mathewhe/aqua_rat huggingface dataset:
Question: A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 175, how many coins of each type are there?
(A) 20 coins
(B) 30 coins
(C) 50 coins
(D) 100 coins
(E) None of these
Rationale: Let number of each type of coin = x. Then,
1 × x + .50 × x + .25x = 175
⇒ 1.75x = 175 ⇒ x = 100 coins
Answer D
Answer: (D) 100 coins
Question: A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?
(A) 89.2 km/hr
(B) 79.9 km/hr
(C) 99.2 km/hr
(D) 79.2 km/hr
(E) 72.2 km/hr
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/20 = y
y = 22
Speed = 22 m/sec = 22 * 18/5
= 79.2 km/hr.
Answer: D
Answer: (D) 79.2 km/hr
Question: In a certain town, the ratio of NY Yankees fans to NY Mets fans is 2:1, and the ratio of NY Mets fans to Boston Red Sox fans is 3:7. If there are 320 baseball fans in the town, each of whom is a fan of exactly one of those three teams, how many NY Mets fans are there in this town?
(A) 48
(B) 52
(C) 56
(D) 60
(E) 64
Rationale: The ratio of Yankees:Mets:Red Sox = 6:3:7
The Mets fans are 3/16 of the population.
(3/16)*320 = 60
The answer is D.
Answer: (D) 60
Question: There is 60% increase in an amount in 6years at SI. What will be the CI of Rs. 14,000 after 3 years at the same rate?
(A) 2372
(B) 4634
(C) 4542
(D) 2343
(E) 3972
Rationale: Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.
R = 100 x 60 = 10% p.a.
100 x 6
Now, P = Rs. 14000. T = 3 years and R = 10% p.a.
C.I.
= Rs. 14000 x 1 +	10 3	- 1
100
= Rs. 14000 x	331
1000
= 4634.
B
Answer: (B) 4634
Question: If the simple interest on a certain amount in at 4% rate 5 years amounted to Rs.2400 less than the principal. What was the principal?
(A) 1500
(B) 2500
(C) 2507
(D) 3000
(E) 11500
Rationale: P - 2400 = (P*5*4)/100
P = 3000
Answer: D
Answer: (D) 3000
Question: Flat 40% discount. a girl buys jacket for 480. what is the marked price?
(A) 600
(B) 700
(C) 800
(D) 850
(E) 900
Rationale: 40% discount.. means buy on 60% Marked price.
then 480 is 60% of the marked price
480/60=8
8 is 1% of marked price
then 8*100=800
ANSWER:C
Answer: (C) 800
Question: 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 3m3 , then the rise in the water level in the tank will be:
(A) 20 cm
(B) 25 cm
(C) 35 cm
(D) 18.75 cm
(E) None of these
Rationale: Explanation:
Total volume of water displaced =(3 x 50) m3 = 150 m3
Rise in water level = 150/40Ã—20= 0.1875m = 18.75cm
Answer: D
Answer: (D) 18.75 cm
Question: In an examination amar got 8% less than the pass mark and mohan got 20% more than the pass mark. If the difference between the percentage of their mark is 14, then what is the pass percentage
(A) 40%
(B) 50%
(C) 60%
(D) cannot be determined.
(E) None of these
Rationale: Let P be the pass percentage, then
Amar got 0.92 P% and mohan got 1.2 p%
Given that, 1.2 P – 0.92 p = 14
P =14/0.28 = 50%
ANSWER:B
Answer: (B) 50%
Question: If 8 goldsmiths, working 9 hours a day, can make 20 ornaments in 24 days, how many ornaments will 18 goldsmiths make in 36 days, each working 8 hours a day?
(A) 126
(B) 60
(C) 92
(D) 138
(E) 140
Rationale: Explanation :
(Goldsmiths 8: 18) : (His/Day 9:8 ) : (Days 24 : 36) : : 20 : x
8 * 9 * 24*x =18 * 8 * 36 * 20 or x = 60
Answer : B
Answer: (B) 60
Question: Susan, John, Daisy, Tim, Matt, Jane and Kim need to be seated in 7 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ?
(A) 36
(B) 120
(C) 800
(D) 2400
(E) 2520
Rationale: Total # of arrangement of 7 people is 7!.
In half of the cases Susan will be seated left to Tim and in half of the cases Susan will be seated right to Tim (why should one seating arrangement have more ways to occur than another?).
So, # of arrangements to satisfy the given condition is 7!/2=2520.
Answer: E.
Answer: (E) 2520
Question: The successive discounts 20% and 15% are equal to a single discount of?
(A) 12%
(B) 45%
(C) 32%
(D) 98%
(E) 78%
Rationale: C
Let the CP of an article be Rs. 100
Given that successive discounts are 20% and 15%.
SP = 85% of 80% of 100 = (85/100)(80/100)(100)
=> SP = Rs. 68
Clearly, single discount is 32%.
Answer: (C) 32%
Question: A can do a piece of work in 80 days and B in 100 days. They work together for 20 days and then B goes away.In how many days will A finish the remaining work?
(A) 33 days
(B) 44 days
(C) 55 days
(D) 42 days
(E) 32 days
Rationale: Explanation:
In this type of questions we first get the finishing of work in 1 minute for both pipes then we will add them to get the result, as:
Part finished by A in 1 day= 1/80
Part finished by B in 1 day = 1/100
Part finished by (A+B) in 1 day = 1/80 + 1/100
= 9/400
So (A+B)'s 20 days work =20*9/400=9/20 Remaining work =1-9/20=11/20. Number days to finish the remaining work by A =80*11/20=44 days.
Option B
Answer: (B) 44 days
Question: The average of first five prime numbers greater than 17 is?
(A) 32.2
(B) 32.98
(C) 32.3
(D) 32.8
(E) 27.8
Rationale: 19 + 23 + 29 + 31 + 37
= 139/5
= 27.8
Answer: E
Answer: (E) 27.8
Question: Shanti's school normally FINISHES AT 4 PM. her mom drives from home to pick her up, reaching the school exactly at 4 pm. one day, a half holiday is announced and the School finishes for the day at 1 pm. Rather than sitting and Waiting , Shanti decides to start walking towards home. Her mother meets her along the way and as a result they reach home an hour earlier than normal. what is the ratio of the Shanti's walking speed to her mother's driving Speed?
(A) 1:2
(B) 1:3
(C) 1:4
(D) 1:5
(E) 1:6
Rationale: together they save 1hr, i.e, in a one way trip, they would save half Hour each.
therefore, instead of meeting Shanti at 4pm in the school, her mother meets her at 3.30pm(half an hour earlier, to & fro will save 1 hour)
Therefore from the meeting point, to reach the school, the car would take .5 hrs
However, Shanti took 2.5 hrs(3.30-1) to reach the meeting point
Therefore, .5 Times Mom's speed = 2.5 Times Shanti's speed----->(distance=time x speed, since distance is same, equating the product of time and speed for both the cases)
therefore, ratio of the speeds is 1:5
ANSWER:D
Answer: (D) 1:5
Question: A and B can together complete a piece of work in 4 days. If A can alone can complete the same work in 12 days, in how many days can B alone complete that work?
(A) 6
(B) 5
(C) 4
(D) 3
(E) 2
Rationale: (A+B)'s 1 day work = 1/4
A's 1 day work = 1/12
B's 1 day work = 1/6
ANSWER A
Answer: (A) 6
Question: Tim's garden is shaped like a square whose side is 28 meters. What's the length of the fence which surrounds the garden?
(A) 110 meters
(B) 111 meters
(C) 112 meters
(D) 113 meters
(E) 114 meters
Rationale: Solution:
All sides of the square are equal. The length of the fence is 4 times the side. P = 4 × 28 = 112 meters
Answer C
Answer: (C) 112 meters
Question: A train 700 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 288 m
(B) 256 m
(C) 600 m
(D) 278 m
(E) 287 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (700 + x)/60
= 65/3
x = 600 m.
Answer:C
Answer: (C) 600 m
Question: A lady bought five books namely A,B,C,D,E to distribute her 4 children. How many ways she can distribute books?
(A) 4^3
(B) 4^4
(C) 4^5
(D) 4^6
(E) 4^2
Rationale: 4*4*4*4*4
4^5
ANSWER:C
Answer: (C) 4^5
Question: A man performs 3/5 of the total journey by rail, 17/20 by bus and the remaining 6.5km on foot. His total journey is
(A) 65km
(B) 100km
(C) 120km
(D) 130km
(E) 140km
Rationale: Explanation:
Let the journey be x km
Then, 3x/5 + 7x/20 +6.5 =x
12x +7x+130 =20x
X = 130km
Answer: Option D
Answer: (D) 130km
Question: If p^3 is divisible by 80, then the positive integer p must have at least how many distinct factors?
(A) 2
(B) 3
(C) 6
(D) 8
(E) 10
Rationale: Let say p = 10, checking divisibility by 80
10∗10∗10/80=25/2
Numerator falling short of 2
So, lets say p = 20, again checking divisibility by 80
20∗20∗20/80=100
20 is the least value of p for which p3 can be completely divided by 80
There are 6 distinct factors of 20 >> 1, 2, 4, 5, 10, 20
Answer = C
Answer: (C) 6
Question: What is x if x + 2y = 10 and y = 1?
(A) A)10
(B) B)8
(C) C)6
(D) D)4
(E) E)2
Rationale: x = 10 - 2y
x = 10 - 2.
x = 8
Answer : B
Answer: (B) B)8
Question: When m is divided by 9, the remainder is 2. When m is divided by 13, the remainder is 7. If 1 < m < 300, what is the greatest possible value of m?
(A) 20
(B) 120
(C) 137
(D) 187
(E) 254
Rationale: 13*9 = 117
Starting with 13+7 = 20, this also has the form 9k+2.
The next possible number is 20 + 117 = 137
The next possible number is 137 + 117 = 254
The next possible number would be greater than 300.
The answer is E.
Answer: (E) 254
Question: . In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 60 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?
(A)  50%
(B)  53%
(C)  44%
(D)  55%
(E)  57%
Rationale: Registered voters = 100
D = 60
R = 40
60% of D ( 60) = 36
20% of R ( 40 ) = 8
Total voter% of registered voters = 44 / 100
44% Ans C
Answer: (C)  44%
Question: In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors R?
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
Rationale: I like to put the numbers in prime factors so it is easier and faster to visualize.
14*n/60
If we write the factors of 14 --> 2, 7, and the factors of 60 --> 2, 2, 3, 5, we have
(2*7*n)/(2^2*3*5)
Simplifying
7*n/(2*3*5)
The only way the equation above has an integer value is if n has AT LEAST the factors 2, 3 and 5, so we can simplify again and we have the number 7.
The number could be 2*3*5, or 2*3*5*2, or 2*3*5*.....
However to be less than 200 we can not add any prime number.
2*3*5 = 120
If we added the next prime factor 7, we would have R=2*3*5*7 = 840
Thus, answer B
Answer: (B) 3
Question: The cube root of what integer power of 2 is closest to 50?
(A) 16
(B) 17
(C) 18
(D) 19
(E) 20
Rationale: Integer powers of 2 = 2 , 2^2, 2^3, 2^4, 2^5, 2^6, 2^7 etc.
Let, Cube root of x is closest to 50
i.e. x is closest to cube of 50 = 50*50*50 = 125000
But x must be equivalent to an Integer power of 2
2^10 = 1024
2^7 = 128
i.e. 2^17 = 128*1024 = 128000 (approx.)
i.e. 2^18 = 256*1024 = 256000 (approx.)
i.e. 2^16 = 64*1024 = 64000 (approx.)
i.e. 2^17 which is closest to 125000
i.e. Integer power of 2 must be 7
Answer: option B
Answer: (B) 17
Question: Simplify: (4 +3)+(8-3-1)
(A) -11
(B) –12
(C) 11
(D) 12
(E) 10
Rationale: Solution:
(4 +3)+(8-3-1)
=7+(8-3-1)
=7+8-3-1
=15-1
=11
Answer: (C)
Answer: (C) 11
Question: A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 90
(B) 70
(C) 50
(D) 80
(E) 60
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Hence, total number of notes = 3x = 90.
Answer is A.
Answer: (A) 90
Question: A pharmaceutical company received $3 million in royalties on the first $20 million in sales of and then $8 million in royalties on the next $108 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales?
(A) 8%
(B) 15%
(C) 46%
(D) 52%
(E) 56%
Rationale: (8/108)/(3/20) = 30/54 = 49,3% it means that 8/108 represents only 49,3%. Therefore a decrease of 46%.
Answer C
Answer: (C) 46%
Question: A pipe can fill a cistern in 18 minutes whereas the cistern when fill can be emptied by a leak in 20 minutes. When both pipes are opened, find when the cistern will be full?
(A) 17
(B) 180
(C) 70
(D) 120
(E) 12
Rationale: 1/18 - 1/20 = 1/180
180 minutes
Answer: B
Answer: (B) 180
Question: The ratio of local and international calls made by Amy this week is 5 to 2. If the ratio changes to 5 to 3 after Amy makes three more international calls, how many local calls did Amy make this week?
(A) 3
(B) 5
(C) 10
(D) 15
(E) 21
Rationale: The ratio of local and international calls made by Amy this week is 5 to 2
let the current ratio be 5x/2x
the ratio changes to 5 to 3 after Amy makes three more international calls
5x/(2x+3)= 5/3
solving we get x=3
initial ratio 15:6 (5:2) final ratio 15:(6+3)= 15:9= 5:3
so total number of local calls=15
ANSWER:D
Answer: (D) 15
Question: Two trains A and B start simultaneously in the opposite direction from two points P and Q and arrive at their destinations 16 and 9 hours respectively after their meeting each other. At what speed does the second train B travel if the first train travels at 120 km/h
(A) 334
(B) 160
(C) 387
(D) 278
(E) 112
Rationale: Answer: B) 160 km/h
Answer: (B) 160
Question: An alloy of zinc and copper contains the metals in the ratio 5 : 3. The quantity of zinc to be added to 16 kg of the alloy so that the ratio of the metal may be 3 : 1 is:
(A) 2
(B) 4
(C) 8
(D) 3
(E) 1
Rationale: 5/8*16=10
3/8*16=6
(10+x)/6=3/1
=8
ANSWER:C
Answer: (C) 8
Question: Find the area of a parallelogram with base 24 cm and height 16 cm.
(A) 277 cm2
(B) 384 cm2
(C) 670 cm2
(D) 266 cm2
(E) 265 cm2
Rationale: Area of a parallelogram = base * height
= 24 * 16 = 384 cm2
Answer: B
Answer: (B) 384 cm2
Question: In the exam the average was found to be p mark. After deducting typographical error the average marks of 104 student reduced from 94 to 64 . Due to this the average came down by 16 marks. What was the number of students who took the exam?
(A) 100
(B) 120
(C) 110
(D) 195
(E) 160
Rationale: Explanation :
Number of student = (94-64) * 104/16 = 195
Answer : D
Answer: (D) 195
Question: A rectangular parking space is marked out by painting three of its sides.If the length of the unpainted side is 9 feet, and the sum of the lengths of the painted sides is 37 feet, then what is the area of the parking space in square feet?
(A) 126sq.ft
(B) 120sq.ft
(C) 130sq.ft
(D) 135sq.ft
(E) 148sq.ft
Rationale: Let l = 9 ft.
Then l + 2b = 37
=> 2b = 37 – l = 37 – 9 = 28
b = 28/2 = 14 ft.
Area = lb = 9 × 14 = 126 sq. ft. Answer: A
Answer: (A) 126sq.ft
Question: In how many different ways can pennies (1 cent), nickels (5 cents), dimes (10 cents), and quarters (25 cents) be combined for a total of $1.05 (105 cents), if at least two of each type of coin must be included?
(A) 0
(B) 9
(C) 12
(D) 15
(E) 73
Rationale: I. Case I = Four Quarters = this is impossible, because if we already have a dollar in quarters, then we cannot have any dimes. We can't have all four coins represented if we have four quarters.
II. Case II = Three Quarters (75 cents)
Two dimes and two nickels would bring us up to $1.05, and we wouldn't have any pennies.
III. Case III = Two Quarters (50 cents)
This allows for 2-4 dimes.
Subcase 1 = 2 Q, 4 D (90 cents)
(1 way) two nickels allows for 5 pennies
Subcase 2 = 2 Q, 3 D (80 cents)
(3 ways) we could have 2-4 nickels
Subcase 3 = 2 Q, 2 D (70 cents)
(5 ways) we could have 2-6 nickels
Case III allows for a total of 9 ways
There's no other case, because we have to have at least two quarters and two dimes. The total over the cases equals
Total = 0 + 0 + 9 =9 ways.
OA =(B)
Answer: (B) 9
Question: A, B, C are three consecutive positive integers (A>B>C). What is the value of the expression A +B +3C?
(A) 6A+7.
(B) 5A+1.
(C) 5A-1.
(D) 6A-5.
(E) 5A-7.
Rationale: B = A-1
C= A-2
Putting these values in A +B +3C we get 5A-7
E is the answer
Answer: (E) 5A-7.
Question: Find the smallest number of five digits exactly divisible by 16,24,36 and 54.
(A) 10368
(B) 10638
(C) 10836
(D) 10846
(E) None of them
Rationale: Smallest number of five digits is 10000.
Required number must be divisible by L.C.M. of 16,24,36,54 i.e 432,
On dividing 10000 by 432,we get 64 as remainder.
Therefore, Required number = 10000 +( 432 – 64 ) = 10368.
Answer is A.
Answer: (A) 10368
Question: Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 70% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?
(A)  5%
(B)  10%
(C)  15%
(D)  35%
(E)  30%
Rationale: Total = n(A) + n(B) - n(Exactly 2 products) -2 (AnBnC) + Neither.
Neither is zero.
Hence 100 = 70 + 50 + 35 - n (Exactly 2 products) - 2*10
100 = 135 - n (Exactly 2 products) => n (Exactly 2 products) = 35.
Answer: D
Answer: (D)  35%
Question: What percent is 3 gm of 1 kg?
(A) 1.5 %
(B) 0.3 %
(C) 2.5 %
(D) 3.5 %
(E) 4 %
Rationale: 1 kg = 1000 gm
3/1000 × 100 = 300/1000
=3/10 = 0.3 %
B)
Answer: (B) 0.3 %
Question: |-3| (|-15|-|5|)= ??
Source: Preparation Material MBA Center
(A) 30
(B) 35
(C) 40
(D) 75
(E) 100
Rationale: Absolute value will turn negatives into their positive 'equivalents', and will leave positives unchanged, so |-3| = 3, |-15| = 15, and |5| = 5. Getting rid of our absolute values we have:
|-3| (|-15|-|5|) = (3) (15 - 5) = 3*10 = 30
Answer: (A) 30
Question: The incomes and expenditures of P, Q, R are in the ratio of 6 : 8 : 11 and 5 : 8 : 12 respectively. If P saves 1/4th of his income, what is the ratio of the savings of P, Q and R ?
(A) 15 : 8 : 8
(B) 15 : 8 : 6
(C) 15 : 8 : 2
(D) 15 : 8 : 3
(E) 15 : 8 : 9
Rationale: Explanation:
Let the incomes of P, Q, R be 6x, 8x, 11x and expenditure be 5y, 8y and 12y respectively.
Therefore, savings are : (6x – 5y), (8x – 8y) and (11x – 12y)
Now, 6x – 5y = 1/4(6x)
24x – 20y = 6x
18x = 20y
x/y = 20/18 = 10 / 9
Savings of P / Savings of Q = 6x – 5y / 8x – 8y
= [6(x/y) – 5] / [8(x/y) – 8]
= [(6 * 10/9) – 5] / [(8 * 10/9) – 8]
= 15/8
Savings of Q / Savings of R = 8x – 8y / 11x – 12y
= [8(x/y) – 8] / [11(x/y) – 12]
= (8 * 10/9) – 8 / (11* 10/9) – 12
= 8/2
Ratio of savings of P : Q : R = 15 : 8 : 2
ANSWER: C
Answer: (C) 15 : 8 : 2
Question: In a group of cows and hens, the number of legs are 30 more than twice the number of heads. The number of cows is
(A) 15
(B) 7
(C) 10
(D) 12
(E) 14
Rationale: Explanation:
Let the number of cows be x and the number of hens be y.
Then, 4x + 2y = 2 (x + y) + 30
4x + 2y = 2x + 2y + 30
2x = 30
x = 15
Answer: A
Answer: (A) 15
Question: A can do a work in 6days. B can do in 12days. If both A&B are working together in how many days they can finish the work?
(A) 4
(B) 5
(C) 6
(D) 10
(E) 15
Rationale: 1day work of A = 1/6
1day work of B = 1/12
1day work of A&B = 1/6 + 1/12 = 1/4
A&B finish the work in 4days
Answer is A
Answer: (A) 4
Question: Fesdus goes out cycling outdoors. He travels at an average speed of 3km/h, to the top of the hill where the midpoint of the trip is. Going down hill, Juan travels at an average speed of 9km/h. Which of the following is the closest approximation of Fesdus's average speed, in kilometers per hour, for the round trip?
(A) 4.2
(B) 4.5
(C) 7.6
(D) 3.6
(E) 2.2
Rationale: Since we're not given a distance to work with, we can TEST any distance that we like. Here, since the speeds are 3 km/hour and 9 km/hour, using a multiple of both 3 and 9 would make the math easiest.
Let's set the Distance up the hill at 36 km.
So, going uphill, we have....
D = (R)(T)
36 = (3)(T)
36/3 = 13 = T
13 hours to go uphill
Going downhill, we have....
D = (R)(T)
36 = (9)(T)
36/9 = 4 = T
4 hours to go downhill
Total Distance = 120 km
Total Time = 13+4 = 17 hours
Average Speed = 72/17 = 4.2 km/hour
A
Answer: (A) 4.2
Question: All the water in container A which was filled to its brim was poured into two containers B and C. The quantity of water in container B was 62.5% less than the capacity of container A. If 148 liters was now transferred from C to B, then both the containers would have equal quantities of water. What was the initial quantity of water in container A?
(A) 1167 liters
(B) 1546 liters
(C) 8157 liters
(D) 1184 liters
(E) 1467 liters
Rationale: B has 62.5% or (5/8) of the water in A. Therefore, let the quantity of water in container A(initially) be 8k.
Quantity of water in B = 8k - 5k = 3k.
Quantity of water in container C = 8k - 3k = 5k
Container: A B C
Quantity of water: 8k 3k 5k
It is given that if 148 liters was transferred from container C to container B, then both the containers would have equal quantities of water.
5k - 148 = 3k + 148 => 2k = 296 => k = 148
The initial quantity of water in A = 8k = 8 * 148 = 1184 liters.
Answer: D
Answer: (D) 1184 liters
Question: A project manager needs to select a group of 4 people from a total of 4 men and 4 women. How many possible group combinations exist such that no group has all women?
(A) 72
(B) 68
(C) 69
(D) 82
(E) 48
Rationale: Since the order in which the group is selected does not matter, we are dealing with a combinations problem (and not a permutations problem).
The formula for combinations is:
N!/((N-K)!K!)
Where N = the total number of elements from which we will select, 8 people in this case.
Where K = the total number of elements to select, 4 people in this case.
The total number of combinations is therefore:
8!/((8-4)!4!) = 70
However, one of these combinations are not valid since they have all members of women
The correct answer is 70-1= 69.Ans C
Answer: (C) 69
Question: A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems?
(A) 2817
(B) 2728
(C) 1023
(D) 1627
(E) 1625
Rationale: Given that, the question paper consists of five problems. For each problem, one or two or three or none of the choices can be attempted.
Hence, the required number of ways = 45 - 1.
= 210 - 1 = 1024 - 1 = 1023
Answer:C
Answer: (C) 1023
Question: Joe needs to paint all the airplane hangars at the airport, so he buys 360 gallons of paint to do the job. During the first week, he uses 1/6 of all the paint. During the second week, he uses 1/5 of the remaining paint. How many gallons of paint has Joe used?
(A) 18
(B) 120
(C) 175
(D) 216
(E) 250
Rationale: Total paint initially = 360 gallons
Paint used in the first week = (1/6)*360 = 60 gallons.
Remaning paint = 300 gallons
Paint used in the second week = (1/5)*300 = 60 gallons
Total paint used = 120 gallons.
Option B
Answer: (B) 120
Question: In a box carrying one dozen of oranges, one-third have become bad. If 3 oranges are taken out from the box at random, what is the probability that at least one orange out of the three oranges picked up is good?
(A) 1⁄55
(B) 54⁄55
(C) 45⁄55
(D) 3⁄55
(E) None of these
Rationale: n(S) = 12C3 = 12×11×10 /3×2=2×11×10=220
No. of selection of 3 oranges out of the total 12 oranges
= 12C3 = 2 × 11 × 10 = 220
No. of selection of 3 bad oranges out of the total 4 bad oranges = 4C3 = 4
\n(E) = no. of desired selection of oranges
= 220 – 4 = 216
\ P(E) = n(E)/n(S)=216/220=54/55
Answer B
Answer: (B) 54⁄55
Question: In how many different number of ways 4 boys and 2 girls can sit on a bench?
(A) 600
(B) 640
(C) 720
(D) 740
(E) 760
Rationale: npn = n!
6p6 = 6 × 5 × 4 × 3 × 2 × 1 = 720
C)
Answer: (C) 720
Question: The speed of a boat in upstream is 40 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 10 kmph.
(B) 17 kmph.
(C) 18 kmph.
(D) 11 kmph.
(E) 20 kmph.
Rationale: Speed of the boat in still water = (40+80)/2 = 60 kmph. Speed of the stream = (80-40)/2
= 20 kmph.
Answer:E
Answer: (E) 20 kmph.
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
(A) 88
(B) 27
(C) 23
(D) 20
(E) 27
Rationale: M = 15
S = 5
DS = 15 + 5 = 20
Answer:C
Answer: (C) 23
Question: The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 30,000 is made?
(A) 328897
(B) 120000
(C) 877888
(D) 277768
(E) 126000
Rationale: The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000
SP such that a profit of Rs. 30,000 is made = 96,000 + 30,000 = Rs. 1,26,000
Answer: E
Answer: (E) 126000