RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Nitin's age was equal to square of some number last year and the following year it would be cube of a number. If again Nitin's age has to be equal to the cube of some number, then for how long he will have to wait?
A.10 years
B.38 years
C.39 years
D.64 years
Answer: B.38 years
Explanation: current age = 26 years because Nitin's age was equal to square of some number ( 25= 5^2) last year and the following year it would be cube of a number (27= 3^3).
Next cube age will be 64 =4^3 which will come after 64-26 = 38 years.
ANSWER:B
Question: A freight elevator can carry a maximum load of 1140 pounds. Sean, who weighs 200 pounds, is in the elevator with two packages weighing 150 pounds and 280 pounds. If he needs to fit three more packages in the elevator that weigh as much as possible without exceeding the elevator limit, what is the difference between their average and the average of the two packages already in the elevator?
A.45
B.85
C.190
D.215
Answer: A.45
Explanation: The average of existing 2 package is150 + 280/2 = 430/2 = 215
Remaining allowed weight = 1140 - 200 - 430 = 510.
allowed per package = 510 / 3 = 170
So difference in average of existing and allowable = 215 - 170 = 45
Hence A
Question: The product of a and b is equal to 14 more than twice the sum of a and b. If b = 8, what is the value of b - a?
A.2
B.3
C.7
D.24
Answer: B.3
Explanation: ab= 14 + 2(a+b)
8a= 14+2a +16
6a= 30
a=5
b-a= 8-5=3
B is the answer
Question: A batsman makes a score of 76 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning.
A.36
B.28
C.42
D.45
Answer: B.28
Explanation: Let the average after 17th inning = x.
Then, average after 16th inning = (x – 3).
∴ 16(x – 3) + 76 = 17x or x = (76 – 48) = 28.
Answer B
Question: If the price has fallen by 10% what percent of its consumption be: increased so that the expenditure may be the same as before?
A.11 1/8%
B.11 1/5%
C.11 1/9%
D.11 7/9%
Answer: C.11 1/9%
Explanation: 100 – 10 = 90
90------10
100------? => 11 1/9%
Answer: C
Question: A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. IN what ratio will the profit be shared at the end of 3 years?
A.3:6:7
B.3:4:7
C.9:4:7
D.3:4:6
Answer: B.3:4:7
Explanation: A:B:C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12)
= 144:192:336 = 3:4:7
Answer: B
Question: Suresh Raina and Gautam Gambhir after a scintillating IPL match decide to travel by cycle to their respective villages. Both of them start their journey travelling in opposite directions. Each of their speeds is 6 miles per hour. When they are at a distance of 50 miles, a housefly starts flying from Suresh Raina's cycle towards Gautam Gambhir at a relative speed of 17 miles per hour with respect to Raina's speed. What will be the time taken by housefly to reach Gambhir?
A.37
B.10
C.27
D.36
Answer: B.10
Explanation: Fly speed is 17 kmph w.r.t to suresh as fly is moving in opposite direction to suresh, its actual speed is 17 - 6 = 11.
Now relative speed of fly and gambhir = 11 - 6 = 5 kmph
So fly takes = 5011−65011−6 = 10 Hrs
Answer:B
Question: If 5+3+2=151022, 9+2+4=183652, then 7+2+5=?
A.223888
B.143547
C.2607778
D.126997
Answer: B.143547
Explanation: If the given number is a + b + c then a.b | a.c | a.b + a.c - b
⇒⇒ 5+3+2 = 5.3 | 5.2| 5.3 + 5.2 - 3 = 151022
⇒⇒ 9+2+4 = 9.2 | 9.4 | 9.2 + 9.4 - 2 = 183652
7+2+5= 7.2 | 7.5 | 7.2 + 7.5 - 2 = 143547
Answer:B
Question: A person can row at 10 kmph in still water. If the velocity of the current is 2 kmph and it takes him 15 hour to row to a place and come back, how far is the place?
A.24km
B.30km
C.48km
D.72km
Answer: D.72km
Explanation: Speed of down stream = 10+2 = 12kmph
speed of upstream = 10-2 = 8kmph
Let the required distance be xkm
x/12 + x/8 = 15
2x+3x = 360
x = 72 km
Answer is D
Question: Bombay Express left Delhi for Bombay at 14.30 hrs, travelling at a speed of 60 kmph and Rajdhani Express left Delhi for Bombay on the same day at 16.30 hrs, travelling at a speed of 80 kmph. How far away from Delhi will the two trains meet?
A.120 km
B.360 km
C.480 km
D.500 km
Answer: C.480 km
Explanation: Sol.
Suppose they meet x hours after 14.30 hrs.
Then, 60x = 80 (x - 2) or x = 8.
∴ Required distance = (60x8)km = 480 km.
Answer C
Question: If x/y = 3/z, then 9z^2 =
A.y²/ x²
B.x²y²
C.81y²/ x².
D.9y/x
Answer: C.81y²/ x².
Explanation: This question is most easily solved by isolating y in the equation and substituting into the expression 9z²:
x/y = 3/z
x = 3y/z
3y = xz
z = 3y/x.
If we substitute 3y/xinto the expression for z, we get:
9(3y/x)² = 9(9y²/ x²) = 81y²/ x².
The correct answer is choice (C)
Question: A train running at the speed of 100 km/hr crosses a pole in 9 sec. What is the length of the train?
A.298 m
B.250 m
C.208 m
D.988 m
Answer: B.250 m
Explanation: Speed = 100 * 5/18 = 250/9 m/sec
Length of the train = speed * time = 250/9 * 9
= 250 m
Answer:B
Question: 30% of Ram's marks is equal to 20% of Rahim's marks which percent is equal to 30% of Robert's marks. If Robert's marks is 80, then find the average marks of Ram and Rahim?
A.70
B.97
C.87
D.100
Answer: D.100
Explanation: Given, 30% of Ram's marks = 20% of Rahim's marks = 30% of Robert's marks.
Given, marks of Robert = 80
30% of 80 = 30/100 * 8 = 24
Given, 30% of Ram's marks = 24.
=> Ram's marks = (24 * 100)/30 = 80
Also, 20% of Rahim's marks = 24
=> Rahim's marks = (24 * 100)/20 = 120
Average marks of Ram and Rahim = (80 + 120)/2 = 100.
Answer:D
Question: Sharmeeka is putting all of her pens in order by number. One has the number 4 on it, the next has number 8, the next has number 12, and the next has number 16.
What number will the next pen have on it?
A.20
B.25
C.32
D.22
Answer: A.20
Explanation: A) 20, because the pens are ordered by multiples of 4.
4 +4 = 8
8 + 4=12
12+4=16
16+4=20
Question: A standard Veggiematik machine can chop 20 carrots in 2 minutes. How many carrots can 3 standard Veggiematik machines chop in 3 minutes?
A.81
B.90
C.121
D.130
Answer: B.90
Explanation: Direct Relationship:-
1 standard Veggiematik machine - 20 Carrots - 2 minutes,
1 standard Veggiematik machine - 10 Carrots - 1 minute,
Now
3 standard Veggiematik machine - ? Carrots - 3 minutes,
Hence = 10X3X3 =90 Carrots
Answer B
Question: A distributor sells a product through an on-line store, which take a commission of 20% of the price set by the distributor. The distributor obtains the product from a producer at the price of $15 per item. What is the price that the buyer observers on-line if the distributor wants to maintain a 40% profit on the cost of the item?
A.18
B.30
C.22
D.22.5
Answer: B.30
Explanation: Producer price = $15;
The distributor wants to maintain a 20% profit on the cost of the item, thus he must get $15*1.2 = $18 after the store takes a commission of 40% of the final price --> (final price)*0.6 = $18 --> (final price) = $30.
Answer: B.
Question: The sector of a circle has radius of 14 cm and central angle 135o. Find its perimeter?
A.91.5 cm
B.61 cm
C.28.9 cm
D.29.2 cm
Answer: B.61 cm
Explanation: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 14) + 2(14)
= 33 + 28 = 61 cm
Answer:B
Question: If sales tax is reduced from 5% to 4%, then what difference it will make if you purchase an item of Rs. 1000
A.10
B.20
C.30
D.40
Answer: A.10
Explanation: Explanation:
Clue: Answer will be 5% of 1000 - 4% of 1000
Option A
Question: The simple interest on a sum of money is 5/9 of the principal and the number of years is equal to the rate percent. Find the rate and the time?
A.5 4/9%
B.17 4/9%
C.7 4/9%
D.8 4/9%
Answer: C.7 4/9%
Explanation: 5/9 P = (P*R*R)/100
R = 22.36/3 = 7 4/9%
ANSWER:C
Question: The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:
A.3500
B.3900
C.3750
D.3840
Answer: B.3900
Explanation: Let the cost of a chair and that of a table be Rs. x and Rs. y respectively.
Then, 10x = 4y or y =	(5/2)x.
15x + 2y = 4000
15x + 2 x	(5/2)	x = 4000
20x = 4000
x = 200.
So, y =(5/2)x 200= 500.
Hence, the cost of 12 chairs and 3 tables = 12x + 3y
= Rs. (2400 + 1500)
= Rs. 3900.
Answer is B.
Question: The greatest number by which the product of three consecutive multiples of 4 is always divisible is
A.54
B.76
C.152
D.384
Answer: D.384
Explanation: Solution
Required number	= Product of first three multiplies of 3
= (4 Ã— 8 Ã— 12)= 384.
Answer D
Question: A man whose speed is 7.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
A.10
B.8
C.9
D.7.2
Answer: D.7.2
Explanation: M = 7.5
S = 1.5
DS = 9
US = 6
AS = (2 * 9 * 6) /15 = 7.2
Answer: D
Question: What is the smallest integer n that satisfies both of the following equations, in which p and q
are positive integers?
n = p2 + p
n = q2 + q + 2014
A.2024
B.2034
C.2056
D.2070
Answer: D.2070
Explanation: The term 2014 in the second equation suggests trying small numbers for q, and a
little experimentation with p close to the square root of 2014 and n = p(p + 1) leads fairly
quickly to q = 7, giving n = 2070, which is (45)(46)
correct answer D
Question: What is the two-digit number whose first digit is a and the second digit is b?. The number is greater than 9.
I. The number is multiple of 51.
II. The sum of the digits a and b is 6.
A.I alone sufficient while II alone not sufficient to answer
B.II alone sufficient while I alone not sufficient to answer
C.Either I or II alone sufficient to answer
D.Both I and II are not sufficient to answer
Answer: A.I alone sufficient while II alone not sufficient to answer
Explanation: From statement I:
A two digit number, greater than 9 and multiple of 51 should be 51 itself.
Because, 2 x 51 = 102 (3 digit number). Therefore, I alone sufficient to answer.
From statement II:
A two digit number, greater than 9 and sum of the digit is 6.
It can be 15, 24, 33, 42, 51. So we cannot determine the required answer from the statement II alone.
Thus, I alone give the answer while II alone not sufficient to answer.
ANSWER A I alone sufficient while II alone not sufficient to answer
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm?
A.187 cm2
B.178 cm2
C.285 cm2
D.178 cm22
Answer: C.285 cm2
Explanation: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (15)
285 cm2
Answer: C
Question: Two pipes A and B can fill a tank in 15 min and 20 min respectively. Both the pipes are opened together but after 4 min, pipe A is turned off. What is the total time required to fill the tank?
A.14 min 19 sec
B.14 min 42 sec
C.14 min 20 sec
D.14 min 40 sec
Answer: D.14 min 40 sec
Explanation: :
Part filled in 4 minutes = 4(1/15 + 1/20) = 7/15
Remaining part = 1 - 7/15 = 8/15
Part filled by B in 1 minute = 1/20
1/20 : 8/15 :: 1 ; x
x = 8/15 * 1 * 20 = 10 2/3 min = 10 min 40 sec.
The tank will be full in (4 min. + 10 min. 40 sec) = 14 min 40 sec.Answer: D
Question: Jerry and Jim are opposing participants in an online auction. Each has a constant bidding strategy: Jerry always bids up by raising $40 over any previous bid. Jim always bids up by doubling any previous bid. The auction begins with an initial bid by a third player, and progresses as follows: Jerry bids up first, and Jim follows. Jerry bids up again, and Jim follows and raises the bid to a final $600. What was the dollar value of the initial price?
A.90
B.465
C.656
D.345
Answer: A.90
Explanation: Initial bid = p$
Jerry = p+40
Jim = 2p
The sequence is R---> B ---> R -----> B ---> 600
Thus per the sequence we have: p+40, 2(p+40), 2p+80+40 , 2(2p+120)
Now given, 2(2p+120) = 600----> p =90$. Thus A is the correct answer.
Question: In a triangle ABC,point D is on side AB and point E is on side AC,such that BCED is a trapezium.DE:BC =3:5.Calculate the ratio of the area of triangle ADE and the trapezium BCED.
A.9/16
B.8/16
C.7/16
D.6/16
Answer: A.9/16
Explanation: area of tri(ADE)/area of tri(ABC) = DE^2 / BC^2 since tri(ADE) -tri(ABC)
area of tri(ADE)/area of tri(ABC) = 9/25
area of tri(ABC)/area of tri(ADE) = 25/9
area of tri(ABC) = area of tri(ADE) + area of trap(BCDE)
(area of tri(ADE) + area of trap(BCDE))/area of tri(ADE) = 25/9
1 + area of trap(BCDE)/area of tri(ADE) = 25/9
take1on both sides
area of trap(BCDE)/area of tri(ADE) = (25/9) - 1 = 16/9
since question is asking for area of tri(ADE)/area of trap(BCDE) = 9/16
ANSWER:A
Question: Look at this series: 53, 53, 40, 40, 27, 27, ... What number should come next?
A.12
B.14
C.57
D.53
Answer: B.14
Explanation: In this series, each number is repeated, then 13 is subtracted to arrive at the next number.
27-13=14
Option B
Question: A train running at a speed of 36 km/h passes an electric pole in 15 seconds. In how many seconds will the whole train pass a 380-meter long platform?
A.47
B.49
C.51
D.53
Answer: D.53
Explanation: Let the length of the train be x meters.
When a train crosses an electric pole, the distance covered is its own length x.
speed = 36 km/h = 36000 m / 3600 s = 10 m/s
x = 15 * 10 = 150 m.
The time taken to pass the platform = (150 +380)/ 10 = 53 seconds
The answer is D.
Question: The difference between the place value and the face value of 5 in the numeral 856973 is
A.973
B.6973
C.5994
D.49995
Answer: D.49995
Explanation: (Place value of 5) - (Face value of 5) = (50000 - 5) = 49995
Answer: Option D
Question: A group of 8 cups need to be arranged. There are 2 blue cups and 2 red cups and the two of the pair of cups must be kept togather. in how many arrangements can the cups be arranged?
A.A.1296
B.B.1850
C.C.2880
D.D.3546
Answer: C.C.2880
Explanation: Glue cupstogether: {AB}, {CD}.
6 units {AB}, {CD}, {E}, {F}, {G}, {H} can be arranged in 6! ways. Each cups within their unit can be arranged in 2! ways.
Therefore the final answer is 6!*2!*2!=2,880.
Answer: C.
Question: Given a number, there is an algorithm described here to find it's sum and number of factors. For example, let us take the number 1225?
A.1767
B.1800
C.1812
D.1890
Answer: A.1767
Explanation: Solving for 1225=52×72
Sum of divisors = (ap+1–1)/(a–1)×(bq+1–1)/(b–1)
Here a=5, b=7 prime factors
p=2 and q=2
Sum of divisors = (53–1)/(5–1)×(73–1)/(7–1)
= (124/4)×(342/6)
= (31×57)
= 1767
Option A
Question: Last year, Company X made q dollars in profit. One thrid of the profit went to the company’s founder. The rest was split evenly among his four other partners. In terms of q, how much did each of the other partners receive?
A.q/4
B.q/5
C.q/8
D.q/6
Answer: D.q/6
Explanation: Profit = q
Profit to company founder = q/3
Profit to other partners = 2q/3
Number of other partners = 4
Profit to each partner = (2q/3)/4 = q/6
Answer: D
Question: For some integer n, n^2 - 5 is divisible by all of the following EXCEPT
A.41
B.38
C.29
D.30
Answer: D.30
Explanation: Hint: n^2-5 (n is an integer) is never multiple of 3 (try to prove this), hence 30 is out.
Answer: D
Question: Riya and Priya set on a journey. Riya moves eastward at a speed of 30 kmph and Priya moves westward at a speed of 50 kmph.How far will be priya from Riya after 45 minutes
A.25kms
B.60kms
C.50kms
D.30kms
Answer: B.60kms
Explanation: total eastward distance= 30kmph*3/4hr=22.50 km
total westward distance= 50kmph*3/4hr=37.5 km
total distn betn them= 22.5+37.5=60km
ans 60km
ANSWER:B
Question: Two cars are traveling in the same direction along the same route. The red car travels at a constant speed of 40 miles per hour, and the black car is traveling at a constant speed of 50 miles per hour. If the red car is 10 miles ahead of the black car, how many hours will it take the black car to overtake the red car?
A.0.1
B.0.6
C.1
D.1.2
Answer: C.1
Explanation: Option C
10+40t=50t
t=1
Question: There are 3 kids in a family-Anna, Peter and Maria. Anna can clean the house
for 1 hour, Peter can do the same job for 3 hours and Maria needs 6 hours.
How much time do they need to work to finish the same cleaning if they do it
together?
A.20min
B.40min
C.30min
D.50min
Answer: B.40min
Explanation: In 6 hours, Anna will do 6 times the work, Peter will do
2 times the work and Maria will just finish the work. So if they
work together they would do 9 times the work required in 6 hours.
Answer:40 minutes
correct answer B
Question: A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?
A.19 cm2
B.30 cm2
C.17 cm2
D.18 cm2
Answer: B.30 cm2
Explanation: The circumference of the circle is equal to the permeter of the rectangle.
Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5
=> x = 1
Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5
= 30 cm2
Answer:B
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is?
A.153600
B.153629
C.151299
D.153129
Answer: A.153600
Explanation: Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m^2 = 153600 m^2.
Answer: A
Question: Pipe A can fill a tank in 4 hours, pipe B in 8 hours and pipe C in 24 hours. If all the pipes are open,in how many hours will the tank be filled ?
A.2.4
B.2.6
C.3.4
D.2.5
Answer: A.2.4
Explanation: 1/4+1/8+1/24=10/24=1/2.4. so 2.4 hrs
ANSWER:A
Question: Lexy walks 5 miles from point A to point G in one hour, then bicycles back to point A along the same route at 15 miles per hour. Ben makes the same round trip, but does so at half of Lexy’s average speed. How many minutes does Ben spend on his round trip?
A.40
B.80
C.120
D.160
Answer: D.160
Explanation: Lexy walks 5 miles from point A to point G in one hour, then bicycles back to point A along the same route at 15 miles per hour. Ben makes the same round trip, but does so at half of Lexy’s average speed. How many minutes does Ben spend on his round trip?
Average speed = total distance/total time
We know the total distance is 5+5 (going from A to G then from G to A)
Time = distance/speed
Time = 5/15
Time = 1/3 hour
Average speed = (10)/(1hr + 1/3hr)
Average speed (lexi) = 10 / 1.33
Therefore, if Ben's average speed is 1/2 of lexi's then his speed = 10/2.66.
This means it took him 2.66 hours to cover the same 10 miles Lexi did. 2.66 hours = roughly 160 minutes.
Answer: D). 160
Question: Difficulty:
There are five sales agents in a certain real estate office. One month Andy sold four times as many properties as Ellen, Bob sold 3 more than Ellen, Cary sold four times as many as Bob, and Dora sold as many as Bob and Ellen together. Who sold the most properties that month?
A.Andy
B.Bob
C.Cary
D.Dora
Answer: C.Cary
Explanation: a= 4e
b =3 +e
c = 4b = 12+ 4e (highest of all)
d = b + e = 3+ e +e = 3 + 2e
Ans. C
Question: What is the smallest number which when diminished by 12, is divisible 8, 12, 22 and 24?
A.276
B.295
C.230
D.225
Answer: A.276
Explanation: Required Number
= (LCM of 8, 12, 22 and 24) + 12
= 264 + 12 = 276
Answer: Option A
Question: The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 5 months, find for how much time did Q invest the money?
A.19
B.17
C.13
D.10
Answer: D.10
Explanation: 7*5: 5*x = 7:10
x = 10
Answer: D
Question: A certain series is defined by the following recursive rule: Sq=K(Sq-1) , where k is a constant. If the 1st term of this series is 64 and the 25th term is 192, what is the 9th term?
A.ROOT 2
B.ROOT 3
C.64*ROOT 3
D.64*3^1/3
Answer: D.64*3^1/3
Explanation: Ans...D
No need for any GP formula here
The rule is that qth term is K times the (q-1)th term.
1st = 64
2nd = k.64
3rd = k^2.64
.
.
.
9th term = k^8 *64
.
.
.
so 25th = k^24*64
Using this solve for k and substitute k in the equation for the 9th term
Question: If YWVSQ is 25 - 24 - 21 - 19 - 17, Then MLIGF
A.13 - 11 - 9 - 7 - 8
B.13 - 11 - 9 - 7 - 6
C.13 - 11 - 9 - 7 - 7
D.13 - 11 - 9 - 7 - 3
Answer: A.13 - 11 - 9 - 7 - 8
Explanation: MLIGF = 13 - 11 - 9 - 7 - 8
Note: this is a dummy question. Dont answer these questions
Answer:A
Question: How many seconds will a train 100 meters long take to cross a bridge 180 meters long if the speed of the train is 36 kmph?
A.54 sec
B.28 sec
C.25 sec
D.45 sec
Answer: B.28 sec
Explanation: D = 100 + 180 = 280
S = 36 * 5/18 = 10 mps
T = 280/10 = 28 sec
Answer:B
Question: At a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 11. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 14. How many cooks does the restaurant have?
A.4
B.6
C.9
D.12
Answer: D.12
Explanation: Originally there were 3k cooks and 11k waiters.
14k = 11k+12
k=4
There are 12 cooks.
The answer is D.
Question: There are 6 boxes numbered 1, 2, ... 6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is:
A.5
B.21
C.33
D.60
Answer: B.21
Explanation: Explanatory Answer
List down possibilities: From only 1 box all the way to all 6
If only one of the boxes has a green ball, it can be any of the 6 boxes. So, we have 6 possibilities.
If two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes. 12, 23, 34, 45, 56.
If 3 of the boxes have green balls, there are 4 possibilities: 123, 234, 345, 456.
If 4 boxes have green balls, there are 3 possibilities: 1234, 2345, 3456.
If 5 boxes have green balls, there are 2 possibilities: 12345, 23456.
If all 6 boxes have green balls, there is just 1 possibility.
Total number of possibilities = 6 + 5 + 4 + 3 + 2 + 1 = 21.
Choice B
Question: At a particular pizza shop, a pizza can be created from any combination of 3 different types of spice, 7 different types of meat, among which are pepperoni and anchovies, and 4 different types of cheese. If a customer at the shop decides to order a pizza with 1 type of spice, 2 types of cheese, and 4 types of meat but without pepperoni and anchovies together, how many possible ways to garnish the pizza are available to the customer?
A.6
B.35
C.120
D.450
Answer: D.450
Explanation: Number of possible ways to select 1 type of spice = 3c1 = 3
Number of possible ways to select 2 types of cheese = 4c2 = 6
(Here we can pick our answer as D- 450 since it is the only answer that is divisible by 3*6= 18 , but most likely on the GMAT there will be more another answer that will be divisible by 18 )
Number of possible ways to select 4 types of meat but without pepperoni and anchovies together
= Total number of ways without any restriction - Total number of ways in which pepperoni and anchovies together
= 7c4 - 5c2
=35 - 10
=25
Possible ways to garnish the pizza are available to the customer = 3*6 * 25
=450
Answer D