RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Ram can finish a puzzle in 3 hours and Shyam can do the same in 2 hours. Both of them finish the puzzle and get 15 candies. What is Ram’s share?
A.6
B.7
C.5
D.8
Answer: A.6
Explanation: Explanation:
The question is based on efficiency to do work.
Ram can finish a puzzle in 3 hours. Shyam can finish the puzzle in 2 hours.
=>In one hour Ram can finish 1/3rd of a puzzle
=>In one hour Shyam can finish half the puzzle
A total of 15 candies are to be shared amongst both of them
Hence Ram’s share must be = ((Work done by Ram in 1 hour)/(Work done by Shyam in one hour)+(Work done by Ram in hour))*15
=> 1/3/((1/2)+(1/3))*15
=> (1/3/(5/6))*15
=> 6/15*(15)
=>6 candies
ANSWER: A
Question: The cost of 10 packets of sugar, each weighing 900 grams is Rs. 28. What will be the cost of 27 packets, if each packet weighs 1 kg?
A.Rs 52.50
B.Rs 56
C.Rs 58.50
D.Rs 84
Answer: D.Rs 84
Explanation: Explanation :
Let the required cost be Rs. x. Then,
More packets, More cost (Direct Proportion)
More weight, More cost (Direct Proportion)
Packets 10 : 27
Weight 900 : 1000 :: 28 : x
(10 x 900 x x) = (27 x 1000 x 28)
x = (27 x 1000 x 28) /10 x 900
= 84
Answer D
Question: A furniture store bought chairs for 60% of their list price and sold them for 10% off the list price. What is their percent gain?
A.25
B.50
C.60
D.75
Answer: B.50
Explanation: Cost = 60% of List Price = .6*LSale = (100-10)% of List Price = .9*LGain Ratio = (Sale - Cost) / Cost = (.9*L - .6*L) / .6*L = .3*L / .6*L = 0.50Gain Percent = 100 * Gain Ratio = 100 * 0.5 = 50% = Answer B
Question: The area of a square garden is A square feet and the perimeter is p feet. If a=2p+26.25, what is the perimeter of the garden, in feet?
A.28
B.36
C.40
D.42
Answer: D.42
Explanation: Perimeter of square = P
Side of square = P/4
Area of Square = (P^2)/16 =A
Given that A = 2P + 26.25
(P^2)/16 = 2P + 26.25
P^2 = 32P + 420
P^2 -32P -420 = 0
P^2 -42P +10 P -420 = 0
P(P-42)+10(P+42) = 0
(P-42)(P+10) = 0
P = 42 or- 10
Discarding negative value , P = 42
Answer is D
Question: What is the greatest integer m for which the number 20!/10^m is an integer?
A.3
B.4
C.5
D.6
Answer: B.4
Explanation: 10^m = 2^m*5^m.
Let's figure out how many 5's are in the prime factorization of 20!
The multiples of 5 are: 5, 10, 15, 20.
Thus 5^4 will divide 20! but 5^5 will not.
Clearly 2^4 will divide 20!
So m=4 is the largest possible integer.
The answer is B.
Question: What is the square root of 16, divided by 2?
A.9
B.2
C.122
D.6
Answer: B.2
Explanation: Square root is a number times itself
Square root of 16=4, 4/2=2
(B)2
Question: One-sixth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/15 of the non defective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?
A.1.8%
B.2.9%
C.4.1%
D.5.6%
Answer: C.4.1%
Explanation: 1/6 of the switches are defective.
The defective switches that are not rejected are 1/5*1/6 = 1/30 = 3/90 of all switches.
The non defective switches that are sold are 5/6*14/15 = 70/90 of all switches.
The percent of switches sold that are defective is 3/73 which is about 4.1%.
The answer is C.
Question: If 5 spiders make 5 webs in 5 days, then 1 spider will make 1 web in how many days?
A.7
B.6
C.5
D.4
Answer: C.5
Explanation: Let the required number days be x.
Less spiders, More days (Indirect Proportion)
Less webs, Less days (Direct Proportion)
spiders 1:5
Webs 5:1
1 x 5 x x = 5 x 1 x 5
=> x= 5
Answer is C
Question: P and Q can do a work in 30 days. Q and R can do the same work in 24 days and R and P in 20 days. They started the work together, but Q and R left after 6 days. How many days more will P take to finish the work?
A.30
B.15
C.18
D.20
Answer: A.30
Explanation: Let work done by P in 1 day = p,
Work done by Q in 1 day = q,
Work done by R in 1 day = r
p + q = 1/30
q + r = 1/24
r + p = 1/20
Adding all the above, 2p + 2q + 2r = 1/30 + 1/24+ 1/20 = 15/120 = 1/8
=> p + q + r = 1/16
=> Work done by P,Q and R in 1 day = 1/16
Work done by P, Q and R in 6 days = 6 × (1/16) = 6/16 = 3/8
Remaining work = 1 = 3/8 = 5/8
Work done by P in 1 day = Work done by P,Q and R in 1 day - Work done by Q and R in 1 day
= 1/16 – 1/24 = 1/48
Number of days P needs to work to complete the remaining work = (5/8) / (1/48) = 30
Option A
Question: If p and q are positive integers each greater than 1, and 17(p+1)=28(q+1), what is the least possible value of p+q?
A.36
B.42
C.44
D.43
Answer: D.43
Explanation: 17(p+1)=29(q+1) --> (p+1)/(q+1) = 28/17 --> the least positive value of p+1 is 28, so the least value of p is 27 and the least positive value of q+1 is 17, so the least value of q is 16 --> the least value of p+q is 27+16=43.
Answer: D
Question: An article is bought for Rs.1000 and sold for Rs.1100, find the gain percent?
A.33 1/7%
B.10%
C.33 1/3%
D.38 1/3%
Answer: B.10%
Explanation: 1000 ---- 100
100 ---- ? => 10%
Answer:B
Question: 85% of a number is added to 24, the result is the same number. Find the number?
A.257
B.267
C.187
D.160
Answer: D.160
Explanation: (85/100) * X + 24 = X
3X = 480
X = 160
Answer:D
Question: A dealer offers a cash discount of 20% and still makes a profit of 20%, when he further allows 16 articles to a dozen to a particularly sticky bargainer. How much percent above the cost price were his wares listed?
A.100%
B.80%
C.75%
D.66(2/3)%
Answer: A.100%
Explanation: Solution: Let the CP of the article be Rs. x, since he earns a profit of 20%, hence SP= X + 20% of X = 1.2x.
It is given that he incurs loss by selling 16 articles at the cost of 12 articles [loss = (16-12)/16 = 25%]
His selling price = SP - 25% of SP = SP*0.75;
Hence, SP*0.75 = 1.2X.
Or, SP = (1.2*x/0.75) = 1.6X.
This SP is arrived after giving a discount of 20% on MP.
Let MP = Y.
Y - 20% of Y = SP
0.80Y = 1.6X.
Y = 2X.
It means that the article has been marked 100% above the cost price. Or Marked Price was twice of cost price.
Answer: Option A
Question: At present, the ratio between the ages of Shekhar and Shobha is 4:3. After 6 years, Shekhar's age will be 26 years. Find out the age of Shobha at present?
A.10
B.12
C.14
D.15
Answer: D.15
Explanation: After 6 years, Shekhar's age will be 26 years
Therefore, Present age of Shekhar =26−6=20
Let present age of Shobha =x
Then,
20x=43x=20×34=15
Answer is D.
Question: The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
A.177
B.156
C.199
D.750
Answer: D.750
Explanation: Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 25 è x = 25 * 60 / 2 = 750
Answer:D
Question: P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?
A.5
B.5 3/5
C.5 5/7
D.6
Answer: C.5 5/7
Explanation: P can complete the work in (12 x 8) hrs. = 96 hrs.
Q can complete the work in (8 x 10) hrs. = 80 hrs.
P's1 hour's work =	1	and Q's 1 hour's work =	1	.
96	80
(P + Q)'s 1 hour's work = 1	+	1 =	11	.
96	80	480
So, both P and Q will finish the work in 480 hrs.
11
Number of days of 8 hours each = 480	x	1 =	60	days = 5	5	days.
11	8	11	11
Option C
Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
A.21
B.16
C.18
D.12
Answer: B.16
Explanation: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 280 * 2/35 = 16 sec.Answer: B
Question: If 0.20: x : : 4 : 2, then x is equal to
A.0.2
B.0.3
C.0.1
D.0.5
Answer: C.0.1
Explanation: Sol.
(x×4) = (0.20×2) ⇒ x = 0.4/4 = 0.1.
Answer C
Question: Today Mary’s father is four times as old as Mary. Ten years ago, he was 14 times as old. How old is Mary today?
A.7
B.9
C.11
D.13
Answer: D.13
Explanation: Dad's age = 4M
14*(M-10) = 4M-10
10M = 130
M = 13
The answer is D.
Question: A father is two times as old as his daughter. 2 decades ago, the age of the father was 12 times the age of the daughter. The current age of the father is
A.44 years
B.43 years
C.42 years
D.48 years
Answer: A.44 years
Explanation: A
44 years
Let daughter’s age = A.
Then father’s age = 2A
12 (A – 20) = (2A – 20)
10A = 220
A = 22
Father’s current age = 44 years.
Question: John,Anny, Markov, David and Philip line up at a theatre ticket window. In how many ways can they arrange themselves so that philip is second in line from the window?
A.a 24
B.b 12
C.c 9
D.d 6
Answer: A.a 24
Explanation: A
Philip's position is fixed. Now we need to arrange all others around philip.
There are 4x3x2x1= 24 ways to arrange four people.
Question: A bat is bought for Rs.430 and sold at a gain of 20% find its selling price
A.s.430/-
B.s.480/-
C.s.400/-
D.s.516/-
Answer: D.s.516/-
Explanation: 100 % ------> 430
120 % ------> 430*120/100
Selling price = Rs.516
D
Question: Average of all prime numbers between 30 to 50
A.37
B.37.8
C.39
D.39.8
Answer: D.39.8
Explanation: Explanation:
Prime numbers between 30 and 50 are:
31, 37, 41, 43, 47
Average of prime numbers between 30 to 50 will be
(31+37+41+43+475)=1995=39.8
Answer: Option D
Question: Water tax is increased by 40% but its consumption is decreased by 40%. The increase or decrease in the expenditure is?
A.16% decrease
B.16% increase
C.8% decrease
D.8% increase
Answer: A.16% decrease
Explanation: Since Tax x Consumption = Expenditure .
Therefore, Net % change in expenditure
= ( x + y + xy/100) %
= [40 - 40 + (40 x - 40)/100]% or -16%.
Therefore, expenditure decreased by 16%.
ANSWER:A
Question: The speed of light is approximately 93 * 10^5 miles per second. This approximate speed is how many miles per hour?
A. 3,35 * 10^8
B.70 * 10^7
C. 11 * 10^8
D. 16 * 10^8
Answer: A. 3,35 * 10^8
Explanation: The easiest way to answer this question is by POE, it does not require any calculation (answered in 30seconds). In one hour there are 3600 seconds, therefore speed in miles/hour will be.
(.93*10^5)*3600 = (.93*10^5)*(3.6*10^3) = some number*10^8...
The key is realizing that thesome numberhas to be bigger thatn .93(because .93*3.6), and the only answer that fits that is A
Question: A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
A.30 kmph
B.10 kmph
C.5 kmph
D.25 kmph
Answer: A.30 kmph
Explanation: Explanation:
US = 25
DS = 35
M = (35 + 25)/2 = 30 kmph
Answer: A
Question: Bernice's income is 70 percent more than Cathy's income, and Cathy's income is 65 percent less than Camilla's income. What percent of Camilla's income is Bernice's income?
A.54.5%
B.52.5%
C.59.5%
D.51.5%
Answer: C.59.5%
Explanation: Camilla's income = 100 (assume);
Cathy's income = 35 (65 percent less than Camilla's income);
Bernice's income = 59.5 (70 percent more than Cathy's income).
Thus, Bernice's income (59.5) is 59.5% of Camilla's income (100).
Answer: C
Question: A popular website requires users to create a password consisting of the digits {1,2,3,4,5,6,7,8}. If no digit may be repeated and each password must be at least 7 digits long, how many passwords are possible?
A.7! + 8!
B.2 x 8!
C.7! x 8!
D.15!
Answer: B.2 x 8!
Explanation: If we choose the 8 different digits then they can be arranged in 8! ways.
The number of possible 7-digit passwords is 8*...*2 = 8!
The total number of passwords is 8! + 8! = 2*8!
The answer is B.
Question: In baseball, the batting average is defined as the ratio of a player’s hits to at bats. If a player had anywhere from 6 to 9 at bats in a recent game and had anywhere from 4 to 5hits in the same game, the player’s actual batting average for that game could fall anywhere between
A.0.25 and 1.50
B.0.25 and 0.75
C.0.30 and 1.00
D.0.30 and 0.50
Answer: C.0.30 and 1.00
Explanation: Average Range = Hits to Bats i.e 4/9 to 5/6 = 0.44 to 0.83
Answer: C
Question: At the end of a business conference the 18 people present all shake hands with each other once. How many handshakes will there be altogether ?
A.20
B.45
C.153
D.90
Answer: C.153
Explanation: number of handshakes = 18C2= 18*17/2 = 153
ANSWER:C
Question: If the sum of three consecutive even numbers is 24 more than the average of these numbers, then the largest of these numbers is?
A.10
B.12
C.14
D.16
Answer: C.14
Explanation: Explanation:
Let the smallest of these number be x. The other two numbers are (x + 2) and (x + 4).
x + (x + 2) + (x + 4) = (X + (X+2) + (x+4)) / 3 + 24
3x + 3*(x + 2) + 3*(x + 4) = x + (x + 2) + (x + 4) + 72
9x + 18 = 3x + 78
6x = 60
x = 10
Therefore, the largest number is 14.
ANSWER C
Question: Aaron will jog from home at 6 miles per hour and then walk back home by the same route at 12 miles per hour. How many miles from home can Aaron jog so that he spends a total of 3 hours jogging and walking?
A.12
B.14
C.16
D.15
Answer: A.12
Explanation: xyt/(x+y)
x= 6, y=12 t= 3
6*12*3/6+12 = 12
Answer : A
Question: How many digits are there to the right of the decimal point in the product of .32546 and 75.21 ?
A.7
B.6
C.8
D.2
Answer: A.7
Explanation: Product of is .32546 and 75.21 is 24.4778466.
Therefore number of digits to right of decimal point is 7
Answer is A.
Question: Paul is going with 5 friends on a trip to Rome for spring break. Airfare and hotel costs a total of $3600.00 for the group of 6 friends. How much does each person have to pay for their hotel and airfare?
A.$400
B.$500
C.$600
D.$660
Answer: C.$600
Explanation: Answer= C
The total cost of the trip ($3600.00) divided by 6 equals $600.00.
Question: The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 5 years hence?
A.58
B.59
C.62
D.70
Answer: D.70
Explanation: Explanation:
A + B = 60, A = 2B
2B + B = 60 => B = 20 then A = 40.
5 years, their ages will be 45 and 25.
Sum of their ages = 45 + 25 = 70.
D)
Question: A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?
A.12.2
B.12.9
C.12.6
D.12.5
Answer: D.12.5
Explanation: Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.
Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7
Solving the equation, the speed of man in still water is 12.5 kmph.
Answer: D
Question: If the sum of three consecutive even numbers is 30 more than the average of these numbers, then the largest of these numbers is?
A.20
B.19
C.18
D.17
Answer: D.17
Explanation: Explanation:
Let the smallest of these number be x. The other two numbers are (x + 2) and (x + 4).
x + (x + 2) + (x + 4) = (X + (X+2) + (x+4)) / 3 + 30
3x + 3*(x + 2) + 3*(x + 4) = x + (x + 2) + (x + 4) + 90
9x + 18 = 3x + 96
6x = 78
x = 13
Therefore, the largest number is 17.
ANSWER D
Question: If a coin is tossed three times, what is the probability that on the first toss the coin lands tails, on the second toss the coin lands tails, and on the third toss the coin lands heads.
A.1/2
B.1/8
C.1/6
D.1/4
Answer: B.1/8
Explanation: Since there are two options for how a coin can land (heads or tails), that means there is a 1/2 chance to land on tails and a 1/2 chance to land heads. To solve this problem you multiply each probability for each flip together. (1/2) chance to land tails the first time * (1/2) chance to land tails the second time * (1/2) chance to land heads the third time = (1/8) chance to land tails the first two times and heads the third time.
Answer: B
Question: Source: Knewton
A cyclist's speed varies, depending on the terrain, between 6.0 miles per hour and 14.0 miles per hour, inclusive. What is the maximum distance, in miles, that the cyclist could travel in 6 hours?
A. 42
B. 56
C. 84
D. 98
Answer: C. 84
Explanation: We are told that:generallya cyclist's speed varies, depending on the terrain, between 6.0 miles per hour and 14.0 miles per hour, inclusive. Is it possible the cyclist to travel with maximum speed for some time? Why not, if there is right terrain for that. So, if there is long enough terrain for the maximum speed of 14 mph then the maximum distance, in miles, that the cyclist could travel in 6 hours would be 6*14=98 miles.
Answer: C.
Question: If a dozen of oranges cost $5, what would be the cost of 10 oranges?
A.3.56
B.4.16
C.4.86
D.5.1
Answer: B.4.16
Explanation: The cost of one orange=5/12=0.416
The cost of ten oranges= 0.416x10= $ 4.16
Answer: B
Question: If the President and Vice President must sit next to each other in a row with 2 other members of the Board, how many different seating arrangements are possible?
A.10
B.16
C.18
D.12
Answer: D.12
Explanation: We need to take President and VP as one unit. Therefore we have 3 people to arrange=3! ways
Also, we both President and VP can be arranged in 2 ! ways.
Reqd no of ways=3!*2!=12 ways
Answer D
Question: On a certain farm the ratio of horses to cows is 3:1. If the farm were to sell 15 horses and buy 15 cows, the ratio of horses to cows would then be 5:3. After the transaction, how many more horses than cows would the farm own?
A.20
B.30
C.40
D.50
Answer: B.30
Explanation: Originally, there were 3k horses and k cows.
3(3k-15) = 5(k+15)
9k-5k = 75+45
4k = 120
k = 30
The difference between horses and cows is (3k-15)-(k+15) = 2k-30 = 30
The answer is B.
Question: If 12 men or 20 women can do a piece of work in 54 days, then in how many days can 9 men and 39 women together do the work?
A.10 days
B.30 days
C.20 days
D.80 days
Answer: C.20 days
Explanation: C
20 days
Given that 12m = 20w => 3m = 5w
9 men + 39 women = 15 women + 39 women = 54 women
20 women can do the work in 54 days. So, 54 women can do it in (20 * 54) /54 = 20 days.
Question: A 70 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
A.73
B.20
C.83
D.21
Answer: B.20
Explanation: Explanation:
1: 2/5 = 5: 2
2/7 * 70 = 20
Answer: Option B
Question: A tap can fill a tank in 12 hours. After half the tank is filled three more similar taps are opened. What is the total time taken to fill the tank completely?
A.13 hrs 30 mins
B.14 hrs 30 mins
C.15 hrs 30 mins
D.16 hrs 30 mins
Answer: A.13 hrs 30 mins
Explanation: Time taken by one tap to fill the tank = 6 hrs.
Part filled by the taps in 1 hour = 4 * 1/12 = 1/3
Remaining part = 1 - 1/2 = 1/2
1/3 : 1/2 :: 1 : x
x = 1/2 * 1 * 3 = 1.5 hrs = 1 hrs 30 min
So, total time taken = 13 hrs 30 mins
ANSWER: A
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
A.18 seconds
B.27 seconds
C.26 seconds
D.12 seconds
Answer: D.12 seconds
Explanation: Speed of the boat downstream = 15 + 3
= 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m = 60/5
= 12 seconds.
Answer:D
Question: The average age of three boys is 24 years and their ages are in proportion 2:4:8. What is the age in years of the youngest boy?
A.16
B.9
C.18
D.12
Answer: D.12
Explanation: 2x + 4x + 6x = 72
x =6
2x = 12
Answer: D
Question: What ratio must a shopkeepermix Peas and Soybean of Rs.16 and Rs. 25/kg, As to obtain a mixture of Rs.19.50 ?
A.10 : 7
B.9 : 8
C.11 : 7
D.13 : 11
Answer: C.11 : 7
Explanation: Correct option: (C)
Use rule of alligation, to determine the ratio
The required ratio of Soybean and Peas = 5.50 : 3.50 = 11 : 7
Question: Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?
A.12:15:15
B.12:15:16
C.12:15:19
D.12:45:15
Answer: B.12:15:16
Explanation: Aman : Rakhi : Sagar = (70000 * 36) : (105000 * 30) : (140000 * 24)
= 12:15:16
Answer: B
Question: A man on tour travels first 160km at 64km/hr and the next 160km at 80km/hr. The average speed for the first 320km of the tour is?
A.56.45km/hr
B.71.11km/hr
C.68.78km/hr
D.75.63km/hr
Answer: B.71.11km/hr
Explanation: Total time taken = 160/64 + 160/8 = 9/2 hrs
Average speed = 320*2/9 = 71.11km/hr
Answer is B
Question: Kramer can pack X boxes of cigarettes per minute. If there are Y boxes of cigarettes in one case, how many cases can Kramer pack in 5 hours?
A.60X/Y.
B.300X/Y.
C.60Y/X.
D.120Y/X.
Answer: B.300X/Y.
Explanation: Kramer can pack X boxes per min.
Therefore in 5 hrs(300mins)he can pack 300X boxes.
If there are Y boxes in one case then then the total number of cases packed by Kramer = 300X/Y
(ANSWER B)
Question: The volumes of two cones are in the ratio 1 : 35 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
A.7:5
B.2:9
C.7:2
D.2:2
Answer: A.7:5
Explanation: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/35 = (1)2h1/(2)2h2
=> h1/h2 = 7/5
i.e. h1 : h2 = 7:5
Answer: A
Question: A box has exactly 100 balls, and each ball is either red, blue, or white. If the box has 20 more blue balls than white balls, and thrice as many red balls as blue balls, how many white balls does The box has ?
A.4
B.10
C.12
D.14
Answer: A.4
Explanation: x = the number of red balls
y = the number of blue balls
z = the number of white balls
From the first sentence we have
Equation #1: x + y + z = 100
...the box has 20 more blue balls than white balls...
Equation #2: y = 20 + z
...thrice as many red balls as blue balls...
Equation #3: x = 3y
Solve equation #2 for z: z = y - 20
Now, we can replace both x and z with y in Equation #1
3y + y + (y - 20) = 100
5y - 20 = 100
5y = 120
y = 24
There are 24 blue balls. This is 20 more than the number of white balls, so z = 4. That's the answer. Just as a check, x = 72, and 72 + 24 + 4 = 100.
Answer = 4,(A)
Question: How many four-digit numbers that do not contain the digits 3 or 6 are there?
A.2401
B.3584
C.4096
D.5040
Answer: B.3584
Explanation: 1st Digit can be filled up by the numbers - { 1 , 2 , 4 , 5 , 7 , 8 , 9 } = 7 ways
2nd Digit can be filled up by the numbers - { 0, 1 , 2 , 4 , 5 , 7 , 8 , 9 } = 8 ways
3rd Digit can be filled up by the numbers - { 0, 1 , 2 , 4 , 5 , 7 , 8 , 9 } = 8 ways
So, total No of ways is 7 * 8 * 8 => 3584
Hence answer will be (B)
Question: If 8/ |x| <0, which of the following must be true?
A.x>8
B.x<8
C.x=8
D.x=4
Answer: A.x>8
Explanation: if x<8
then x=6, 8/6>0
if x=8
then 8/8=1
if ifx > 8
for example
x=9 then 8/9<0
ANSWER A x>8
Question: The least common multiple of positive integer e and 3-digit integer n is 690. If n is not divisible by 3 and e is not divisible by 2, what is the value of n?
A.115
B.230
C.460
D.575
Answer: B.230
Explanation: The LCM of n and e is 690 = 2*3*5*23.
e is not divisible by 2, thus 2 goes to n
n is not divisible by 3, thus 3 goes to e.
From above:
n must be divisible by 2 and not divisible by 3: n = 2*... In order n to be a 3-digit number it must take all other primes too: n = 2*5*23 = 230.
Answer: B.
Question: If x = 1 + √2, then what is the value of x4 - 4x3 + 4x2 + 4?
A.-1
B.0
C.5
D.2
Answer: C.5
Explanation: Answer
x = 1 + √2
∴ x4 - 4x3 + 4x2 + 5 = x2(x2 - 4x + 4) + 4
= x2(x - 2)2 + 4
= (1 + √2)2(1 + √2 - 2)2 + 4
=(√2 + 1)2 (√2 - 1)2 + 4
=[(√2)2 - (1)2]2 + 4
=(2 - 1)2 =1 + 4=5
Correct Option: C
Question: In a camp, there is a meal for 140 men or 240 children. If 180 children have taken the meal, how many men will be catered to with remaining meal?
A.20
B.35
C.50
D.10
Answer: B.35
Explanation: There is a meal for 240 children. 180 children have taken the meal.
Remaining meal is to be catered to 60 children.
Now, 240 children 140 men.
60 children (140/240)	* 60 = 35 men
Answer is B.
Question: Point X is located on line segment AB and point Y is located on line segment CD. If AB = CD and AX < CY, then
A.XB > YD
B.XB < YD
C.AX > XB
D.CY < YD
Answer: A.XB > YD
Explanation: A--X------B
C------Y--D
XB > YD.
Answer: A.