RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: In a 120-mile trip, the first 40 miles were completed at 60 mph. If the average speed for the whole trip was 50 mph, what was the average speed in the last 80 miles?
A.585/13 mph
B.590/13 mph
C.595/13 mph
D.600/13 mph
Answer: D.600/13 mph
Explanation: The time to complete the first 40 miles was (40 miles / 60 mph) = (2/3) hours.
The time to complete the whole trip was (120 miles / 50 mph) = (12/5) hours.
The time to complete the last 80 miles was (12/5) - (2/3) = (26/15) hours.
The average speed in the last 80 miles was (80 miles / (26/15) hours) = 600/13 mph.
The answer is D.
Question: If set A={3,3,3,....,n times} , set B={3,3,3,3....m times} and set C={11,11,11...k time} , then in terms of m,n and k , how many possible subsets from sets A,B, and C can be created ?
A.a) k(n+m+mn)+ k
B.b) (1+n+m+mn)(k+1)
C.c) k^2(mn+n/m)
D.d) kmn(k+m+n)
Answer: D.d) kmn(k+m+n)
Explanation: a) how many 2's are included?
b) how many 3's are included?
and
c) how many 11's are included?
For the number of 2, we could have zero 2's, or one 2, or two 2's, all the way up to n 2's. That's (n + 1) possibilities for the 2's. Similarly, (m + 1) possibilities for the 3's and (k + 1) possibilities for the 11's. We simply multiply these three numbers.
NOTICE that one set, the set that includes no 2's, no 3's, and no 11's, is included. This is known in mathematics as thenull set, sometimes called the empty set, a set with no members. Technically, this is a subset of every possible set, but that's a technical detail of set theory that goes well beyond what the GMAT would expect students to know. Even the the calculation is not that difficult, some of the technical aspects of this question are not in line with the GMAT's expectations.
The number of subsets is (m + 1)(n + 1)(k + 1). The answer is not given in that form. Instead, the first two factors have been FOILed together:
(mn + m + n + 1)(k + 1).
Mike
D
Question: If A and B are two prime numbers bigger than 2, which of the following can't be true?
(1) A + B is an even number.
(2) A - B is also a Even number.
(3) A^B is also a prime number.
A.1 only.
B.2 only.
C.3 only.
D.2 and 3 only.
Answer: C.3 only.
Explanation: Answer is D : 2 and 3 only
(1) A + B is an even number. : All primes beyond 2 are odd, so odd+odd = even, so true
(2) A - B is also a Even number. : True
(3) A^B is also a prime number. : Beats the property of primes, so false
Ans : C
Question: There are 24 students in a seventh grade class. They decided to plant birches and roses at the school's backyard. While each girl planted 3 roses, every three boys planted 1 birch. By the end of the day they planted 2424 plants. How many birches and roses were planted?
A.6
B.7
C.8
D.2
Answer: A.6
Explanation: Let xx be the number of roses. Then the number of birches is 24−x24−x, and the number of boys is 3×(24−x)3×(24−x). If each girl planted 3 roses, there are x3x3 girls in the class.
We know that there are 24 students in the class. Therefore x3+3(24−x)=24x3+3(24−x)=24
x+9(24−x)=3⋅24x+9(24−x)=3⋅24
x+216−9x=72x+216−9x=72
216−72=8x216−72=8x
1448=x1448=x
x=18x=18
So, students planted 18 roses and 24 - x = 24 - 18 = 6 birches.
Answer:A
Question: A train ride from Two P to Town Q costs $6.85 more than does a bus ride from Town P to Town Q. Together, the cost of one train ride and one bus ride is $9.85. What is the cost of a bus ride from Town P to Town Q?
A.$1.50
B.$2.50
C.$4.10
D.$4.70
Answer: A.$1.50
Explanation: Let x be the cost of a bus ride.
x + (x+685) = 985
2x = 300
x = $1.50
The answer is A.
Question: A fruit salad mixture consists of apples, peaches, and grapes. There are 3 times as many pounds of apples as grapes and 2.5 times as many pounds of peaches as grapes. If a mixture that has an average (arithmetic mean) of 39 pounds per fruit, how many more pounds of apples than grapes does the mixture have?
A.5
B.12
C.19
D.36
Answer: D.36
Explanation: A+P+G= 39*3
A=3G
P=2.5G
3G+2.5G+G= 39*3
G=39*3/6.5= 18
A= 6*3=54
Difference = 36
'D' is the answer
Question: A businessman earns $24800 in December, thus decreasing his average annual (January to December) earnings by $1500. His average annual earnings would be
Source: CMAT Preparation
A.$29000
B.$33500
C.$40200
D.$41300
Answer: D.$41300
Explanation: (x - 24,800)/11 - x/12 = 1,500
x = 495,600
x/12 = 41,300
Answer: D.
Question: The average of six numbers is 3.9. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers ?
A.4.7
B.4.45
C.4.2
D.4.1
Answer: B.4.45
Explanation: Explanation:
Sum of the remaining two numbers = (3.9 * 6) - [(3.4 * 2) + (3.85 * 2)]
= 23.40 - (6.8 + 7.7) = 23.40 - 14.5 = 8.90.
Required average = (8.9 / 2) = 4.45.
Answer: B) 4.45
Question: A train of length 250 m runs at a speed of 70 km/hr. What will be the time taken to cross any stationary object standing at the railway station?
A.20 sec
B.17.23 sec
C.12.86 sec
D.9.5 sec
Answer: C.12.86 sec
Explanation: EXPLANATION:
Length of train = 250 m, speed of train = 70 km/hr
Length of train is always considered as distance, and hence here distance = 250 m
1) First convert speed of km/hr into m/s
Speed of train = 70 x	5	= 19.44 m/s
18
2) We know that,
Speed =	Distance /Time
Time taken to cross stationary object =	250 / 19.44
Time taken to cross stationary object= 12.86 sec
ANSWER IS C
Question: if someone is ‘confounded’ means – he is puzzled, confused, bewildered stunned and ‘baffled’. Ask doubt using Question Id: 6320
A.21
B.87
C.278
D.277
Answer: C.278
Explanation: Answer:C
Question: In a certain government school, 40% of students are below 10 years of age. The number of students above 10 years of age is 5/6 th of the number of students of 10 years age which is 36. What is the total number of students in the school ?
A.100
B.72
C.110
D.135
Answer: C.110
Explanation: Explanation :
Solution: let the number of students be x. then, number of students of or above 10 years = (100-40)% of x = 60% of x.
.'. 60% of x = 36 +5/6 *36
=>60/100 * x = 66
=>x = 110
Answer : C
Question: The area of a sector of a circle of radius 5 cm formed by an arc of length 5.5 cm is?
A.13.78
B.13.67
C.13.75
D.13.98
Answer: C.13.75
Explanation: (5 * 5.5)/2
= 13.75
Answer:C
Question: What is the smallest no. that should be added to 41381 to make it exactly divisible by 9?
A.1
B.3
C.5
D.6
Answer: A.1
Explanation: If a number is divisible by 9, the sum of its digits must be a multiple of 9.
Here, 4+1+3+8+1=17, the next multiple of 9 is 18.
1 must be added to 41381 to make it divisible by 9
A
Question: A number a is squared and then multiplied by negative 6. The result of this operation is equal to three times the sum of FOURTH times a and two. What is one possible value of a ?
A.2
B.3
C.4
D.1
Answer: D.1
Explanation: -6*a^2=3(4a+2)
a= -1 or -1
a=-1=B
ANSWER:D
Question: If a is an integer and b = 3a + 2, which of the following CANNOT be a divisor of b?
A.6
B.7
C.8
D.9
Answer: A.6
Explanation: Just to add some more to Bunuel's explanation, if a number is a multiple of 3, it will be in a form:
n = 3*k, where k is an integer
And if a number is a multiple of 6, it will be in a form :
m = 6*l, where l is an integer
so m = 2 * 3 * l = (2*l) * 3 = 3 * p, where p is an integer.
In other words, the prime factorization of m must have 3 as a factor, if it's a multiple of 6, but the expression can't have that (as explained by Bunuel), so it can't be a multiple of 6 either.
Answer is A
Question: The volume of a certain substance is always directly proportional to its weight. If 48 cubic inches of the substance weigh 112 ounces, what is the volume, in cubic inches, of 63 ounces of this substance?
A.27
B.36
C.42
D.64
Answer: A.27
Explanation: 112 ounces of a substance has a volume of 48 cubic inches
63 ounces of a substance has a volume of (48/112)*63 = 27 cubic inches
Answer A
Alternatively , we can use estimation
112 ounces of a substance has a volume of 48 cubic inches
56 ounces of a substance has a volume of 24 cubic inches
Therefore , 63 will have a volume a little more than 24 ,that is 27
ANSWER:A
Question: Find the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs.15of money?
A.1500
B.1992
C.9921
D.2798
Answer: A.1500
Explanation: P = 15(100/10)2
=> P = 1500
Answer: A
Question: A train which has 600 m long, is running 60 kmph. In what time will it cross a person moving at 6 kmph in same direction ?
A.42 sec
B.44 sec
C.46 sec
D.40 sec
Answer: D.40 sec
Explanation: Time taken to cross a moving person = length of train/ relative speed
Time taken = 600/((60-6) (5/18) = 600/ 54*(5/18) = 600/15= 40 sec
Answer: D
Question: Look at this series: 7, 10, 8, 11, 9, 12, ... What number should come next?
A.7
B.10
C.12
D.13
Answer: B.10
Explanation: This is a simple alternating addition and subtraction series. In the first pattern, 3 is added; in the second, 2 is subtracted.
12-2=10
Option B
Question: If the given two numbers are respectively 7% and 14% of a third number, then what percentage is the first of the second ?
A.20%
B.25%
C.18%
D.50%
Answer: D.50%
Explanation: Here, l = 7 and m = 14
Therefore, first number = l/m x 100% of second number = 7/14 x 100% of second number = 50% of second number
ANSWER:D
Question: A milk seller has certain quantity of milk to sell. In what ratio, should he mix water to gain 5% by selling the mixture at the cost price ?
A.1:10
B.1:5
C.1:20
D.1:15
Answer: C.1:20
Explanation: Let Cost price of 100 g milk was Rs. 100.
x +5% of x = 100
x + 0.05x = 100
1.05x = 100
x = 100/1.05 = 95.23
Water = 100 - 95.23 = 4.76
Ratio of water and Milk = 4.76 /95.23 = 1/20 = 1 : 20.
ANSWER : C
Question: Find the odd man out. 15, 20, 25, 32, 30, 45
A.15
B.20
C.30
D.32
Answer: D.32
Explanation: All numbers except 32 are multiples of 5
Answer is D
Question: In a box of 8 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?
A.2/10
B.3/11
C.4/13
D.5/14
Answer: D.5/14
Explanation: P(neither pen is defective) = 5/8*4/7 = 5/14
The answer is D.
Question: A five-digit number is formed by using digits 1, 2, 3, 4 and 5 without repetition. What is the probability that the number is divisible by 4?
A.1/5
B.2/5
C.3/5
D.4/5
Answer: A.1/5
Explanation: A number divisible by 4 formed using the digits 1, 2, 3, 4 and 5 has to have the last two digits 12 or 24 or 32 or 52.
In each of these cases, the five digits number can be formed using the remaining 3 digits in 3! = 6 ways.
A number divisible by 4 can be formed in 6 x 4 = 24 ways.
Total number that can be formed using the digits 1, 2, 3, 4 and 5 without repetition = 5! = 120.
Hence, the required probability would be 24/120 = 1/5.
ANSWER:A
Question: In 1937, the ship of the great sailor SINBAD left an Egyptian port heading Ivory coast at W mile/month .
One month later another ship of the greatest pirate ever CHENG I SAO was 5000 miles due south of the same Egyptian port and heading due north at Y miles/month. Six months later after the leaving of Sinbad’s ship from Egyptian port, how far apart were the ships? [Ivory coast is in the west of Egypt]
A.{ (6W)^2 + (5000-5y)^2 }^1/2
B.{ (36x)^2 + (5000-7y)^2 }^1/2
C.{ (16x)^2 + (5000-7y)^2 }^1/2
D.{ (7x)^2 + (5200-7y)^2 }^1/2
Answer: A.{ (6W)^2 + (5000-5y)^2 }^1/2
Explanation: The chinese ship sailed for 5 months i.e. 5Y miles @Y miles/month, therefore distance from Egyptian port is 5000-5Y. Since A is the only option with this value ...therefore A is the answer
Question: A car finishes a journey in five hours at the speed of 100 km/hr. If the same distance is to be covered in two hours how much more speed does the car have to gain?
A.8 km/hr
B.10 km/hr
C.150 km/hr
D.16 km/hr
Answer: C.150 km/hr
Explanation: Distance covered by the car = 100 × 5 = 500 km
\ Speed = 500⁄2 = 250 km/hr
\ Speed gain = 250 – 100 = 150 km/hr
Answer C
Question: The ratio of speeds of a car, a train and a bus is 5:9:4. The average speed of the car, the bus and the train is 72 km/hr together. What is the average speed of the car and the train together ?
A.84 km/hr
B.74 km/hr
C.34 km/hr
D.64 km/hr
Answer: A.84 km/hr
Explanation: Let the speeds of the car, train and bus be 5x, 9x and 4x km/hr respectively.
Average speed = 5x + 9x + 4x/3 = 18x /3 = 6x km/hr.
Also, 6x = 72 => x = 12 km/hr
Therefore, the average speed of the car and train together is = = 7x = 7 x 12 = 84 km/hr.
Answer: A
Question: A certain protective additive increases from 30 days to 45 days the time between required maintenance checks on an industrial vehicle. By what percent is the time between maintenance checks increased by using the additive?
A.25%
B.33 1/3%
C.50%
D.66 2/3%
Answer: C.50%
Explanation: General formula for percent increase or decrease, (percent change):
percent=Change/Original∗100
So, the time between maintenance checks increased by 45−30/30∗100=50
Answer: C.
Question: In digging a hole 10 m * 10 m * 100 m the volumes of the sand extracted will be?
A.100 cu.m
B.1000 cu.m
C.10000 cu.m
D.2000 cu.m
Answer: C.10000 cu.m
Explanation: 10 * 10 * 100 = 10000
ANSWER:C
Question: Suppose that f(x) is a function such that for every real number x,i)f(x)+f(1-x) = 14 and (ii) f(1+x) = 3+f(x). Then f(x)+f(-x)
must equal
A.8
B.9
C.10
D.11
Answer: D.11
Explanation: Since (ii) holds for every real number x, it will remain valid if we replace x with
-x. Therefore, f(1-x) = 3+f(-x). Now, from (i), 14 = f(x)+f(1-x) = f(x)+3+f(-x)
so that f(x) + f(-x) = 14-3 = 11. (Observe that f(x) = 3x + 4 satisfies the conditions
in the problem.)
correct answer D
Question: Youseff lives x blocks from his office. It takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work. It is takes him exactly 6 minutes more to walk to work than to ride his bike to work, then x equals?
A.4
B.7
C.9
D.15
Answer: C.9
Explanation: Please follow posting guidelines, link is in my signatures.
As for your question, x/60 = blocks/time/block = block^2/time . This is not what you want. You are given x blocks and 60 seconds PER BLOCK. Thus you need to put it as 60*x to give you units of seconds as you are equating this to 360 (which is TIME in seconds.).
Thus the correct equation is : 60*x-20*x=360 ----> 40x=360--> x = 9.
option C
Question: What is greatest positive integer n such that 2^n is a factor of 12^13?
A.a)10
B.b)12
C.c)16
D.d)26
Answer: D.d)26
Explanation: The given number is 12^13
=(2*2*3)^13
=(2^26)*(3^13)
So the greatest possible value for n such that 2^n can be factor of given number is 26.
Answer D
Question: A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did C get in a profit of Rs.2490 ?
A.s. 332
B.s. 498
C.s. 822
D.s. 812
Answer: B.s. 498
Explanation: Let the total amount in the partnership be 'x'.
Then A's share = x/3
B's share = x/4
C's share = x/5
D's share = x - (x/3 + x/4 +x/5) = 13x/60
A : B : C : D = x/3 : x/4 : x/5 : 13x/60 = 20 : 15 : 12 : 13
C's share in the profit of Rs. 2490 = 12 (2490/60) = Rs. 498.
Answer: B
Question: Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is?
A.9:39
B.9:31
C.9:36
D.9:32
Answer: B.9:31
Explanation: 1/4 : 3/4 = (1:3)5 = 5:15
1/5 : 4/5 = (1:4)4 = 4:16
------
9:31
Answer: B
Question: Before January, the price of a dress was D and the price of a matching pair of shoes was H. In January, the price of the dress increased by 40% and the price of the shoes increased by 50%. In March, Roberta bought both items with a 30% discount. If D = 1H, which of the following represents the amount that Roberta paid?
A.D + 40
B.D + H – 1
C.D + 2H
D.2.03H
Answer: D.2.03H
Explanation: before Discount price was: 1.4D+1.5H
After Discount: 1.4D +1.5H-.42D-.45H
substitute D=H
final value: 2.03H
Ans Is D :
Question: Triangle XYZ is an isosceles right triangle. If side XY is longer than side YZ, and the area of the triangle is 25, what is the measure of side XY?
A.10
B.4√2
C.8
D.8√2
Answer: A.10
Explanation: ans A ..10..
xy being larger means it is the hyp..
area =(1/2)*(yz)^2=25 or yz=5*\sqrt{2}..
therefore hyp=xy=10
Question: Series 3,15,35,__,99
A.43
B.53
C.63
D.73
Answer: C.63
Explanation: 1*3=3
3*5=15
5*7=35
7*9=63
9*11=99
ANSWER:C
Question: The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is:
A.279
B.283
C.308
D.318
Answer: C.308
Explanation: Other number =	(11 x 7700)/275= 308. Answer : C
Question: 9/5 of 11/122 of 8% of 33550 = ?
A.432.2
B.433.4
C.435.6
D.436.8
Answer: C.435.6
Explanation: Explanation :
? = 9x11x8x33550/5x122x100 = 435.6
Answer : Option C
Question: 675.987 - ? + 56.84 =289.654
A.A)443.173
B.B)752.804
C.C)714.642
D.D)629.906
Answer: A.A)443.173
Explanation: Explanation:
443.173
Answer: Option A
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.22887
C.26877
D.26771
Answer: A.81000
Explanation: 64000* 9/8 * 9/8 = 81000
Answer:A
Question: The average of six numbers is X and the average of three of these is Y.If the average of the remaining three is Z, then
A.x = y + z
B.2x = y + z
C.x = 2y + 2z
D.None of these
Answer: B.2x = y + z
Explanation: Solution
Clearly, we have	X =(3y+3z/6)
or
2x= y + z
Answer B
Question: A certain set of numbers has an average (arithmetic mean) of 50 and a standard deviation of 50.5. If k and n, two numbers in the set, are both within 2 standard deviations from the average, then which of the following could be the sum of k and n?
A.-200
B.-130
C.-104
D.51
Answer: D.51
Explanation: 2 standard deviations from the average is from mean - 2*SDtomean + 2*SD, thus from 50-2*50.5=51 to 50+2*50.5=151:
-51 < k < 151
-51 < n < 151
-102 < k+n < 302.
Only option D is in this range.
Answer: D.
Question: A certain car can travel 40 minutes on a gallon of gasoline at 60 miles per hour. If the car had started with a full tank and had 8 gallons of gasoline left in its tank at the end, then what percent of the tank was used to travel 120 miles at 60 mph?
A.15%
B.20%
C.25%
D.27%
Answer: D.27%
Explanation: Total time for travelling 120 miles @ 60 mph = 120/60 = 2 hour = 120 minutes.
Given, the car uses 1 gallon for every 40 minutes of driving @ 60 mph. Thus in 120 minutes it will use = 3 gallons. Thus, full tank = 3+8 = 11 gallons --->3/11= 27% of the fuel used. D is the correct answer.
Question: The sum of the non-prime numbers between 20 and 30, non-inclusive, is
A.173
B.185
C.197
D.209
Answer: A.173
Explanation: sum of consecutive integers from 21 to 29, inclusive ====> (A1 + An)/2 * # of terms = (21 + 29)/2 * 9 = 25 * 9 = 225
sum of non-prime numbers b/w 20 and 30, non inclusive ===> 225 - 52 (i.e., 23 + 29, being the prime #s in the range) =173
Answer: A
Question: Two cars are driving toward each other. The first car is traveling at a speed of 100 km/h, which is 20% slower than the second car's speed. If the distance between the cars is 1125 km, how many hours will it take until the two cars meet?
A.4
B.4.5
C.4.8
D.5
Answer: D.5
Explanation: The speed of the first car is 100 km/h.
The speed of the second car is 100 / 0.8 = 125 km/h.
The two cars complete a total of 225 km each hour.
The time it takes the cars to meet is 1125 / 225 = 5 hours.
The answer is D.
Question: In an hour a boat goes 10 Km along the stream and 4 Km against the stream. The speed of the boat in still water (in Kmph) is:
A.7 Kmph
B.8 Kmph
C.10 Kmph
D.12 Kmph
Answer: A.7 Kmph
Explanation: Explanation:
Let the speed of stream = X Kmph
and the speed of water = 8 Kmph
X + Y = 10
X - Y = 4
X = 7, Y = 3
Speed of stream = 7 Kmph
Answer: Option A
Question: Jim is now twice as old as Fred, who is eight years older than Sam. Four years ago, Jim was four times as old as Sam. How old is Jim now?
A.36
B.40
C.44
D.48
Answer: C.44
Explanation: J = 2F = 2(S+8) = 2S+16
J-4 = 4*(S-4)
(2S+16)-4 = 4S-16
S = 14 and so J = 44
The answer is C.
Question: A firm of ready made garments makes both men’s and women’s shirts. Its average profit is 6% of the sales. Its profit in men’s shirts average 8% of the sales and women’s shirts comprise 60% of the output. The average profit per sale rupee in women shirts is
A.0.0466
B.0.0666
C.0.0166
D.0.0366
Answer: A.0.0466
Explanation: Women's shirt comprise 60% of the output.
∴ Men's shirts comprise (100 – 60) = 40% of the output.
∴ Average profit from men's shirt = 8% of 40 = 3.2 out of 40
Overall average profit = 6 out of 100
∴ Average profit from women's shirts = 2.8 out of 60
i.e. 0.0466 out of each shirt.
Answer A
Question: In a group of ducks and cows, the total number of legs are 32 more than twice the number of heads. Find the total number of cows.
A.12
B.14
C.16
D.18
Answer: C.16
Explanation: Let the number of ducks be d
and number of cows be c
Then, total number of legs = 2d + 4c = 2(d + 2c)
total number of heads = c + d
Given that total number of legs are 32 more than twice the number of heads
=> 2(d + 2c) = 32 + 2(c + d)
=> d + 2c = 16 + c + d
=> 2c = 16 + c
=> c = 16
i.e., total number of cows = 16
Answer is C.
Question: A man buys a scooter for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the scooter?
A.Rs. 1240
B.Rs. 1190
C.Rs. 1090
D.Rs. 1130
Answer: B.Rs. 1190
Explanation: SP=1400×85/100=14×85=1190
Answer : Option B
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
A.978
B.789
C.999
D.778
Answer: C.999
Explanation: a2 = 3136
=> a = 56
56 * 4 * 3
= 672 – 6
= 666 * 1.5
= 999
Answer: C
Question: Nine family members are seated around their circular dinner table. If only arrangements that are considered distinct are those where family members are seated in different locations relative to each other, and Michael and Bobby insist on sitting next to one another, then how many distinct arrangements around the table are possible?
A.7080
B.8080
C.9080
D.10,080
Answer: D.10,080
Explanation: Let's consider Michael and Bobby as one unit.
There are 8! possible arrangements of 8 units.
Around a table, there would be repetitions of each arrangement, so we divide by 8.
Then there are 7! arrangements around a circular table.
For each arrangement, Michael and Bobby can switch places, so we multiply by 2.
The number of arrangements is 7!*2 = 10,080.
The answer is D.
Question: Of the integers between 100 and 999, inclusive, how many do not have digit 3 and 5?
A. 310
B. 320
C. 448
D. 428
Answer: C. 448
Explanation: Options for the first digit 9-2(2 and 5)=7;
Options for the second digit 10-2=8;
Options for the third digit 10-2=8;
Total numbers possible 7*8*8=320.
Answer: C.
Question: If 3x=6y=z, what is x+y, in terms of z?
A.z/2
B.2z
C.z/3
D.3z/5
Answer: A.z/2
Explanation: 3x=6y=z
x = z/3
and y = z/6
x+y = z/3 + z/6 = z/2
Answer is A
Question: What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?
A.12 ways
B.14 ways
C.30 ways
D.61 ways
Answer: C.30 ways
Explanation: The number of ways to select three men and two women such that one man and one woman are always selected = Number of ways selecting two men and one woman from men and five women
= 4C2 * 5C1
= (4 * 3)/(2 * 1) * 5
= 30 ways.
Answer: C
Question: If the cost price of 8 articles is the same as the selling price of 10 articles. Find the gain or loss percentage?
A.20% gain
B.20% loss
C.30% gain
D.30% loss
Answer: D.30% loss
Explanation: Explanation:
Ex:-
2X = 3Y
X = 3
Y = 2
12 cp = 15 sp
Cost price CP = 15
Selling price SP = 12
Formula = (SP-CP)/CP * 100 = (12 - 15)/10 * 100 = 30 % Loss
Answer: Option D
Question: If $x is invested at a constant annually compound interest rate of k percent, what is the ratio of the total amount including interest after 7n years to that after 3n years?
A.(1+k/100)^n
B.(1+k)^n
C.(1+kn/100)
D.(1+k/100)^4n
Answer: D.(1+k/100)^4n
Explanation: Amount after 7n years will be = x ( 1 + k/100)^4n
Amount after 3n years will be = x ( 1 + k/100)^3n
So, required ratio will be -
{ x ( 1 + k/100)^7n } / {x ( 1 + k/100)^3n } = (1+k/100)^4n
Hence answer will be a. (1+k/100)^4n
D