together	30/2+ 1 = 16 times.
ANSWER IS D
Answer: (D) 16
Question: Income and expenditure of a person are in the ratio 10 : 7. If the income of the person is Rs. 10000, then find his savings?
(A) 3005
(B) 3098
(C) 3300
(D) 3010
(E) 3000
Rationale: Let the income and the expenditure of the person be Rs. 10x and Rs. 7x respectively.
Income, 10x = 10000 => x = 1000
Savings = Income - expenditure = 10x - 7x = 3x = 3(1000)
So, savings = Rs. 3000.
Answer:E
Answer: (E) 3000
Question: Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years. What is definitely the difference between R and Q's age?
(A) 16
(B) 17
(C) 13
(D) 50
(E) 27
Rationale: R - Q = R - T
Q = T.
Also R + T = 50; R + Q
= 50
So, (R - Q) cannot be determined.
Answer: D
Answer: (D) 50
Question: What is the lowest possible common multiple of 2 distinct integers, each greater than 130?
(A) 131
(B) 131*132
(C) 131*131
(D) 262
(E) 132
Rationale: The least common multiple of two numbers greater than 130 is 2(131) = 262, where the two distinct integers are 131 and 262.
The answer is D.
Answer: (D) 262
Question: One side of a rectangle is 3 cm shorter than the other side. If we increase the length of each side by 1 cm, then the area of the rectangle will increase by 22 cm2. Find the lengths of all sides.
(A) 10 and 3
(B) 7 and 10
(C) 10 and 7
(D) 3 and 10
(E) 12 and 9
Rationale: Let x be the length of the longer side x>3, then the other side's length is x−3 cm. Then the area is S1 = x(x - 3) cm2. After we increase the lengths of the sides they will become (x+1) and (x−3+1)=(x−2) cm long. Hence the area of the new rectangle will be A2=(x+1)⋅(x−2) cm2, which is 22 cm2 more than the first area. Therefore
A1+22=A2
x(x−3)+22=(x+1)(x−2)
x2−3x+22=x2+x−2x−2
2x=24
x=12. So, the sides of the rectangle are 12 cm and (12−3)=9 cm long.
So answer is E.
Answer: (E) 12 and 9
Question: A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance (in km) is:
(A) 35
(B) 36 2/3
(C) 37 1/2
(D) 40
(E) 45
Rationale: Explanation:
Let distance = x km and usual rate = y kmph.
Then,	x/y-x/y + 3=40/60 =>2y(y + 3) = 9x ....(i)
And, x/y -2-x/y =40/60 =>y(y - 2) = 3x ....(ii)
On dividing (i) by (ii), we get: x = 40.
ANSWER IS D
Answer: (D) 40
Question: The average of seven numbers is 15. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
(A) 6
(B) 29
(C) 31
(D) 34
(E) 35
Rationale: The total of seven numbers = 7X15 = 105
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (105 - 99 ) = 6
A
Answer: (A) 6
Question: A fast food company plans to build 5 new restaurants. If there are 14 sites that satisfy the company's criteria for location of new restaurant, in how many different ways can company select the 5 sites needed for the new restaurant if the order of selection doesn't matter.
(A) 1001
(B) 2002
(C) 495
(D) 1532
(E) 395
Rationale: The number of ways of choosing 5 sites out of 14 are counted by = 14C5 ways = 2002
Answer: Option B
Answer: (B) 2002
Question: The ratio of the cost price and the selling price is 4:5. The profit percent is:
(A) 33
(B) 77
(C) 25
(D) 66
(E) 711
Rationale: Let C.P. = Rs. 4x. Then, S.P. = Rs. 5x
Gain = (5x - 4x) = Rs. x
Gain % = (x * 100)/ 4x = 25%.
Answer: C
Answer: (C) 25
Question: In a certain game of dice, the player’s score is determined as a sum of two throws of a single die. The player with the highest score wins the round. If more than one player has the highest score, the winnings of the round are divided equally among these players. If Jim plays this game against 21 other players, what is the probability of the minimum score that will guarantee Jim some monetary payoff?
(A) 41/50
(B) 1/221
(C) 1/216
(D) 1/36
(E) 1/42
Rationale: Toguaranteethat Jim will get some monetary payoff he must score the maximum score of 6+6=12, because if he gets even one less than that so 11, someone can get 12 and Jim will get nothing.
P(12)=1/6^2=1/36.
Answer: D
Answer: (D) 1/36
Question: What least number must be added to 1120, so that the sum is completely divisible by 23 ?
(A) 2
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 49*23 = 1127
1127 - 1120 = 7
Answer : E
Answer: (E) 7
Question: A sum of Rs 468.75 was lent out at simple interest and at the end of 1 year and 8 months, the total amount of Rs 500 is received. find the rate of interest?
(A) 3%
(B) 4%
(C) 5%
(D) 6%
(E) 7%
Rationale: Here P=468.75 which is the principle.
Amount=Rs 500
Amount =SI+P
500=[468.75*(20/12)*R]/100 + 468.75
31.25=156.25*5R/100
R=4%
ANSWER:B
Answer: (B) 4%
Question: A was born when B was 1 year and 3 months old. C was born when A was 2 years 1 month old. What is the age of B when C is 4 years and 6 months old?
(A) 4 yr 10 month
(B) 6 yr 10 month
(C) 7 yr 11 month
(D) 7 yr 10 month
(E) 8 yr 10 month
Rationale: When C is 4yr 6 month i.e. 54 months old
A is 79 month old..
B is 15 month older than A
When A is 79 months old then,
B is 94 months old i.e. 7yr 10 month
ANSWER:D
Answer: (D) 7 yr 10 month
Question: Y and Z started a business investing Rs. 10,000 and Rs. 15,000 respectively. Out of a total profit of Rs. 5,000, Z’s share is :
(A) 3000
(B) 3300
(C) 3600
(D) 3900
(E) 4200
Rationale: Ratio of their shares = 10000 : 15000 = 2 : 3.
Z’s share = Rs. 5000 * 3/5
= Rs. 3000
ANSWER:A
Answer: (A) 3000
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 7000 envelopes.
(A) 2
(B) 3
(C) 4
(D) 5
(E) 60/7
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 7000 envelopes B will take 7000/1400 hrs = 5 hrs
So the answer is choice D
Answer: (D) 5
Question: The triplicate ratio of 1:5 is?
(A) 1:7
(B) 1:8
(C) 1:3
(D) 1:1
(E) 1:125
Rationale: 1^3: 5^3 = 1:125
Answer: E
Answer: (E) 1:125
Question: The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?
(A) 6
(B) 8
(C) 1
(D) 5
(E) 2
Rationale: S = 1
M = x
DS = x + 1
US = x - 1
35/(x + 1) + 35/(x - 1) = 12
x = 6
Answer:A
Answer: (A) 6
Question: If Yury has been writing programming code for 12 hours at a rate of 5 lines of code per 20 seconds, how many lines of code has he written?
(A) 126(10^2)
(B) 126(10^3)
(C) 12.6(10^5)
(D) 108(10^2)
(E) .126(10^9)
Rationale: 5 LINES IN 20 SECONDS
SO FOR 1 MINUTE ( 5 X 3 = 15 LINES )
I HOUR = 60 MINUTES
15 X 60 = 900 LINES IN AN HOUR
12 HOURS = 900 X 12 = 108(10^2)
ANSWER D
Answer: (D) 108(10^2)
Question: There are 36 students in a certain geometry class. If two thirds of the students are boys and three fourths of the boys are under six feet tall, how many boys in the class are under six feet tall?
(A) 6
(B) 12
(C) 18
(D) 24
(E) 27
Rationale: Total Students = 36
Two thirds of the students are boys = 2/3*36 = 24
Three fourths of the boys are under six feet tall = 3/4*24 = 18 ...
Therefore Number of boys in the class under six feet tall = 18 ... Answer C....
Alternatively... Number of boys in the class under six feet tall = 3/4 of 2/3 of Total Students = 3/4*2/3*36 = 18...
Answer C
Answer: (C) 18
Question: A magician has five animals in his magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, what is the chance X that he will have a matched pair?
(A) X=2/5
(B) X=3/5
(C) X=1/5
(D) 1/2
(E) 7/5
Rationale: P(both doves) + P(both rabbits) = p(matched pair)
(3/5)*(2/4) + (2/5)*(1/4) = 2/5
Hi How did you get the probability 2/4 and 1/4???
You have 3 doves and 2 rabbits i.e. a total of 5 animals.
The probability that you pick a dove on your first pick is 3/5 (since there are 3 doves)
The probability that you pick a dove on your second pick too is 2/4 (because now only 2 doves are left after we picked a dove in the first pick. ALso only 4 animals are left to choose from)
Similarly,
The probability that you pick a rabbit on your first pick is 2/5 (since there are 2 rabbits)
The probability that you pick a rabbit on your second pick too is 1/4 (because now only 1 rabbit is left after we picked a rabbit in the first pick. Also only 4 animals are left to choose from)
Probability of picking a matched pair = 3/5 * 2/4 + 2/5 * 1/4 = 2/5
Answer: (A) X=2/5
Question: Two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 40 kmph respectively. In what time will they cross each other completely?
(A) 15 sec
(B) 19 sec
(C) 12 sec
(D) 10 sec
(E) 11 sec
Rationale: Explanation:
D = 250 m + 250 m = 500 m
RS = 80 + 40 = 120 * 5/18 = 100/3
T = 500 * 3/100 = 15 sec
Answer: Option A
Answer: (A) 15 sec
Question: In shop contains 500 articles each of a cost of $10. He sold them at a price of $15. If the shop keeper has a order of 200 articles, how much profit he will get?
(A) A)200
(B) B)2000
(C) C)1500
(D) D)1000
(E) E)600
Rationale: Total money after selling articles = 200*15 = 3000
cost price = 200*10 = 2000
profit = 1000
correct option is D
Answer: (D) D)1000