mathewhe/aqua_rat huggingface dataset:
Question: Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?
(A) 4:3:2
(B) 4:2:3
(C) 3:2:4
(D) 2:3:4
(E) None of them
Rationale: Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.
Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).
= (140/100 x 5x), (150/100 x 7x) and (175/100 x 8x)
= 7x, 21x/2 and 14x.
Therefore, The required ratio = 7x : 21x/2 : 14x
= 14x : 21x : 28x
= 2 : 3 : 4.
Answer is D.
Answer: (D) 2:3:4
Question: Find the compound interest and the amount on Rs.5000 at 5% per annum for 3 years when C.I is reckoned yearly?
(A) s.1261.13
(B) s.1440.13
(C) s.1185.13
(D) s.1346.13
(E) s.788.13
Rationale: A = 5000(21/20)3
= 5788.13
= 5000
---------
788.13
ANSWER:E
Answer: (E) s.788.13
Question: When a number is divided by 6 &then multiply by 12 the answer is 9 what is the no.?
(A) 4.5
(B) 5
(C) 5.6
(D) 5.7
(E) 6.5
Rationale: if $x$ is the number, x/6 * 12 = 9
=> 2x = 9
=> x = 4.5
A
Answer: (A) 4.5
Question: In a is a positive integer smaller than 200 and (14a)/60 is an integer, then a has how many different positive prime factors?
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
Rationale: 7a/30 tells us that a is a factor of 30, which has 2, 3, and 5 as its prime factors. Each of them is distinct. Moreover, all multiples of 30 less than 200 can be derived by multiplying these prime factors alone. Thus, number of different prime factors is 3.
Answer: B
Answer: (B) 3
Question: A thief goes away with a MARUTHI car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start ?
(A) 8 hrs
(B) 2 hrs
(C) 5 hrs
(D) 4 hrs
(E) 1 hrs
Rationale: Explanation:
|-----------20--------------------|
50 40
Difference = 20kms
Relative Speed = 50 â€“ 40 = 10 kmph
Time = 20/10 = 2 hours.
Answer: B
Answer: (B) 2 hrs
Question: A room is 7 meters 68 centimeters in length and 4 meters 32 centimeters in Width. Find the least number of square tiles of equal size required to cover the entire floor of the room.
(A) 107
(B) 144
(C) 175
(D) 165
(E) 130
Rationale: Let us calculate both the length and width of the room in centimeters.
Length = 7 meters and 68 centimeters = 768 cm
width = 4 meters and 32 centimeters = 432 cm
As we want the least number of square tiles required, it means the length of each square tile should be as large as possible.Further,the length of each square tile should be a factor of both the length and width of the room.
Hence, the length of each square tile will be equal to the HCF of the length and width of the room = HCF of 768 and 432 = 48
Thus, the number of square tiles required = (768 x 432 ) / (48 x 48) = 16 x 9 = 144
Answer: B
Answer: (B) 144
Question: In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 48. What is the total number of students in the school?
(A) 100
(B) 102
(C) 110
(D) 90
(E) None of these
Rationale: Explanation :
Let the total number of students = x
Given that 20% of students are below 8 years of age
then The number of students above or equal to 8 years of age = 80% of x -----(Equation 1)
Given that number of students of 8 years of age = 48 -----(Equation 2)
Given that number of students above 8 years of age = 2/3 of number of students of 8 years of age
=> number of students above 8 years of age = (2/3) × 48 = 32-----(Equation 3)
From Equation 1,Equation 2 and Equation 3,
80% of x = 48 + 32 = 80
⇒ 80x/100 = 80
⇒ x/100 = 1
⇒ x = 100
Answer : Option A
Answer: (A) 100
Question: The diameter of the driving wheel of a bus in 140 cm. How many revolutions per minute must the wheel make in order to keep a speed of 66 kmph?
(A) 210
(B) 220
(C) 230
(D) 240
(E) 250
Rationale: distance covered in 1 min=(66*1000)/60=1100m
circumference of the wheel=(2*(22/7)*.70)=4.4m
no of revolution per min=1100/4.4=250
ANSWER:E
Answer: (E) 250
Question: If a number p is prime, and 2p+5 = q, where q is also prime, then the decimal expansion of 1/q will produce a decimal with q-1 digits. If this method produces a decimal with 166 digits, what is the units digit of the product of p and q?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: 1/7 = 014285... (a repeating pattern one digit long)
A
Answer: (A) 1
Question: Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.64000?
(A) 81000
(B) 81028
(C) 81287
(D) 29766
(E) 81372
Rationale: 64000* 9/8 * 9/8
= 81000
Answer: A
Answer: (A) 81000
Question: 7log7(8) = ?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 8
Rationale: Exponential and log functions are inverse of each other. Hence
aloga(x) = x , for all x real and positive.
and therefore
7log7(8) = 8
correct answer E
Answer: (E) 8
Question: In a certain population, there are 4 times as many people aged thirtty-one or under as there are people over thirtty-one. The ratio of those thirty-one or under to the total population is
(A)  1 to 2
(B)  1 to 3
(C)  4 to 5
(D)  2 to 3
(E)  3 to 4
Rationale: Consider the ratio of the under population of 21 to over the 21 as 4:1
therefore 4x:1X
Now the ratio of the under to the whole population becomes 4x/4x+1x
= 4/5
Answer is C
Answer: (C)  4 to 5
Question: † and ¥ represent nonzero digits, and (†¥)² - (¥†)² is a perfect square. What is that perfect square?
(A) 121
(B) 361
(C) 576
(D) 961
(E) 1089
Rationale: If AB is a 2 digit number such that A is the tens digit and B is the units digit, the place value of A is 10 and place value of B is 1.
So AB = 10A + B
Say, AB = 15
A = 1
B = 5
Is AB = A + B? No. 15 is not equal to 1 + 5 = 6
AB = 10A + B = 10*1 + 5 = 15
When you square AB, what will you get?
Is it (A + B)^2 = (1 + 5)^2 = 36? No. 15^2 = 225
Then what is missing? A's place value of 10.
So it will be (10A + B) = (10*1 + 5)^2 = 225
So, in terms of AB, AB^2 = (10A + B)^2.
Answer: E.
Answer: (E) 1089
Question: If a 3-digit integer is selected at random from the integers 300 through 349, inclusive, what is the probability that the first digit and the last digit of the integer are each equal to two more than the middle digit?
(A)  50/349
(B)  1/313
(C)  1/49
(D)  1/100
(E)  1/50
Rationale: Hundreds digit has to be 3 . So units digit needs to 3 as well
And both Hundreds and Units digit needs to be 2 more than ten's digit
The number is 313
Total numbers between 300 and 349 = (349-300)+1 = 50
Probability = 1/50
Answer E
Answer: (E)  1/50
Question: 18 men can complete a piece of work in 20 days. In how many days can 15 men complete that piece of work?
(A) 23
(B) 27
(C) 20
(D) 24
(E) 11
Rationale: 18 * 20 = 15 * x => x = 24 days
Answer:D
Answer: (D) 24
Question: A train covers the first 16 km at a speed of 20 km per hour another 20 km at 40 km per hour and the last 10 km at 15 km per hour. Find the average speed for the entire journey.
(A) 24 km
(B) 26 km
(C) 21 km
(D) 23(23/59) km
(E) None
Rationale: Solution: Average speed = total distance covered/ total time
Total distance = (16+40+10) = 46 km
Time taken = (16/20)+ (20/40)+ (10/15) = 59/30
Average speed = 46*30/59 = 23(23/59) km/hr.
Answer: Option D
Answer: (D) 23(23/59) km
Question: The circumferences of two circles are 268 meters and 380 meters. Find the difference between the areas of the larger and the smaller circles.
(A) 388.15
(B) 2992
(C) 4312.5
(D) 2887.27
(E) 5773.09
Rationale: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 268 and 2∏l = 380
s = 268/2∏ and l = 380/2∏
Difference between the areas = ∏l2 - ∏s2
= ∏{1902/∏2 - 1342/∏2}
= 1902/∏ - 1342/∏
= (190 - 134)(190 + 134)/∏
= (56)(324)/(22/7) = (18144)/(22)(7) = 5773.09 sq m.Answer: E
Answer: (E) 5773.09
Question: If m=9^(x−1), then in terms of m, 3^(4x−6) must be which of the following?
(A) m/3
(B) 9m
(C) 9m^2
(D) m^2/3
(E) m^2/9
Rationale: m = 9 ^ (X-1)
m = 3 ^ (2x-2)
m^2 = 3 ^ (4x-4)
m^2/9 = 3 ^ (4x-6)
Answer E
Answer: (E) m^2/9
Question: A large tanker can be filled by two pipes A and B in 60 and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?
(A) 67 min
(B) 45 min
(C) 97 min
(D) 30 min
(E) 16 min
Rationale: Part filled by (A + B) in 1 minute
= (1/60 + 1/40) = 1/24
Suppose the tank is filled in x minutes.
Then, x/2(1/24 + 1/40)
= 1
x/2 * 1/15 = 1 => x
= 30 min.
Answer: D
Answer: (D) 30 min
Question: If a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing thesame no. by 31
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: P ÷ 44 = 432
=> P = 432 * 44 = 19008
P / 31 = 19008 / 31 = 613, remainder = 5
C
Answer: (C) 5
Question: 4 dice are thrown simultaneously on the board. Find the probability show the same face.
(A) 1/209
(B) 1/211
(C) 1/216
(D) 1/117
(E) 1/119
Rationale: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let XX be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability,
=n(X)n(S)=664=n(X)n(S)=664
=1/216
C
Answer: (C) 1/216
Question: 3 candidates in an election and received 1136, 8236 and 11628 votes respectively. What % of the total votes did the winning candidate gotin that election?
(A) 40%
(B) 55.4%
(C) 57%
(D) 60%
(E) 62%
Rationale: Total number of votes polled = (1136 + 8236 + 11628) = 21000
So, Required percentage = 11628/21000 * 100 = 55.4%
B
Answer: (B) 55.4%
Question: There were 35 students in a hostel. Due to the admission of 7 new students, ;he expenses of the mess were increased by Rs. 42 per day while the average expenditure per head diminished by Rs 1. What was the original expenditure of the mess?
(A) 320
(B) 120
(C) 400
(D) 420
(E) 514
Rationale: Sol. Let the original average expenditure be Rs. x. Then,
42 (x - 1) - 35x=42		7x= 84		x =12.
Original expenditure = Rs. (35 x 12) =Rs. 420. .
ANSWER D
Answer: (D) 420
Question: What is the sum of natural numbers between 20 and 100
(A) 4800
(B) 4860
(C) 5000
(D) 5500
(E) 5550
Rationale: a = first number
l = last number
Sn = n/2[a + l]
between 20 and 100 numbers = 81 => 100 - 20 = 80 + 1 = 81
Sn = 81/2 × 120 = 81 × 60 = 4860
B)
Answer: (B) 4860
Question: Three partners A,B,C starts a business. Twice A's capital is equal to thrice B's capital and B's capital is four times C's capital. Out of a total profit of Rs.12000 at the end of the year, B's share is
(A) Rs.4000
(B) Rs.4320
(C) Rs.7500
(D) Rs.6600
(E) None
Rationale: Solution
Let C = x.
Then, B = 4x and 2A = 3x4x = 12x or A = 6x.
âˆ´ A : B : C = 6x : 4x : x	= 6 : 4 : 1.
So B's capital	= Rs(12000 x 4 / 11)
= Rs.4320.
Answer B
Answer: (B) Rs.4320
Question: An plane covers a distance at a speed of 180 kmph in 5 hours. To cover the same distance in 3/2 hours, it must travel at a speed of ?
(A) 100
(B) 200
(C) 720
(D) 600
(E) 500
Rationale: We know
Distance = speed * time
= 180 * 5
= 900 km
Now to cover 900 km in 3/2 hrs ,
speed = distance / time
= 900 / (3/2)
= 600 KMPH
Ans- D
Answer: (D) 600
Question: A Water Heater is available for $39000 cash or $17000 as down payment followed by five equal monthly instalments of $4800 each. The simple rate of interest per annum under the instalment plan would be
(A) 18%
(B) 19%
(C) 21.2%
(D) 21.81%
(E) 22.07%
Rationale: Simple interest SI = (P*R*T)/100
where P is the principal amount
R is the rate of interest
and T is time in years
the way I see it: Water Heater on down payment of 17,000, customer is not paying any interest. it is the remaining sum which will be paid for 5 months that will bear an interest. Therefore, the principal amount for which interest is being charged is 39,000 - 17,000 = 22,000
For this 22,000 a total sum of 5*4800 = 24,000 was pain. (Time is five months, so T = 5/12, as T is in years.)
thus, SI = 2000 or
2000 = (P*R*T)/100
2000 = (22,000*R*5)/(100*12)
R = (2,000*12*100)/22,000*5
R = 21.81%
Therefore answer is D
Answer: (D) 21.81%
Question: In a business there are three partners sum of A and B investments to total investment is in the ratio 4 : 5, and sum of B and C investments to total investment is in the ratio 4 : 5, then which of the following is correct with regard to investments, if investments of two of the partners are equal ?
(A) A = B
(B) B = C
(C) A = B = C
(D) B > (A + C)
(E) A > C
Rationale: If ( A + B ) : ( A + B + C ) = 4 : 5, then C = 5 – 4 = 1 unit
If ( B + C ) : ( A + B + C ) = 4 : 5, then A = 5 – 4 = 1 unit
Therefore B = ( A + B + C ) – ( A + C ) = 5 – 2 = 3
Clearly B > ( A + C )
Option D
Answer: (D) B > (A + C)
Question: One millisecond is 0.001 of a second. The costs for a single run of a computer program are $1.36 for operating-system overhead, $0.023 per millisecond of computer time, and $4.35 for the mounting of a data tape. What is the total of these three costs for 1 run of a program that requires 1.5 seconds of computer time ?
(A)  $7.15
(B)  $8.87
(C)  $35.96
(D)  $40.21
(E)  $59.92
Rationale: Operating system overhead for 1 run = 1.36 $
Mounting of data tape = 4.35$
Cost per 1 millisecond of computer time = .023 $
Total cost of 1 run of a program that requires 1.5 seconds of computer time
= 1.36 + (.023*1500) + 4.35
=1.36 + 34.5 + 4.35
= 40.21$
Answer D
Answer: (D)  $40.21
Question: 15 times a positive integer is more than its square by 56, then the positive integer is
(A) 13
(B) 8
(C) 11
(D) 12
(E) 14
Rationale: Explanation:
Let the number be x. Then,
15x = x2 + 56
=> x2 - 15x + 56 = 0
=>(x - 7)(x - 8) = 0
=> x = 7 or 8
Answer: Option B
Answer: (B) 8
Question: if a@b = a * b^(1/2) then 2@9 = ?
(A) 2
(B) 6
(C) 3
(D) 8
(E) 4
Rationale: a@b = a * b^(1/2)
2@9 = 2*9^(1/2) = 2*3 = 6
Correct Option: B
Answer: (B) 6
Question: Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 8 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
(A) 33:1
(B) 33:7
(C) 33:8
(D) 33:5
(E) 33:2
Rationale: Quantity of alcohol in vessel P = 62.5/100 * 2 = 5/4 litres
Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/1 litres
Quantity of alcohol in the mixture formed = 5/4 + 7/1 = 33/4 = 8.25 litres
As 10 litres of mixture is formed, ratio of alcohol and water in the mixture formed
= 8.25 : 1.75 = 33:7.
Answer: B
Answer: (B) 33:7
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m?
(A) 127.8 m
(B) 127.5 m
(C) 127.5 m
(D) 227.5 m
(E) 123.5 m
Rationale: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800 = 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C = (600 * 212.5)/1000
= 127.5 m.
Answer: B
Answer: (B) 127.5 m
Question: The sum of money will be double itself in 40 years and simple interest find rate of interest?
(A) A)1.5%
(B) B)2.5%
(C) C)3.5%
(D) D)4.5%
(E) E)5.5%
Rationale: T = 40 years
P= principle amount = x
A = total amount = 2x
SI = simple interest = A-P = 2x-x = x
R = 100SI/PT = 100x/40x =2.5%
Answer is B
Answer: (B) B)2.5%
Question: In the biology lab of "Jefferson" High School there are 0.036*10^5 germs, equally divided among 18000*10^(-3) Petri dishes. How many germs live happily in a single dish?
(A) 100
(B) 200
(C) 300
(D) 400
(E) 500
Rationale: 0.036*10^5 can be written as 3600
18000*10^(-3) can be written as 18
Required= 3600/18= 200
ANSWER:B
Answer: (B) 200
Question: 1/0.05 is equal to
(A) 25.5
(B) 2.5
(C) 25
(D) 20
(E) None of these
Rationale: Explanation:
1/0.05 = (1 * 100)/5 = 100/5 = 20
Option D
Answer: (D) 20
Question: A man buys an article and sells it at a profit of 5%. If he had bought it at 5% less and sold it for Rs.25 less, he could have gained 5%. What is the cost price?
(A) 197
(B) 476
(C) 279
(D) 278
(E) 268
Rationale: CP1 = 100 SP1 = 105
CP2 = 95 SP2 = 95 * (105/100) = 99.75
5.25 ----- 100
25 ----- ? => 476
Answer:B
Answer: (B) 476
Question: The length of a bridge in meters, which a train 110-meters long and traveling at 45 km/hr can cross in 30 seconds is?
(A) 245
(B) 265
(C) 295
(D) 325
(E) 375
Rationale: 45 km/h = 45000 m/3600 s = 12.5 m/s
In 30 seconds, the train can go 30(12.5) = 375 meters
Let x be the length of the bridge.
x+110 = 375 meters
x = 265 meters
The answer is B.
Answer: (B) 265
Question: In a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps. The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps. If 4,000 have been vaccinated against both, how many have been vaccinated only against rubella?
(A) 2,5000
(B) 8,000
(C) 10,000
(D) 15,000
(E) 17,500
Rationale: Use a single variable as far as possible.
Number vaccinated only against mumps = x
Number vaccinated against both = 2x = 4000 (so x = 2000)
Then, number vaccinated against mumps (including both) = x + 2x = 3x
Number vaccinated against rubella = 2*3x = 6x
Then, number vaccinated against only rubella = 6x - 2x = 4x = 4*2000 = 8,000
Answer (B)
Answer: (B) 8,000
Question: Each of the dogs in a certain kennel is a single color. Each of the dogs in the kennel either has long fur or does not. Of the 45 dogs in the kennel, 26 have long fur, 22 are brown, and 8 are neither long-furred nor brown. How many long-furred dogs are brown?
(A) 26
(B) 19
(C) 11
(D) 8
(E) 6
Rationale: No of dogs=45
Long fur=26
Brown=22
Neither long fur nor brown=8
Therefore, either long fur or brown=45-8=37
37=26+22-Both
Both=11
Answer C
Answer: (C) 11
Question: A man can row 5 kmph in still water. If the river is running at 1kmph, it takes him 75 minutes to row to a place and back. How far is the place?
(A) 3km
(B) 2.5 km
(C) 4 km
(D) 5 km
(E) 6 km
Rationale: Speed downstream = (5+1)km/hr = 6 km/hr Speed upstream = (5-1)km/hr = 4 km/hr Let the required distance be x km x/6 + x/4 = 75/60 2x+3x = 15 x = 3km .
ANSWER:A
Answer: (A) 3km
Question: At a recent small town election for mayor a total of 983 votes were cast for the four candidates, the winner exceeding his opponents by 53, 79 and 105 votes, respectively. How many votes were cast for the candidate in fourth place?
(A) 134
(B) 178
(C) 200
(D) 166
(E) 194
Rationale: The number of votes the winning candidate received was
983 + 53 + 79 + 105	/4= 305.
The second received 305 – 53 = 252,
The fourth place received 305 – 105 = 200.
C
Answer: (C) 200
Question: Convert the following unit:
6.5 hectares in mÂ²
(A) 55000 mÂ²
(B) 80000 mÂ²
(C) 70000 mÂ²
(D) 67500 mÂ²
(E) 65000 mÂ²
Rationale: 6.5 hectares in mÂ²
1 hectare = 10000 mÂ²
Therefore, 6.5 hectares = 6.5 Ã— 10000 mÂ²
= 65000 mÂ²
ANSWER : OPTION E
Answer: (E) 65000 mÂ²
Question: A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected if it should have at least one senior?
(A) Â²Â²Câ‚â‚€
(B) Â²Â²Câ‚â‚€+1
(C) Â²Â²Câ‚‰ + Â¹â°Câ‚
(D) Â²Â²Câ‚â‚€ - 1
(E) None of these
Rationale: Explanation:
The total number of ways of forming the group of ten representatives is Â²Â²Câ‚â‚€.
The total number of ways of forming the group that consists of no seniors is Â¹â°Câ‚â‚€ = 1 way
The required number of ways = Â²Â²Câ‚â‚€ - 1
ANSWER IS D
Answer: (D) Â²Â²Câ‚â‚€ - 1
Question: If x is an odd integer and y = 3x + 2, which of the following CANNOT be a divisor of y?
(A) 23
(B) 5
(C) 14
(D) 17
(E) 11
Rationale: x takes odd values as 1,3,5,7.,
y=3x+2
x is an odd term so 3x must be an odd term when it adds with 2 so it must be a odd integer
14 didn't follows this condition ans is C
Answer: (C) 14
Question: Fernando Alonso and Sebastian Vettel go for a car race. Bedore start of race, both of them have the exactly same amount of fuel in their respective cars. With the given fuel Fernando can drive continuously for 4 hours while Vettel can drive 1 hour more i.e five hours.
After a time they realize that amount of fuel left in Sebastian car is 4 times the fuel in Fernando car.
For long they are racing ?
(A) 15/4 hours
(B) 15/3 hours
(C) 15/2 hours
(D) 15/2 hours
(E) None
Rationale: Solution:
15/4 hours
Explanation:
Let us say they drive for "t" hours and initial fuel is "f"
Amount of fuel consumed by Fernando car is ft/4
Amount of fuel consumed by Sebastian car is ft/5
As per given condition,
f - ft/5 = 4(f-ft/4)
t = 15/4 hours
Answer A
Answer: (A) 15/4 hours
Question: If the length of an edge of cube P is thrice the length of an edge of cube Q, what is the ratio of the volume of cube Q to the volume of cube P?
(A) 1/4
(B) 1/5
(C) 1/6
(D) 1/27
(E) 1/9
Rationale: The length of cube Q = 1;
The length of cube P = 3;
The ratio of the volume of cube Q to the volume of cube P = 1^3/3^3 = 1/27
Answer : D
Answer: (D) 1/27
Question: The parameter of a square is equal to the perimeter of a rectangle of length 36 cm and breadth 20 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)?
(A) 23.56
(B) 23.59
(C) 44.0
(D) 23.53
(E) 23.57
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(36 + 20) = 112 cm Parameter of the square = 112 cm
i.e. 4a = 112
A = 28
Diameter of the semicircle = 28 cm
Circimference of the semicircle
= 1/2(âˆ)(28)
= 1/2(22/7)(28) = 44cm to two decimal places
Answer:C
Answer: (C) 44.0
Question: If an item that originally sold for c dollars was marked up by a percent and then discounted by b percent, which of the following expressions represents the final price of the item?
(A) (10,000c + 100c(a – b) – abc)/10,000
(B) (10,000c + 100c(b – a) – abc)/10,000
(C) (100c(a – b) – abc)/10000
(D) (100c(b – a) – abc)/10000
(E) 10000 /(a – b)
Rationale: Assume c=100, a=10, b=10. So final price is 99. Now put these value each option. Only option A will give right answer.
Answer: (A) (10,000c + 100c(a – b) – abc)/10,000
Question: A couple who own an appliance store discover that if they advertise a sales discount of 10% on every item in the store, at the end of one month the number of total items sold increases 30%. Their gross income from sales for one month increases by what percent?
(A) 9%
(B) 11%
(C) 13%
(D) 15%
(E) 17%
Rationale: Let P be the original price and let x be the number of items sold originally.
The original income is P*x.
After the changes, the income is 0.9P*1.3x = 1.17*(P*x), an increase of 17%.
The answer is E.
Answer: (E) 17%
Question: Can you find the missing number in the sequence given below?
11 17 23 12 18 ? 13 19 25 14 20 26
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
Rationale: Solution:
24
Explanation :
The sequence is given in the puzzle is :
11 17 23 12 18 ? 13 19 25 14 20 26
Let's break the given series as below:
11 17 23
12 18 ?
13 19 25
14 20 26
Now read the number from left hand side from top to bottom as :
So the number that will replace '?' is 24.
Answer E
Answer: (E) 24
Question: A train 110 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train. Find the speed of the train.
(A) 45 kmph
(B) 50 kmph
(C) 55 kmph
(D) 61 kmph
(E) 70 kmph
Rationale: Explanation:
Let the speed of the train be x kmph.
Speed of the train relative to man = (x + 5) kmph = (x + 5) ×5/18 m/sec.
Therefore 110/((x+5)×5/18)=6 <=> 30 (x + 5) = 1980 <=> x = 61
Speed of the train is 61 kmph.
Answer: Option D
Answer: (D) 61 kmph
Question: A bag contains 6 red and 3 green balls. Another bag contains 4 red and 6 green balls. If one ball is drawn from each bag. Find the probability that one ball is red and one is green.
(A) 19/20
(B) 17/20
(C) 7/15
(D) 8/10
(E) 9/40
Rationale: Let A be the event that ball selected from the first bag is red and ball selected from second bag is green.
Let B be the event that ball selected from the first bag is green and ball selected from second bag is red.
P(A) = (2/3) x (3/5) = 2/5.
P(B) = (1/3) x (2/5) = 2/15.
Hence, the required probability is P(A) + P(B) which is nothing but 7/15.
ANSWER:C
Answer: (C) 7/15