RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: In a sample of 800 high school students in which all students are either freshmen, sophomores, juniors, or seniors, 27 percent are juniors and 75 percent are not sophomores. If there are 160 seniors, how many more freshmen than sophomores are there among the sample of students?
A.12
B.18
C.24
D.30
Answer: C.24
Explanation: 200 are sophomores.
The number of freshmen is 600 - 160 - 0.27(800) = 224
The answer is C.
Question: If x and y are nonnegative integers, both less than or equal to 2, then we say that (x; y) is a
friendly point. Compute the number of unordered triples of friendly points that form triangles
with positive area.
A.32
B.45
C.67
D.76
Answer: D.76
Explanation: There are
(9
3)= 84 unordered triples of friendly points. Instead of trying to count
the triples that yield triangles with positive area, we count the ones which have zero area. These
form line segments, of which there are 8 (three vertical, three horizontal, two diagonal), giving
us 76 desired unordered triples.
correct answer D
Question: If 15% of 30% of 50% of a number is 99, then what is the number?
A.4000
B.3050
C.4400
D.4500
Answer: C.4400
Explanation: Let the number be a
Given, 15/100 * 30/100 * 50/100 * a = 99
=> 3/20 * 3/10 * 1/2 * a = 99
=> a = 10 * 20 * 10 * 2 = 4400.
ANSWER:C
Question: The ratio of the number of red cars in a certain parking lot to the number of black cars is 3 to 8. If there are 52 black cars in the lot, how many red cars are there in the lot?
A.11
B.20
C.24
D.27
Answer: B.20
Explanation: B is correct
R/B = 3/8 and B =52
R = 52*3/8 = 20
Question: The original price of a suit is $200. The price increased 20%, and after this increase, the store published a 20% off coupon for a one-day sale. Given that the consumers who used the coupon on sale day were getting 20% off the increased price, how much did these consumers pay for the suit?
A.$192
B.$198
C.$200
D.$208
Answer: A.$192
Explanation: 0.8*(1.2*200) = $192
The answer is A.
Question: Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?
A.19%
B.68%
C.18%
D.48%
Answer: C.18%
Explanation: Total CP = Rs. 42000 + Rs. 13000
= Rs. 55000 and SP = Rs. 64900
Profit(%) = (64900 - 55000)/55000 * 100
= 18%
Answer:C
Question: Look at this series: 52, 49, 54, 51, 56, 53, ... What number should come next?
A.58
B.60
C.52
D.50
Answer: A.58
Explanation: Explanation:
In this simple alternating subtraction and addition series; 3 is subtracted, then 5 is added, and so on.
Answer: Option A
Question: A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit?
A.Rs. 64
B.Rs. 69
C.Rs.72
D.Rs.75
Answer: C.Rs.72
Explanation: C.P. = Rs. (100/122.5)x392
= Rs. (1000/1225)x392
= Rs. 320
Profit = Rs. (392 - 320) = Rs. 72.
Answer:C
Question: A clock is started at noon. By 10 minutes past 5, the hour hand has turned through
A.145 d
B.150 d
C.160 d
D.155 d
Answer: D.155 d
Explanation: Angle traced by hour hand in 12 hrs = 360Âº.
5 hrs 10min = 31/6hrs = (360/12*31/6) = 155
ANSWER D
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 56, the dividend is:
A.5324
B.6334
C.7896
D.8356
Answer: C.7896
Explanation: Divisor = (5 * 56) = 280
= 10 * Quotient = Divisor
=> Quotient = 280/10 = 28
Dividend = (Divisor * Quotient) + Remainder
Dividend = (280 * 28) + 56 = 7896.
C
Question: When n is divided by 5 the remainder is 3. What is the remainder when (n + 1)^2 is divided by 5?
A.0
B.1
C.2
D.3
Answer: B.1
Explanation: n = 5x+3, for some integer x
(n+1)^2=(5x+4)^2=5y+16, for some integer y
When we divide this by 5, the remainder is 1.
The answer is B.
Question: Coins are to be put into 8 pockets so that each pocket contains at least one coin. At most 4 of the pockets are to contain the same number of coins, and no two of the remaining pockets are to contain an equal number of coins. What is the least possible number of coins needed for the pockets?
A.7
B.18
C.17
D.22
Answer: B.18
Explanation: Since at most 3 of the pockets are to contain the same number of coins then minimize # of coins in each, so let each contain just 1 coin;
Next, we are told that no two of the remaining 4 pockets should contain an equal number of coins, so they should contain 2, 3, 4, and 5 coins each (also minimum possible);
Total: 1+1+1+1+2+3+4+5=18
Answer: B
Question: What is the greatest prime factor of 1+2+3+。。。+52?
A.53
B.29
C.31
D.37
Answer: A.53
Explanation: find the sum from direct formula = n(n+1)/2 = 52(52+1)/2 = 26*53...
53 is a PRIME number, so ans is 53..
A is the answer
Question: The ratio, by volume, of soap to alcohol to water in a certain solution is 4:20:60. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 100 cubic centimeters of alcohol, how many cubic centimeters of water will it contain?
A.1200
B.1250
C.1300
D.1400
Answer: A.1200
Explanation: soap:alcohol
Initial ratio soap:alcohol: water --> 4:20:60
Initial soap:alcohol = 4/20 =4:20
after doubled soap:alcohol =2* 4/20 = 8:20
Initial soap:water = 4/60=4:60
after halved soap:water: 1/2 * 4/60 = 2/60 = 2:60
After soap: alcohol:water --> 8:20:240-->2:5:60
given alcohol 100 cubic centimeter.
ratio is 40:100:1200(2:5:60)
For 100 cubic centimeter of Alcohol --- 1200cubic cm water is required.
Question: The food in a camp lasts for 10 men for 50 days. If 10 more men join, how many days will the food last?
A.22 days
B.25 days
C.50 days
D.16 days
Answer: B.25 days
Explanation: one man can consume the same food in 10*50 = 500 days.
10 more men join, the total number of men = 20
The number of days the food will last = 500/20 = 25 days.
Answer:B
Question: if x+y+z=9 and both y and z are positive integers greater than zero, then the maximum value x can take is?
A.7
B.3
C.8
D.6
Answer: A.7
Explanation: if y=z=1, then x will be equal to 7.
ANSWER:A
Question: In a class there are 20 boys and 22 girls. In how many ways can a boy and a girl be selected?
A.508
B.440
C.800
D.570
Answer: B.440
Explanation: We can select one boy from 20 boys in 20 ways.
We select one girl from 22 girls in 22 ways
We select a boy and girl in 20 * 22 ways i.e., = 440 ways.
Answer:B
Question: The L.C.M of two numbers is 495 and their H.C.F is 5. If the sum of the numbers is 10, then their difference is
A.10
B.46
C.70
D.90
Answer: A.10
Explanation: Solution
Let the numbers be x and (100 - x) .
Then, x (100 - x) = 5 ×495
‹=›x2 - 100x + 2475 = 0.
‹=› (x -55) (x - 45) = 0.
x = 55 or x = 45.
Therefore, the numbers are 45 and 55.
Required difference = (55 - 45) = 10.
Answer A
Question: If -2<= x <= 2 and 3 <= y <= 10, which of the following represents the range of all possible values of y-x?
A. 5 <= y-x <= 6
B. 1 <= y-x <= 12
C. 1 <= y-x <= 6
D. 5 <= y-x <= 10
Answer: B. 1 <= y-x <= 12
Explanation: Maximum value of y-x= 10 - (-2)= 12
Minimum value of y-x= 3-2= 1
B mentions the correct range
Question: 5 friends visited a fruit stall, and everyone decided to contribute equally to the total bill of $100. If one of the friends had a coupon for 6% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay?
A.18
B.18.8
C.19
D.17.8
Answer: B.18.8
Explanation: At the non-discounted price, each friend would pay $20, as $100 divided by 5 friends is $20 per friend. But if the bill is 6% off, then each friend would pay 6% less. 6% of $20 is $1.2, so each friend saves $1.2 and pays the remaining 18.8
CORRECT OPTION:OPTION B
Question: Dan can do a job alone in 15 hours. Annie, working alone, can do the same job in just 10 hours. If Dan works alone for 12 hours and then stops, how many hours will it take Annie, working alone, to complete the job?
A.2
B.4
C.6
D.8
Answer: A.2
Explanation: Dan can complete 1/15 of the job per hour.
In 12 hours, Dan completes 12(1/15) = 4/5 of the job.
Annie can complete 1/10 of the job per hour.
To complete the job, Annie will take 1/5 / 1/10 = 2 hours.
The answer is A.
Question: A positive number x is multiplied by 3, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ?
A. 9/4
B. 3/2
C. 4/3
D. 2/3
Answer: C. 4/3
Explanation: We need to produce an equation from the information given in the problem stem. We are first given that x is multiplied by 2 and then the product is divided by 3. This gives us:
2x/3
Next we are given that the positive square root of the result (which is 2x/3) is equal to x. This gives us
√(2x/3) = x
2x/3 = x^2
2x = 3x^2
3x^2 – 2x = 0
x(3x – 2) = 0
x = 0 or
3x – 2 = 0
3x = 2
x =4/3
Because x is positive, x = 4/3. The answer is C.
Question: If the sum of 1/3 and 1/5 is converted to a decimal, what is the 3000th digit to the right of the decimal place?
A.2
B.3
C.5
D.8
Answer: B.3
Explanation: 1/3 +1/5 =0.5333333...
hence, the 3000th digit would also be 3
Ans: B
Question: On the xy-plane, each point on circle C has coordinates such
that x 0 and y 0. If the center of circle C is the point (3; 7),
what is the maximum possible area of C?
A. 6
B. 9
C. 24
D. 32
Answer: C. 24
Explanation: I think that theintentof this question is that the circle will have NO CO-ORDINATES that fit the following 2 forms: (0, Y) or (X, 0). In real basic terms, this circle will NEITHER touch (nor cross) the X-axis NOR will it touch (nor cross) the Y-axis.
With a center at (3,8), the longest possible radius would ALMOST touch the X-axis, so the radius would be a little less than 3.
If the radius WAS 3 exactly, then the area would be 9pi, which is approximately 28.26
Since the circle CAN'T touch the X-axis, the area has to be LESS than approximately 28.26
As it's written, none of the answers is clearly the correct one.
C
Question: what is the sum of all even integers between 99 and 301?
A.20200
B.20000
C.40400
D.40000
Answer: A.20200
Explanation: a=100,tn=300
a+(n-1)d=300=>n=101
Sn=n/2(a+l)=101/2(100+300)
Sn=20200
ANSWER:A
Question: The C.I. on a certain sum for 2 years at 10% per annum is Rs. 525. The S.I. on the same sum for double the time at half the rate percent per annum is?
A.238
B.500
C.287
D.197
Answer: B.500
Explanation: Explanation:
Let the sum be Rs. P. Then,
[P(1 + 10/100)2 - p] = 525
P[(11/10)2 - 1] = 525
P = (525 * 100) / 21 = 2500
Sum = Rs. 2500
So, S.I. = (2500 * 5 * 4)/100 = Rs. 500
Answer:B
Question: Find the total number of prime factors in the expression (4)^11 x (7)^5 x (11)^3
A.26
B.22
C.25
D.30
Answer: D.30
Explanation: (4)^11x (7)^5 x (11)^3
= (2 x 2)^11 x (7)^5 x (11)^3
= 2^11 x 2^11 x7^5x 11^3
= 2^22 x 7^5 x11^3
Total number of prime factors = (22 + 5 + 3) = 30.
Answer is D.
Question: On a scale of map, 0.4 cm represents 5.3 km. If the distance between the points on the map is 64 cm, the actual distance between these points is:
A.9 km
B.72.5 km
C.190.75 km
D.848 km
Answer: D.848 km
Explanation: Explanation :
Let the actual distance be x km. Then,
More distance on the map, More is the actual distance (Direct Proportion)
=> 0.4 : 64 :: 5.3 : x
=> 0.4x = 64 x 5.3
=> x = 64 x 5.3 /0.4
=> x = 848
Answer : D
Question: If three sides of the triangle are 8 , 15 and S respectively then the how many values can S ?
A.[A] 6
B.[B] 7
C.[C] 8
D.[D]9
Answer: D.[D]9
Explanation: Needed: How many Values can S take
Concept: Sum of any two sides of a triangle is greater then the third side.
Case 1: 8+5 > S => S<13
Case 2: 5+S > 8 => S >3
Case 3: 8+S > 5 =>S > -3 (Always true since S is one side of a Triangle)
Finally, 3 < S < 13. So, we can have infinite number of sides between 3 and 13.
Answer = E
PS: If question said S can take only integer value, the S = 9. Answer choice D.
Question: A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 according to the following constraints. The first digit cannot be 0 , 1 or 3, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?
A.144
B.142
C.160
D.168
Answer: B.142
Explanation: The first digit can be filled in 8 ways
For second digit , it can either be 0 or 1 or 3
Case 1 -
If second digit is 1 ,Third digit can take 10 values
number of codes = 7 * 1 * 10 = 70
Case 2 -
If second digit is 0,Third digit can take 9 values ( Third digit can't be zero)
number of codes = 8 * 1 * 9= 72
Total number of codes = 142
Answer B
Question: A paper is in a square form whose one side is 20 cm. Two semi circles are drawn on its opposites as diameters. If these semi circles are cut down what is the area of the remaining paper?
A.8.76
B.8.79
C.8.75
D.8.78
Answer: C.8.75
Explanation: (5 * 3.5)/2
= 8.75
Answer:C
Question: Donald has five different kinds of fruit to choose from at the grocery store. How many ways can he buy one or more types of fruit?
A.125
B.54
C.43
D.31
Answer: D.31
Explanation: Donald needs to buy one or more types of fruit out of five types
=> 2^5 - 1 = 31
Question: What is the unit digit in (4137)^754?
A.9
B.11
C.12
D.13
Answer: A.9
Explanation: Unit digit in (4137)754 = Unit digit in {[(4137)4]188 x (4137)2}
=Unit digit in { 292915317923361 x 17114769 }
= (1 x 9) = 9
A)
Question: The average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is?
A.12
B.72
C.23
D.35
Answer: D.35
Explanation: Excluded number = (27 * 5) - (25 * 4)
= 135 - 100
= 35.
Answer: D
Question: A rectangular football field is fenced on all four sides. The length of the football field is 3 times the length of its breadth. The cost of fencing the field was $360. The football management has decided to change the dimensions of field by increasing the breadth by 50% of its original value and reducing the length by 25% of its original value and fence the field again.. What will be the cost of the new fencing?
A.$360
B.$180
C.$425
D.$337.5
Answer: D.$337.5
Explanation: Let's take x to be the breadth. Then the length of the football field is 3x.
The perimeter of the old football field is x + 3x + x + 3x = 8x.
Now, for the new football field:
The new breadth = 1.5 times old breadth = 1.5x
The new length is 0.75 times old length = (.75)3x = 2.25x
So the new perimeter is 1.5x + 2.25x + 1.5x + 2.25x = 7.5 x.
for old perimeter rate is $360
For new perimeter = (360 * 7.5)/8
= 337.5
Ans - D
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
A.3 : 1
B.3 : 2
C.3 : 4
D.3 : 5
Answer: B.3 : 2
Explanation: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.
Answer: B
Question: REDO’s manufacturing costs for sets of horseshoes include a $10,000 initial outlay, and $20 per set. They can sell the sets $50. If profit is revenue from sales minus manufacturing costs, and the company producessells 500 sets of horseshoes, what was their profit?
A.$4500
B.$3500
C.$5500
D.$5000
Answer: D.$5000
Explanation: Total Manufacturing cost = 10000+500*20 = 20000
Total Selling cost = 500*50= 25000
Profit = 25000-20000 = 5000
Answer : D
Question: The average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years. Find the average age of the women?
A.30
B.35
C.32
D.40
Answer: A.30
Explanation: 20 + 24 + 8 * 2 = 60/2 = 30
ANSWER A
Question: A dealer offers a cash discount of 10% and still makes a profit of 20% when he further allows 45 articles to be sold at the cost price of 40 articles to a particular sticky bargainer. How much percent above the cost price were his articles listed?
A.40%
B.50%
C.55%
D.80%
Answer: B.50%
Explanation: Given
Cash Discount - 10%
Profit - 20%
Items Sold - 45
Price Sold at = List Price of 40
Assume List price = $10
Total Invoice = $400
-10% Cash Discount = $360
Let cost price of 45 items be x
So total cost = 45*x
Given the shopkeeper had a profit of 20%
45 * x * 120/100 = 360
or x = $20/3=$6+(2/3)
Which means his products were listed at $10 which is a 50% markup over $6+(2/3)
Answer B
Question: s(n) is a n-digit number formed by attaching the first n perfect squares, in order, into one integer. For example, s(1) = 1, s(2) = 14, s(3) = 149, s(4) = 14916, s(5) = 1491625, etc. How many digits R are in s(99)?
A.R=350
B.R=353
C.R=354
D.R=356
Answer: B.R=353
Explanation: Focus on the points where the number of digits in squares change:
1, 2, 3 - Single digit squares. First 2 digit number is 10.
4 , 5,...9 - Two digit squares. To get 9, the last number with two digit square, think that first 3 digit number is 100 which is 10^2. so 9^2 must be the last 2 digit square.
10, 11, 12, ... 31 - Three digit squares. To get 31, think of 1000 - the first 4 digit number. It is not a perfect square but 900 is 30^2. 32^2 = 2^10 = 1024, the first 4 digit square.
32 - 99 - Four digit squares. To get 99, think of 10,000 - the first 5 digit number which is 100^2.
So number of digits in s(99) = 3*1 + 6*2 + 22*3 + 68*4 = 3 + 12 + 66 + 272 =R= 353.B
Question: Two equal containers are filled with a mixture of water and petrol. One of them contains three times as much petrol as in the other. The mixtures in the two containers are then mixed and it is found that the ratio of water to petrol is 3: 2: Find the ratio of water to petrol in each of the original containers.
A.2:1, 3:4
B.1:3, 1:2
C.2: 3, 4: 1
D.2: 5, 4: 1
Answer: C.2: 3, 4: 1
Explanation: In the new mixture, water : petrol = 3 : 2 = 12 : 8
=> The capacity of each container =(12 + 8)/2=10 units
= >The ratios of water to petrol of the containers are 4 : 6 and 8 : 2
= 2 : 3 and 4 : 1
ANSWER:C
Question: John was thrice as old as Tom 6 years ago. John will be 9/7 times as old as Tom in 6 years. How old is Tom today?
A.6
B.8
C.10
D.12
Answer: B.8
Explanation: J-6 = 3(T-6), so J = 3T-12
J+6 = 9/7 * (T+6)
7J + 42 = 9T + 54
7(3T-12) + 42 = 9T + 54
12T = 96
T = 8
The answer is B.
Question: Calculate the time it will take for a full tank to become completely empty due to a leak given that
the tank could be filled in 7 hours, but due to the leak in its bottom it takes 8 hours to be filled ?
A.59 hours
B.54 hours
C.59 hours
D.56 hours
Answer: D.56 hours
Explanation: Part filled without leak in 1 hour = 1/7
Part filled with leak in 1 hour = 1/8
Work done by leak in 1 hour
=1/7âˆ’1/8=56 hours
Answer:D
Question: Which greatest possible length can be used to measure exactly 12 meter 34 cm, 8 meter 98 cm and 6 meter 65 cm
A.1cm
B.2cm
C.24cm
D.55cm
Answer: A.1cm
Explanation: Explanation:
Convert first all terms into cm.
i.e. 1234 cm, 898cm, 665cm.
Now whenever we need to calculate this type of question, we need to find the HCF. HCF of above terms is 1.
Option A
Question: In a bag contains 8 White balls and 6 black balls from the bag two balls are taken out at random. Find the Probability that they are of the same color ?
A.43/91
B.45/91
C.52/91
D.61/91
Answer: A.43/91
Explanation: Here S be the sample space so,
n(S) = Number of ways of taken out balls of (8+6) = 14C2 = (14X13)/(2X1)
= 182/2 = 91
E = Event of getting both balls of the same color
Then,n (E) = Number of ways of drawing (2 balls out of 8) or (2 balls out of 6)
= (8C2 + 6C2) = 8 x 7/2 x1 + 6x5/2x1 = 56 /2 + 30/2 = 28 +15 = 43
P(E) = n(E) / n(S) = 43/91
Answer is A
Question: If the square of a Positive Number X is equal to five times the same Number then what is the value of X?
A.1
B.25
C.8
D.5
Answer: D.5
Explanation: X * X = 5X
X = 5
so the correct answer is option D
Question: A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.24000. A's share is?
A.s.7500
B.s.8000
C.s.6000
D.s.5750
Answer: B.s.8000
Explanation: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 24000 = 8000
ANSWER:B
Question: If 1535/ 1038 = a+1/[b+1/{c+(d+1/e)}]. Find a*b*c*d*e?
A.165/2
B.175/2
C.178/3
D.187 by 2
Answer: D.187 by 2
Explanation: by expanding 1535/1038 make form like a+1/[b+1/{c+(d+1/e)}
=1+(497/1038) now a=1
=1+{1/(1038/497)}
=1+{1/ (2+42/497)}
=1+{1/(2+1/(497/42)} now b= 2 similarly expand
c=11 d= 1 e=34/8
finally a*b*b*c*d*e
1*2*11*1*34/8
187/2
ANSWER:D
Question: A is twice as good a workman as B and together they finish a piece of work in 18 days. In how many days will A alone finish the work?
A.11 days
B.22 days
C.27 days
D.12 days
Answer: C.27 days
Explanation: If A takes x days to do a work then B takes 2x days to do the same work.
--> 1/x+1/2x = 1/18
--> 3/2x = 1/18
--> x = 27 days.
Hence, A alone can finish the work in 27 days.
Answer : C
Question: If shares of two persons in profits are Rs.1600 and Rs.1200 then ratio of their capitals is
A.3:4
B.2:3
C.4:3
D.1:3
Answer: C.4:3
Explanation: profit=time*capital
so 1600:1200=4:3
ANSWER:C
Question: The fourth proportional to 9, 14 and 18 is?
A.28
B.66
C.88
D.99
Answer: A.28
Explanation: (14*18)/9 = 28
Answer: A
Question: The diagonals of a rhombus are 15 cm and 20 cm. Find its area?
A.176
B.190
C.150
D.278
Answer: C.150
Explanation: 1/2 * 15 * 20
= 150
Answer:C
Question: The sum of the two digits of a number is 10. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number?
A.13
B.28
C.12
D.45
Answer: B.28
Explanation: Answer: Option B
any two digit number can be written as (10P + Q), where P is the digit in the tens place and Q is the digit in the units place.
P + Q = 10 ----- (1)
(10Q + P) - (10P + Q) = 54
9(Q - P) = 54
(Q - P) = 6 ----- (2)
Solve (1) and (2) P = 2 and Q = 8
The required number is = 28
Question: The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?
A.16 2/3% loss
B.16 7/3% loss
C.16 2/8% loss
D.17 2/3% loss
Answer: A.16 2/3% loss
Explanation: 15 CP = 18 SP
18 --- 3 CP loss
100 --- ? => 16 2/3% loss
Answer: A
Question: In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?
A.3^5
B.2^3
C.5^3
D.2
Answer: A.3^5
Explanation: The first letter can be posted in any of the 3 post boxes. Therefore, we have 3 possibilities.
Similarly, the second, the third, the fourth and the fifth letter can each be posted in any of the 3 post boxes.
Each of the 5 letters has 3 possibilities because we can post any number of letters in all of the boxes.
Therefore, the total number of ways the 5 letters can be posted in 3 boxes is
3 * 3 * 3 * 3 * 3 = 3^5.
Ans: A
Question: When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k + n is a multiple of 40.
A.3
B.4
C.7
D.32
Answer: C.7
Explanation: First, let us say I have a number n which is divisible by 5 and by 7. We all agree that it will be divisible by 35, the LCM of 5 and 7.
Now, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1, we can say the number is of the form
n = 5a + 1 e.g. 5 + 1, 10 + 1, 15 + 1, 20 + 1, 25 + 1, 30 + 1, 35 + 1 etc
and
n = 7b + 1 e.g. 7 + 1, 14 + 1, 21 + 1, 28 + 1, 35 + 1 etc
So when it is divided by the LCM, 35, it will give 1 as remainder (as is apparent above)
Next, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3, we can say the number is of the form
n = 5a + 1
and
n = 7b + 3
Now, the only thing you should try to understand here is that when n is divided by 5 and if I say the remainder is 1, it is the same as saying the remainder is -4. e.g. When 6 is divided by 5, remainder is 1 because it is 1 more than a multiple of 5. I can also say it is 4 less than the next multiple of 5, can't I? 6 is one more than 5, but 4 less than 10.
Therefore, we can say n = 5x - 4 and n = 7y - 4 (A remainder of 3 when divided by 7 is the same as getting a remainder of -4)
Now this question is exactly like the question above. So when you divide n by 40, remainder will be -4 i.e. n will be 4 less than a multiple of 40. So you must add 7 to n to make it a multiple of 40
C