mathewhe/aqua_rat huggingface dataset:
Question: A train is 360 meter long is running at a speed of 36 km/hour. In what time will it pass a train, having same speed, coming from opposite side?
(A) 125 seconds
(B) 27 seconds
(C) 40 seconds
(D) 128 seconds
(E) 18 seconds
Rationale: Effective Speed = (36+36) Km/hr = 72*(5/18) m/sec = 20 m/sec
Total distance = 360 meter
Time = Distance/speed
= 360 * (20) = 18 seconds
Answer: E
Answer: (E) 18 seconds
Question: The average age of applicants for a new job is 31, with a standard deviation of 8. The hiring manager is only willing to accept applications whose age is within one standard deviation of the average age. What is the maximum number of different ages of the applicants?
(A) 8
(B) 14
(C) 15
(D) 17
(E) 30
Rationale: within one standard deviation of the average age means 31 +/- 7
23--31--39
number of dif.ages -23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
total=17
D
Answer: (D) 17
Question: In how many different ways can the letters of the word ‘INDIGO’ be arranged ?
(A) 420
(B) 520
(C) 620
(D) 720
(E) 820
Rationale: D
720
Required number of arrangements = 6! = 720
Answer: (D) 720
Question: A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
(A) 277m
(B) 887m
(C) 350m
(D) 188m
(E) 126m
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 39 = 50/3
3(x + 300) = 1950 è x = 350m.Answer: C
Answer: (C) 350m
Question: Train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. The length of train P is three-fourths the length of train Q. What is the ratio of the speed of train P to that of train Q?
(A) 15:8
(B) 11:8
(C) 18:8
(D) 12:8
(E) 10:8
Rationale: B
15:8
Given that train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds.
Let the length of train P be LP and that of train Q be LQ
given that LP = 3/4 LQ
As the train P and Q crosses the pole in 30 seconds and 75 seconds respectively,
=> Speed of train P = VP = LP/30
Speed of train Q = VQ = LQ/75
LP = 3/4 LQ
=> VP = 3/4 LQ/(30) = LQ/40
Ratio of their speeds = VP : VQ
= LQ/40 : LQ/75 => 1/40 : 1/75 = 15 : 8
Answer: (A) 15:8
Question: If a and b are different values and a – b = 5(√a - √b), then in terms of b, a equals:
(A) √b
(B) b
(C) b - 2√b + 1
(D) b - 10√b + 25
(E) b^2 – 2b√b + b
Rationale: (√a)^2 - (√b)^2 = 5(√a - √b) -----> ( √a + √b) ( √a - √b) = 5(√a - √b) -------> √a + √b = 5, so
√a = 5 - √b, square both sides and solve. Answer is D.
Answer: (D) b - 10√b + 25
Question: In the next Cricket World Cup T-20, Team Q has decided to score 200 runs only through 4s and 6s. In how many ways can the Team Q score these 200 runs?
(A) 13
(B) 15
(C) 16
(D) 17
(E) 18
Rationale: Team Q can score a maximum of 50 fours and a minimum of 2 fours with an interval or spacing of 3 units to accommodate the 6's.
So the number of fours scored forms an AP 2, 5, 8, ... 50 with a common difference of 3.
Number of ways of scoring 200 only through 4's and 6's = (50 - 2)/3 + 1 = 17
Answer: D
Alternate solution: 4x + 6y = 200 --> 2x + 3y = 100
x = (100 - 3y)/2 --> 100 - 3y should be even. This is possible when 3y is even.
There are 17 even multiples of 3 between 0 and 100.
Answer: D
Answer: (D) 17
Question: The compound ratio of 5:8, 3:2 and 4:5?
(A) 1:1
(B) 1:87
(C) 3:4
(D) 1:9
(E) 1:2
Rationale: 5/8 * 3/2 * 4/5 = 3/4
1:1
Answer: C
Answer: (C) 3:4
Question: The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 30% alcohol, is?
(A) 2
(B) 5
(C) 6
(D) 9
(E) 4
Rationale: 4.5 4.5
30% 70%
30% ----- 4.5
70% ------? => 10.5 - 4.5 = 6 ml
Answer:C
Answer: (C) 6
Question: Three years ago the average age of a family of six members was 19 years. A boy have been born, the average age of the family is the same today. What is the age of the boy?
(A) 1
(B) 9
(C) 4
(D) 6
(E) 3
Rationale: 6 * 22 = 132
7 * 19 = 133
--------------
1
Answer: A
Answer: (A) 1
Question: Wavid has d books, which is 3 times as many as Jeff and 1/2 as many as Paula. How many books do the three of them have altogether, in terms of d?
(A)  5/6*d
(B)  7/3*d
(C)  10/3*d
(D)  7/2*d
(E)  9/2*d
Rationale: Wavid has d books;
Jeff has d/3 books;
Paula has 2d books;
Total = d+d/3+2d=10d/3.
Answer: C.
Answer: (C)  10/3*d
Question: In how many different number of ways 5 boys and 2 girls can sit on a bench?
(A) 5020
(B) 5040
(C) 5060
(D) 5080
(E) 5000
Rationale: npn = n!
7p7 =7 x 6 × 5 × 4 × 3 × 2 × 1 = 5040
B
Answer: (B) 5040
Question: If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 58, what is the compound interest on the same sum at the rate and for the same time?
(A) s. 59.45
(B) s. 56.22
(C) s. 51.219
(D) s. 59.18
(E) s. 51.11
Rationale: Explanation:
Sum = (58 * 100) / (2 * 5) = Rs. 580
Amount = [580 * (1 + 5/100)2] = Rs. 639.45
C.I. = (639.45 - 580) = Rs. 59.45
Answer:A
Answer: (A) s. 59.45
Question: A bag contains 6 white and 4 black balls .2 balls are drawn at random. Find the probability that they are of same colour.
(A) 1/2
(B) 7/15
(C) 8/15
(D) 1/9
(E) 2/9
Rationale: Let S be the sample space
Then n(S) = no of ways of drawing 2 balls out of (6+4) = 10C2 = 10x9/2x1 =45
Let E = event of getting both balls of same colour
Then,n(E) = no of ways (2 balls out of six) or (2 balls out of 4)
=6C2 + 4C2 = 6x5/2x1 + 4x3/2x1 15+6 =21
Therefore, P(E) = n(E)/n(S) = 21/45 = 7/15
Answer is B
Answer: (B) 7/15
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is?
(A) 16
(B) 18
(C) 13
(D) 20
(E) 12
Rationale: 1/2 * d (10 + 6)
= 640
d = 80
Answer: D
Answer: (D) 20
Question: A car travels first 160 km at 70 km/hr and the next 160 km at 80 km/hr. What is the average speed for the first 320 km of the tour?
(A) 71.11
(B) 71.12
(C) 71.1
(D) 74.66
(E) 71.13
Rationale: Car travels first 160 km at 70 km/hr
Time taken to travel first 160 km = distancespeed=160/70
Car travels next160 km at 80 km/hr
Time taken to travel next 160 km = distancespeed=160/80
Total distance traveled = 160+160=2×160
Total time taken = 160/70+160/80
Average speed = Total distance traveled/Total time taken=320/(160/70+160/80)=74.66 km/hr
Answer:D
Answer: (D) 74.66
Question: Machine A can produce 1,000 sausages in 4 hours. Machine B can produce 1,000 sausages in 8 hours. Working together at their respective rates, how long will it take the machines to produce 1,000 sausages?
(A) 1 hr 40 min
(B) 2 hrs
(C) 2 hrs 40 min
(D) 3 hrs
(E) 4 hrs 20 min
Rationale: ARate = 1000/4 = 250 Sausages/Hour
BRate = 1000/8 = 125 Sausages/Hour
TotalSausages = (ARate + BRate) * Hours
Hours = TotalSausages / (ARate + BRate)
Hours = 1000 Sausages / (250 Sausages/Hour + 125 Sausages/Hour) = 2.667 Hours
C. 2 hrs 40 mins
Answer: (C) 2 hrs 40 min
Question: Of the three numbers, second is twice the first and is also thrice the third.If the average of the three numbers is 44.Find the largest number.
(A) 12
(B) 36
(C) 72
(D) 24
(E) 18
Rationale: Sol: Let the third number be x.
Then second number = 3x.
First number=3x/2.
Therefore x+3x+(3x/2)=(44*3) or x=24
So largest number= 2nd number=3x=72
Ans: C
Answer: (C) 72
Question: A man rows his boat 60 km downstream and 30 km upstream taking 3 hrs each time. Find the speed of the stream ?
(A) 5 kmph
(B) 6 kmph
(C) 8 kmph
(D) 1 kmph
(E) 2 kmph
Rationale: Explanation:
Speed of the boat downstream =
Speed of the boat upstream
\small \therefore The speed of the stream =
Answer: A
Answer: (A) 5 kmph
Question: A rectangular metallic piece of paper that covers exactly the area of a cube. The length of the piece of paper is 48 inches and the width is 72 inches. What is the volume of the cube in cubic feet is 1 feet is 12 inches?
(A) a 8
(B) b 22
(C) c 27
(D) d 40
(E) e 51
Rationale: l = 48 /12 = 4 ft
w = 72 / 12 = 6 ft
Area of paper = 24
Area of cube = 4 * side^2
side of cube = 2
V of cube = 8
Answer: (A) a 8
Question: Faiza has 4 purses, she gives 3 purse as gift. Now how many purse did she have ?
(A) 2
(B) 5
(C) 1
(D) 9
(E) 4
Rationale: 4-3=1. Answer is C
Answer: (C) 1
Question: A train overtakes 2 girls who are walking inthe opposite direction in which the train is going at the rate of 3 km/hour & 6km/hour and passes them completely in 36sec & 30sec respectively. Find the length of the train is?
(A) 100 m
(B) 130 m
(C) 150 m
(D) 160 m
(E) 190 m
Rationale: Let the length of the train e x meter, and let the speed of train be y km/h, then
\inline x=\left ( y+3 \right )\frac{5}{18}\times 36 ........(1)
and \inline x=\left ( y+6\right )\frac{5}{18}\times 30 ........(2)
From eq (1) and (2), we get
\inline (y+3)\times 36 = ( y+6)\times 30
y = 12 km/h
\inline \therefore \inline x=(y+3)\times \frac{5}{18}\times 36
x= 150 m
C
Answer: (C) 150 m
Question: By selling a watch for Rs.480/-, a man loses 20% what is that watch cost price
(A) s. 700/-
(B) s. 600/-
(C) s. 880/-
(D) s. 900/-
(E) s. 990/-
Rationale: 80 % ------> 480 (80 * 6 = 480)
100 % ------>600 (100 * 6 = 600)
Cost price = Rs. 600/-
B
Answer: (B) s. 600/-
Question: The price of 80 apples is equal to that of 120 oranges. The price of 60 apples and 75 oranges together is Rs.1320. The total price of 25 apples and 40 oranges is
(A) 620
(B) 610
(C) 630
(D) 625
(E) 635
Rationale: Let the price of one apple = a and price of one orange = b
The price of 80 apples is equal to that of 120 oranges
80a = 120b
=> 2a = 3b
⇒b=2a/3-----(Equation 1)
price of 60 apples and 75 oranges together is Rs.1320
=>60a + 75b = 1320
=> 4a + 5b = 88
⇒4a+5(2a)/3=88(∵ Substituted the value of b from equation 1)
=> 12a + 10a = 88 × 3
=> 6a + 5a = 44 × 3
=> 11a = 44 × 3
=> a = 4 × 3 = 12
b=2a/3=(2×12)/3=8
Total price of 25 apples and 40 oranges
= 25a + 40b = (25 × 12) + (40 × 8) = 300 + 320 = 620
Answer is A.
Answer: (A) 620
Question: nine children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Children AB must sit next to each other, and child C must be somewhere to the right of AB. How many possible configurations are there for the children?
(A) 600
(B) 720
(C) 1440
(D) 1650
(E) 4800
Rationale: A, B, C, D, E, F, G- seven children, of which AB must sit next to each other. Considering them as one X (A, B), we have X, C, D, E, F, G. These can be arranged in 6! ways. But A,B can arrange themselves in 2! ways. So a total of 6!*2! ways = 1440. Since in exactly half of them, C will be to the right of AB, and exactly half, C will be to the left of AB, therefore 1440/2 = 1650
D is the right answer.
Answer: (D) 1650
Question: A six faced die is so biased that it is twice as likely to show an even number as an odd. It is thrown twice. What is the probability that the sum of the numbers is even?
(A) 1/3
(B) 2/3
(C) 5/9
(D) 6/11
(E) 7/11
Rationale: Probability of getting an even number = 2/3
Probability of getting an odd number = 1/3
since the dice is biased.
The sum is even if
(even,even) or (odd,odd)
[P(even).P(even)] + [P(odd).P(odd)]
2/3 * 2/3 + 1/3 * 1/3 = 4/9 + 1/9 = 5/9
ANSWER:C
Answer: (C) 5/9
Question: Working alone, pump A can empty a pool in 4 hours. Working alone, pump B can empty the same pool in 2 hours. Working together, how many minutes will it take pump A and pump B to empty the pool?
(A) 65
(B) 70
(C) 75
(D) 80
(E) 85
Rationale: Pump A can empty (1/4) of the pool per hour.
Pump B can empty (1/2) of the pool per hour.
Together the pumps can empty 1/4+1/2=3/4 of the pool per hour.
1 pool / (3/4) pool per hour = 4/3 hours = 80 minutes.
The answer is D.
Answer: (D) 80
Question: A father purchase dresses for his three daughters.The dresses are of same color but of different size. The dress is kept in dark room.What is the probability that all the three will not choose their own dress.
(A) 1/3
(B) 2/3
(C) 4/3
(D) 5/3
(E) 6/3
Rationale: For he first girl: probability for not selecting correct dress is 2/3
for the second girl: it is 1/2
for the third girl: it is 1
2/3*1/2*1=1/3
ANSWER:A
Answer: (A) 1/3
Question: The average (arithmetic mean) of four numbers is 7x + 3. If one of the numbers is x, what is the average of the other three numbers?
(A) x + 1
(B) 9x + 4
(C) 5x + 1
(D) 5x + 4
(E) 15x + 12
Rationale: If the average of four numbers is 7x + 3, then the sum of all four numbers if 4 * (7x + 3) = 28x + 12. If one of the numbers is x, then the average of the remaining three numbers would be: (28x + 12 - x)/3 = (27x + 12)/3 = 9x + 4.
Answer is B.
Answer: (B) 9x + 4
Question: A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 5 days before the project is completed, in how many days total will the project be completed?
(A) 12
(B) 15
(C) 18
(D) 21
(E) 24
Rationale: A's rate is 1/20 of the project per day.
B's rate is 1/30 of the project per day.
The combined rate is 1/12 of the project per day.
In the last 5 days, B can do 1/6 of the project.
Thus A and B must complete 5/6 of the project, which takes 10 days.
The total number of days is 10 + 5 = 15.
The answer is B.
Answer: (B) 15
Question: In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is?
(A) 12
(B) 27
(C) 24
(D) 29
(E) 11
Rationale: Each row contains 12 plants.
There are 11 gapes between the two corner trees (11 x 2) metres and 1 metre on each side is left.
Therefore Length = (22 + 2) m = 24 m.
Answer: C
Answer: (C) 24
Question: A man buys an item at Rs. 750 and sells it at the loss of 10 percent. Then what is the selling price of that item
(A) Rs. 660
(B) Rs. 675
(C) Rs. 860
(D) Rs. 960
(E) None of these
Rationale: Explanation:
Here always remember, when ever x% loss,
it means S.P. = (100 - x)% of C.P
when ever x% profit,
it means S.P. = (100 + x)% of C.P
So here will be (100 - x)% of C.P.
= 90% of 750
= 90/100 * 750
= 675
Option B
Answer: (B) Rs. 675
Question: The length, breadth and height of a room are in the ratio 7 : 4 :4. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will
(A) (a) remain the same
(B) (b) decrease by 13.64%
(C) (c) decrease by 27.27%
(D) (d) decrease by 18.75%
(E) (e) decrease by 30%
Rationale: Length (L) = 7
Breadth (B) = 4
Height (H) = 4
Total Area of Walls = 2(BH + LH) = 2*(4*4 + 7*4) = 2*(16+28) = 88
Then, Finally
Length (L) = 2*7 = 14
Breadth (B) = 4/2 = 2
Height (H) = 4/2 = 2
Total Area of Walls = 2(BH + LH) = 2*(2*2 + 14*2) = 2*(4+28) = 64
% change in Area of four walls = (Final Area-Initial Area)*100 /Initial Area
i.e. % change in Area of four walls = (64-88)*100 /88=- 27.27% (Decrease)
Answer: Option C
Answer: (C) (c) decrease by 27.27%
Question: A boat can move upstream at 20 kmph and downstream at 40 kmph, then the speed of the current is?
(A) 5
(B) 8
(C) 10
(D) 3
(E) 2
Rationale: US = 20
DS = 40
M = (40- 20)/2
= 10
Answer:C
Answer: (C) 10
Question: Abel can complete a work in 10 days, Ben in 14 days and Carla in 15 days. All of them began the work together, but Abel had to leave after 2 days and Ben 3 days before the completion of the work. How long did the work last?
(A) 6
(B) 7
(C) 7 10/29
(D) 9
(E) 10
Rationale: Abel in the 2 days that he worked completed 1/5 of the job = 4/5 remains
Then if Ben had to leave 3 days before the completion, this means that Carla had to work alone for these 3 days in which she completed 1/5 of the job.
Now together, Ben and Carla completed the job in (1/14 + 1/15)(t) = 3/5
29/210 (t) = 3/5 ---> t = 126/29
Therefore, these 4 10/29 days worked plus the 3 days that Carla had to work by herself add to 7 10/29 days
Answer: C
Answer: (C) 7 10/29
Question: First-grade tobacco costs $30 per kilogram while second-grade tobacco costs $20 per kilogram. If a blend contains only first and second grade tobacco, what must be the percentage of second-grade tobacco so that the blend would cost $22 per kilogram?
(A) 20%
(B) 30%
(C) 60%
(D) 75%
(E) 80%
Rationale: Let x denote the share of the second-grade tobacco in the blend. Then the cost of a kilogram of the blend would go down as x∗20+(1−x)30=22 from where x=0.8 or 80%.
Answer: E
Answer: (E) 80%
Question: A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 20.25, the number of the member is the group is:
(A) 57
(B) 67
(C) 45
(D) 47
(E) 97
Rationale: Money collected =(20.25 x 100) paise = 2025 paise
numbers of members = 2025 squareroot = 45
Answer C
Answer: (C) 45
Question: If a is an integer greater than 6, which of the following must be divisible by 3?
(A) a (a+5) (a-6)
(B) a (a+2) (a-1)
(C) a (a+3) (a-5)
(D) a (a+4) (a-2)
(E) a (a+1) (a-4)
Rationale: anything in the form of (a-1) (a) (a+1) is divisible by 3. in other word, a product of any 3 consecutive intevers is divisible by 3.
a (a+1) (a-4) = a (a+1) ((a-1)-3) is equivalant to (a-1) (a) (a+1)
a (a+2) (a-1) is equivalant to (a+1) missing.
a (a+3) (a-5) is equivalant to (a-1) missing and a repeating.
a (a+4) (a-2) is equivalant to odd/even consqcutive integers
a (a+5) (a-6) is equivalant to (a+1) missing and a repeating.
Answer : E
Answer: (E) a (a+1) (a-4)
Question: If xy > 0, which of the following must be negative?
(A) x+y
(B) x-y
(C) -xy
(D) -x * -y
(E) x/y
Rationale: x,y must both positive or both negative. so that mn > 0 is true
positive * negative = negative
Answer : C
Answer: (C) -xy
Question: What is the square root of 96,721?
(A) 476
(B) 489
(C) 289
(D) 511
(E) 311
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) C = 489^2 and E = 511^2
C = (300-11)^2 and E = (300 + 11)^2
Since we need the answer less than 90000 => C is out.
Thus we have E as the ans.
Answer: (E) 311
Question: There is enough provisions for 2400 women in an army camp for 100 days. If there were 1200 men less, how long will the provision last?
(A) 170
(B) 180
(C) 190
(D) 200
(E) 210
Rationale: We have, M1D1 = M2D2
2400*100= 1200* D2
D2 = 2400*100/1200 = 200 days.
ANSWER:D
Answer: (D) 200
Question: Sanji and Sapna start a business investing Rs.9000 each, and after 6 months, Sapna withdraws half of her capital . How should they share the profits at the end of the 24 months?
(A) 4:3
(B) 3:2
(C) 15:11
(D) 8:5
(E) 5:3
Rationale: Sanji invests Rs.9000 for 24 months, but Sapna invests Rs.9000 for the first 6 months and then withdraws Rs.4500. So, the investment of Sapna for remaining 18 months is Rs.4500 only.
Sanji:Sapna
9000*24 : (9000*6) + (4500*18)
216000 : 135000
Sanji:Sapna = 8:5
Answer: D
Answer: (D) 8:5
Question: A father is now three times as old as his son. Five years back, he was four times as old as his son. The age of the son (in years) is
(A) 12
(B) 15
(C) 18
(D) 20
(E) 25
Rationale: If father's age is F and son's age is S, then
F=3S
and
F-5 = 4*(S-5)
3S-5 =4S-20
S=15
F=45 years
ANSWER:B
Answer: (B) 15
Question: Find the quantities of two types of rice to be mixed, first variety is of Rs.12 per kg and second variety is of Rs.20 per kg. to get 12kg of rice mixture worth Rs.15 per kg? (in kg)
(A) 3.5, 8.5
(B) 7, 5
(C) 7.5, 4.5
(D) 8, 4
(E) 8, 5
Rationale: from allegation & mixture ratio=c-m/m-d=20-15/15-12=5/3.
from the option c r=7.5/4.5=5/3
ANSWER:C
Answer: (C) 7.5, 4.5
Question: 3 people decided to put a down payment on a car for 3500 dollars. How much money do they each have to pay, given that that they have to pay the same amount, and they cannot use any bills below $1?
(A) $1166
(B) $1168
(C) $1166.6
(D) $1167
(E) None of the above
Rationale: To keep the amount exact when dividing for 3, we have to work backwards through division.
Dividing 3500 by 3 will give us 1166.66
Then by subtracting .66, we get 1166, and we multiply it by 3 to get 3498.
To get enough for the down payment, we add 3 to 3498.
Dividing the result by 3 gives us our answer.
Correct Option: D
Answer: (D) $1167
Question: What is the scope including 1/51+1/52+1/53+......+1/60?
(A) 1/6~1/5
(B) 1/5~1/4
(C) 1/4~1/3
(D) 1/3~1/2
(E) 1/2~1
Rationale: For Maximum value : It should be less than 1/51 + 1/51 +1/51... 10 times = 10/51 ~ 1/5
For Minimum Value : It should be greater than 1/60+ 1/6+ 1/60 .. 10 times = 10/60 = 1/6.
Thus, the answer should lie between 1/6 and 1/5. Correct ans :A.
Answer: (A) 1/6~1/5
Question: A Cone, a hemisphere and a cylinder stand on equal bases and have the same height .Find ratio of their volumes.
(A) 2:1:3
(B) 2:1:4
(C) 1:2:3
(D) 4:1:7
(E) 5:1:8
Rationale: Let R be the radius of each
Height of the hemisphere = Its radius = R.
Height of each = R.
Ratio of volumes = (1/3)∏ R2 x R : (2/3)∏R3 : ∏ R2 x R = 1:2:3
ANSWER C 1:2:3
Answer: (C) 1:2:3
Question: (9^5.6x 9^10.3) ÷ 9^2.56256 = 9^?
(A) 11.34
(B) 12.34
(C) 13.34
(D) 14.34
(E) 15.34
Rationale: 5.6 + 10.3 = 15.9
i.e.. 15.9 - 2.56 = 13.34
so ur answer is 9^13.34
ANSWER:C
Answer: (C) 13.34
Question: In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 140 marks, the no of questions he attempts correctly is :
(A) 35
(B) 38
(C) 40
(D) 42
(E) 44
Rationale: Explanation:
Let the number of correct answers be X.
Number of incorrect answers = (60 – X).
4x – (60 – x) = 140
=> 5x = 200
=> x = 40
Answer: C
Answer: (C) 40
Question: Two trains of length 150 m and 250 m are 150 m apart. They start moving towards each other on parallel tracks, at speeds 36 kmph and 72 kmph. In how much time will the trains cross each other?
(A) 55/3
(B) 55/7
(C) 55/6
(D) 55/8
(E) 55/9
Rationale: Relative speed = (36 + 72)* 5/18 = 6 * 5 = 30 mps.
The time required = d/s = (150 + 150 + 250)/30
= 550/30 = 55/3 sec.
Answer: A
Answer: (A) 55/3
Question: In a fuel station the service costs $1.65 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty, how much money total will it cost to fuel all cars?
(A) 320$
(B) 380$
(C) 420$
(D) 448.8$
(E) 480$
Rationale: Total Cost = ( 1.65*12 ) + ( 0.65 * 12 * 55 ) = 19.8 + 429 => 448.8
Hence answer will be (D)
Answer: (D) 448.8$
Question: If there are 30 cans out of them one is poisoned if a person tastes very little he will die within 14 hours so if there are mice to test and 24 hours to test, how many mices are required to find the poisoned can?
(A) 3
(B) 2
(C) 5
(D) 6
(E) 1
Rationale: Number the cans from 1 to 30.
Mouse can be forced to taste every can after a gap of 5 minutes.
Calculating the time if death from start, the poisoned can no can be found.
ANSWER:E
Answer: (E) 1
Question: A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 128. The dividend from the stock is:
(A) 7.5%
(B) 8%
(C) 9.7%
(D) 10%
(E) None of these
Rationale: By investing Rs. 1552, income = Rs. 128
By investing Rs. 97, income = Rs. (128/1552 * 97) = Rs. 8
Dividend = 8%
Answer = B
Answer: (B) 8%
Question: The sides of a rectangular field are in the ratio 3 : 4. If the area of the field is 8112 sq. m, the cost of fencing the field @ 25 paise per metre is
(A) Rs. 55.50
(B) Rs. 67.50
(C) Rs. 86.50
(D) Rs. 91.00
(E) None of these
Rationale: Solution
Let length = (3x) metres and breadth = (4x) metres.
Then, 3x × 4x = 7600 ⇔ 12x2 = 8112 ⇔ x2 = 676 ⇔ x = 26
So, length = 78 m and breadth = 104 m.
Perimeter = [2(78 + 104)] m = 364 m.
∴ Cost of fencing = Rs. (0.25 × 364) = Rs. 91. Answer D
Answer: (D) Rs. 91.00
Question: A lady builds 12cm length, 16cm width, and 6cm height box using 3cubic cm cubes. What is the minimum number of cubes required to build the box?
(A) 345
(B) 384
(C) 378
(D) 398
(E) 300
Rationale: Number of cubes required = Volume of box/Volume of cube
= 12*16*6/3
=384 cubes
ANSWER:B
Answer: (B) 384
Question: In an election a candidate who gets 60% of the votes is elected by a majority of 1380 votes. What is the total number of votes polled?
(A) A)4500
(B) B)5200
(C) C)6900
(D) D)7520
(E) E)6000
Rationale: Let the total number of votes polled be x
Then, votes polled by other candidate = (100-60)% of x = 40% of x
60% of x - 40% of x = 1380
20x/100 = 1380
x = 1380*100/20 = 6900
Answer is C
Answer: (C) C)6900