RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The maitre 'd at an expensive Manhattan restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability R that the next couple the maitre 'd seats will not order dessert?
A. 20%
B. 25%
C. 40%
D. 60%
Answer: B. 25%
Explanation: could you use a venn diagram and just go with the number 100.
60 people order dessert and coffee... which is the union of D and C.
R=2/10 of D aren't in D U C = so 8/10 of D are in DUC which means =60 =8/10D. So D in total=75, and 15 D's aren't in D union C. which means 25 people are in C only + Neither.
B 25%
Question: A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning?
A.33
B.44
C.39
D.66
Answer: C.39
Explanation: Let the average after 7th inning = x
Then average after 16th inning = x - 3
inline fn_jvn therefore 16(x-3)+87 = 17x
inline fn_jvn therefore x = 87 - 48 = 39 Answer C
Question: If circles x and y have the same area and circle x has a circumference of 12π, half of the radius of circle y is:
A.16
B.8
C.3
D.2
Answer: C.3
Explanation: x be radius of circle x
y be radius of circle y
given:
pi*x^2 = pi*y^2
also,
2*pi*x = 12*pi
x = 6
thus y =6
y/2 = 3
Ans: C
Question: if the ratio of two number is 4:6 and LCM of the number is 280 then what is the number.
A.12
B.20
C.25
D.30
Answer: A.12
Explanation: product of two no = lcm *hcf
4x*6x=280*x
x=12
ANSWER:A
Question: A family consists of two grandparents, two parents, and three grandchildren. The average age of the grandparents is 64 years, the average age of the parents is 39 years, and the average age of the grandchildren is 6 years. What is the average age (in years) of the family?
A.31
B.32
C.33
D.34
Answer: B.32
Explanation: Total age of the grandparents = 64 Ã— 2 = 128
Total age of the parents = 39 Ã— 2 = 78
Total age of the grandchildren = 6 Ã— 3 = 18
Average age of the family = (128+78+18)/7 = 224/7 = 32 years
The answer is B.
Question: If the sales tax be reduced from 5 (1/3) % to 3 (1/2) %, then what difference does it make to a person who purchases a bag with marked price of Rs. 5000?
A.Rs. 156.66
B.Rs. 111.23
C.Rs. 120.66
D.Rs. 91.66
Answer: D.Rs. 91.66
Explanation: Explanation:
Required difference = (5 (1/3) of Rs. 5000) - (3 (1/2) of Rs. 5000)
= (16/3 – 7/2) % of Rs. 5000
= (11/6) x (1/100) x 5000
= Rs. 91.66
ANSWER D
Question: (5+√3+√5)^2-(√3+√5)^2=?
A.1+2√3+2√5
B.25+10√3+10√5
C.1-√3+√5
D.1+√3-√5
Answer: B.25+10√3+10√5
Explanation: (5+√3+√5)^2-(√3+√5)^2
(5+√3)^2 + 5 +2 (5+√3) (√5) - ( 3 +5 + 2√3√5)
25+ 3+ 10√3 +5 +10 √5 + 2 √15 - 3-5 -2√15
25+10√3+10√5
B is the answer
Question: In 1995, the Jos spent $800 on the family’s water bills. Anticipating that water rates would increase in 1996 by 50%, the Jos cut back their water usage. By how much must the Jos have reduce their 1996 water usage to pay exactly the same amount in 1996 as they paid in 1995?
A.a)	33 1/3 %
B.b)	40 %
C.c) 50 %
D.d)	66 2/3 %
Answer: A.a)	33 1/3 %
Explanation: Let x be the water usage and c be the cost water of Jos
We have
xc =800, c=800/x
Y(1.5c)=800 where Y is the water usage in 1996
Y= 800/ (1.5*800/x)= 1/1.5x=2/3x
Thus reduction will be x-2/3x=1/3x=A
Question: A can do a piece of work in 5 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
A.30
B.20
C.10
D.6
Answer: A.30
Explanation: A's 1 hour's work = 1/5 ;
(B + C)'s 1 hour's work = 1/3 ;
(A + C)'s 1 hour's work = 1/2 .
(A + B + C)'s 1 hour's work = ( 1/5 + 1/3 ) =8/15 .
B's 1 hour's work = ( 8/15 - 1/2 ) = 1/30.
Therefore A alone will take 30 hours to do the work.
A
Question: The average of five results is 46 and that of the first four is 37. The fifth result is?
A.50
B.88
C.77
D.82
Answer: D.82
Explanation: 5 * 46 â€“ 4 * 37
= 82
Answer: D
Question: If 0.75 : x :: 5 : 8, then x is equal to:
A.1.12
B.1.2
C.1.25
D.1.3
Answer: B.1.2
Explanation: Explanation:
(x x 5) = (0.75 x 8)
x=6/5
=1.20
ANSWER IS B
Question: The number 46 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?
A.17
B.16
C.15
D.10
Answer: D.10
Explanation: I think brute force with some common sense should be used to solve this problem.
Write down all perfect squares less than 46: 1, 4, 9, 16, 25, 36.
Now, 46 should be the sum of 3 of those 8 numbers. Also to simplify a little bit trial and error, we can notice that as 46 is an odd numbers then either all three numbers must be odd (odd+odd+odd=odd) OR two must be even and one odd (even+even+odd=odd).
We can find that 46 equals to 1+9+36=1^2+3^2+6^2=46 --> 1+3+6=10.
Answer: D.
Question: A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
A.5
B.4
C.6
D.7
Answer: D.7
Explanation: 7 * 8 : 9 * x = 8:9 => x= 7
Answer:D
Question: How many differentsix letter words can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R?
A.59
B.11!/(2!*2!*2!)
C.55
D.23
Answer: C.55
Explanation: E- -R
We are left with the following 11 letters: {M, D, I, T, R, EE, AA, NN} out of which 8 are distinct: {M, D, I, T, R, E, A, N}.
We should consider two cases:
1. If the two middle letters are the same, we'd have 3 words: EEER, EAAR and ENNR.
2. If the two middle letters are distinct, then we are basically choosing 2 letters out of 8 when the order of the selection matters, so it's 8P2 = 56.
Total = 56 + 3 = 59.
Answer: C.
Question: A factory has a fixed cost of $42,000 a month, and a cost of $2.5 for every item produced. If the selling price of a single item is $5, what is the number of items must be sold monthly for the factory to cover its cost exactly?
A.9,000
B.14,000
C.16,800
D.22,500
Answer: C.16,800
Explanation: selling price - Cost price = 2.5 so per unit profit =2.5
cost to recover =42000
no of items required = 42000/2.5 = 16800
Answer: C
Question: A company conducted a survey about its two brands, A and B. x percent of respondents liked product A, (x – 20) percent liked product B, 23 percent liked both products, and 23 percent liked neither product. What is the minimum number D of people surveyed by the company?
A.46
B.80
C.D.90
D.D.100
Answer: D.D.100
Explanation: 100 = x + x - 20 + 23 - 23
x = 60,
So, Product A = 60%, Product B = 40%, Both = 23%, Neither = 23%
23% of the total no. of people should be an integer. So, A,BC are out.
60% of D and 40% of D are both integers. So, D satisfies all conditions.
So, answer is D.
Question: The greatest number that divides 180, 565 and 705 leaving remainder 5, 5 and 5 respectively is:
A.31
B.33
C.35
D.38
Answer: C.35
Explanation: explanation:
180-5=175 , 565-5=560 and 705-5= 700
Highest number that divides 175, 560 and 700 is HCF of numbers.
HCF of 175, 560 and 700= 35
Answer:C
Question: What is the difference between the compound interests on $5000 for 1 years at 4% per annum compounded yearly and half-yearly?
A.2.04
B.3.06
C.4.8
D.8.3
Answer: A.2.04
Explanation: CI = 5000*(1/4/100)*(1+1/2*4/100)
=(5000*26/25*51/50)
=5304
=5306.04
difference = $(5306.04 - 5304) = $2.04
ANSWER A
Question: Two equal glasses are respectively
1 3
and
1 4 full of milk. They are then filled up with water and the contents are mixed in a tumbler. Find the ratio of milk and water in the tumbler
A.22
B.88
C.27
D.19
Answer: A.22
Explanation: Answer:A
Question: A wooden box of dimensions 8m×7m×6m is to carrry rectangular boxes of dimensions 8cm×7cm×6cm . The maximum number of boxes that can be carried in 1 wooden box is :
A.1200000
B.1000000
C.9800000
D.7500000
Answer: B.1000000
Explanation: Explanation:
Number of boxes = Volume of wooden box in cm3/Volume of 1 small ball = 800×700×600/8×7×6=1000000
Correct Option: B
Question: A, B and C can do a work in 90, 15 and 45 days respectively. If they work together, in how many days will they complete the work?
A.10
B.66
C.77
D.88
Answer: A.10
Explanation: One days's work of A, B and C = 1/90 + 1/15 + 1/45
= (1 + 6 + 2)/90 = 1/10
A, B and C together can do the work in 10 days.
Answer:A
Question: The divisor is 19, the quotient is 6 and the remainder is 1.
What is the dividend?
A.115
B.114
C.113
D.110
Answer: A.115
Explanation: D = d * Q + R
D = 19 * 6 + 1
D = 114 + 1
D = 115
Answer: A
Question: A cistern 6 m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the west surface is :
A.49 m2
B.50 m2
C.53.5 m2
D.55 m2
Answer: A.49 m2
Explanation: Solution
Area of the west surface = [2(lb + bh + lh) - lb] = 2 (bh + lh) + lb
= [2(4 × 1.25 + 6 × 1.25) + 6 × 4]m2 = 49m2.
Answer A
Question: Difficulty:
There are five sales agents in a certain real estate office. One month Andy sold seven times as many properties as Ellen, Bob sold 3 more than Ellen, Cary sold seven 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= 7e
b =3 +e
c = 7b = 21+ 7e (highest of all)
d = b + e = 3+ e +e = 3 + 2e
Ans. C
Question: If the quantity (p − 5) is 5 times the quantity (q + 5), then what is the relationship between p and q?
A.p = 5q + 30
B.p = 5q − 30
C.5p = q + 20
D.p = 5q
Answer: A.p = 5q + 30
Explanation: p-5=5(q+5)
p-5=5q+25
p=5q+30
option A
Question: A freight elevator can carry a maximum load of 1000 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.25
B.85
C.190
D.215
Answer: A.25
Explanation: The average of existing 2 package is150 + 280/2 = 430/2 = 215
Remaining allowed weight = 1000 - 200 - 430 = 1230.
allowed per package = 1230 / 3 = 410
So difference in average of existing and allowable = 410-215 = 195
Hence A
Question: On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.60 per glass on the first day, what was the price per F glass on the second day?
A. $015
B. $0.20
C. $0.30
D. $0.40
Answer: D. $0.40
Explanation: On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade;
On the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade;
So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3.
We are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day.
Say the price of the glass of the orangeade on the second day was $x then 2*0.6=3*x --> x=$0.4.
Answer: D.
Question: In 2010, a basketball team won 30 percent of its 20 basketball games. In 2011, the team won 28 percent of its 25 basketball games. What was the percent increase from 2010 to 2011 in the number of basketball games the team won?
A.5%
B.14 2/7%
C.16 2/3%
D.23 1/3%
Answer: C.16 2/3%
Explanation: 30% of 20 = 6 and 28% of 25 = 7, so percent increase =7−6/6=16.6
Answer C
Question: Farm Tax is levied on the 25% of the cultivated Land. The tax department collected total $ 3840 through the farm Tax from the village of Mr. william. Mr. william paid only $ 480 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is :
A.15%
B.25%
C.50%
D.0.2083%
Answer: C.50%
Explanation: This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (480/3840)x100 =12.5%in percentage terms.
But the question asks ratio between his total land to total cultivated land. Hence the answer is 12.5%x (100/25) = 50%
The correct answer is (C).
Question: A watch passes through three hands and each gains 25%. If the 3rd sells it for Rs250, what did the 1st pay for it?
A.120
B.125
C.128
D.130
Answer: C.128
Explanation: First Purchased = 250 Wes= 128
C
Question: If a1 = 1 and an+1= 2an + 5, n = 1, 2 .. , then a100 is equal to ?
A.5*2^99-6
B.5*2^99+6
C.6*2^99+5
D.6*2^99-5
Answer: D.6*2^99-5
Explanation: a(n+1)= 2a(n) + 5
Even+Odd=Odd
Therefore all the values are Odd. A, B and E out.
a(2)=2+5=7
Now lets take a2 and try solving it with the equations in C and D. Note they are similar and only differ by the sign before 5. So we have to only decide if our equation takes + or - 5.
Now, the equation in C and D looks like this 6*2^99 + (or -) 5.
In other words, a100=6*2^(n-1) + (or -) 5.
Now a2=7=6*2^1 +(or-) 5
7=12+(or-)5
Therefore the sign has to be -
Answer: D
Question: 550−(104÷20.8)=?
A.545
B.525
C.535
D.625
Answer: A.545
Explanation: Explanation:
=550−(104/208X10)
=550−5=545
Option A
Question: Jackson has $313,195 dollars in his investment accounts. What is the least amount of money (in whole number of dollars) that he must remove from his account if he wants to split this money evenly among nine new investors?
A.$1
B.$2
C.$3
D.$4
Answer: D.$4
Explanation: In order to divide the sum in 9 parts, the amount must also be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 313,195 = 22 and 18 is divisible by 9.
Hence we need to subtract 4 to this number for it to be divisible by 9
Correct Option: D
Question: How many odd four-digit integers greater than 9000 are there such that all their digits are different?
A.84
B.104
C.168
D.224
Answer: D.224
Explanation: Case 1: Numbers starting with 9 followed by an EVEN number
The hundreds digit can take 5 numbers (0,2,4 ,6 , 8) so 5 ways
The unit digit can take 4 numbers (1,3,5,7) to be ODD so 4 ways.
The tens digit can take remaining 7 numbers left after using 3 numbers so 7 ways.
Total = 5*4*7=140
Case 2: Numbers starting with 9 followed by an ODD number
The hundreds digit can take 4 numbers (1,3,5,7) so 4 ways
The unit digit can take remaining 3 ODD numbers left after using 2 ODD numbers so 3 ways.
The tens digit can take remaining 7 numbers left after using 3 numbers so 7 ways.
Total = 4*3*7 = 84
Hence 140+84=224, correct answer is D
Question: Speed of a boat in standing water is 11kmph and speed of the stream is 2.5kmph. A man can rows to a place at a distance of 105km and comes back to the starting point. The total time taken by him is?
A.21.12hours
B.20.12hours
C.19.12hours
D.18.12hours
Answer: B.20.12hours
Explanation: Speed upstream = 8.5kmph
Speed downstream = 13.5kmph
Total time taken = 105/8.5 + 105/13.5 = 20.12 hours
Answer is B
Question: If Jimmy drinks 8 ounces of water each time for 8 times a day. How much gallons of water he would have to prepare ahead to drink for 5 days? (1 ounce = 0.0078125 gallon)
A.1
B.1.5
C.2
D.2.5
Answer: D.2.5
Explanation: 8 ounces* 8 times/day = 64 ounces of water = 64 * 0.0078125 = 0.5 gallon. 5 days need 0.5 * 5 = 2.5 gallons. Correct Option: 2.5 Answer: D
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green?
A.23/35
B.23/37
C.23/29
D.23/30
Answer: A.23/35
Explanation: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green
= (⁶C₁ * ⁹C₁)/¹⁵C₂ + ⁶C₂/¹⁵C₂
= (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7
= 46/70 = 23/35
Answer: A
Question: 5 cards have to be put into their 5 respective envelopes. If the letters are inserted randomly into the envelopes, what is the probability that all the cards go into their respective envelopes?
A.1/30
B.1/60
C.1/240
D.1/120
Answer: D.1/120
Explanation: A-B-C-D-E (envelopes)
a-b-c-d-e (letters)
5 letters (a, b, c, d, and e) can be assigned to 5 envelopes (arranged) in 5! ways, out of which only one will be correct, thus the probability is 1/5! = 1/120.
Answer: D.
Question: In how many ways can 15 people be seated around two round tables with seating capacities of 7 and 8 people?
A.15! /8!
B.7! *8!
C.15C7 *6! *7!
D.2 * 15C7 *6! *7!
Answer: C.15C7 *6! *7!
Explanation: Solution:
'n' objects can be arranged around a circle in (n−1)! ways.
If arranging these 'n' objects clockwise or counter clockwise means one and the same, then the number arrangements will be half that number.
i.e., number of arrangements =(n−1)! /2.
You can choose the 7 people to sit in the first table in 15C7 ways.
After selecting 7 people for the table that can seat 7 people, they can be seated in:
(7−1)! =6!
The remaining 8 people can be made to sit around the second circular table in: (8−1)! =7! Ways.
Hence, total number of ways: 15C7 *6! *7!.
Answer: Option C
Question: Solve using synthetic division or long division(x2 + 13x + 40) ÷ (x + 8)
A.x + 9
B.x + 0
C.x + 5
D.x + 2
Answer: C.x + 5
Explanation: e solved the division in both the ways;
(x2 + 13x + 40) ÷ (x + 8) by using synthetic division
Synthetic Division
Save
Quotient = x + 5
Remainder = 0
Answer: C
Question: A car traveled 420 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 6 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city?
A.14
B.16
C.21
D.24
Answer: D.24
Explanation: Let the speed in highway be h mpg and in city be c mpg.
h = c+6
h miles are covered in 1 gallon
420 miles will be covered in 420/h.
Similarly c miles are covered in 1 gallon
336 miles will be covered in 336/c.
Both should be same (as car's fuel capacity does not change with speed)
=> 336/c = 420/h
=> 336/c = 420/(c+6)
=> 336c+336*6=420c
=>c=336*6/84=24
Answer D.
Question: The y intercept of a line L is 6. If the slope of L is negative, which of the following could be the x intercept of L.
I. -1
II. 0
III. 6
A.I only
B.II only
C.III only
D.I and II
Answer: C.III only
Explanation: C) III only
The y-intercept is 6. Therefore we have y=mx+6
It is given that the slope is negative. Therefore the line must go from top left to bottom right.
i.e: the x-intercept has to be positive. That itself rules out III.
If you choose to go with the options directly, here's an approach.
y=mx+6. For the x-intercept, y=0.
i.e. mx+6=0.
We know that the slope m is negative. Therefore, if x=-1 or x=0, the equation mx+6 =0 would never be satisfied.
If x=6, we have 6m+6=0. A value of m=-1 would satisfy this equation. 9answer C)
Question: A football coach must choose 5 freshers from a team of 12players. How many different ways can the coach choose the freshers?
A.650
B.670
C.729
D.740
Answer: C.729
Explanation: Choose 5 starters from a team of 12 players. Order is not important.
\inline {\color{Black} 12C_{5}}= 729
C
Question: A trader purchased two colour televisions for a total of Rs. 35000. He sold one colour television at 30% profit and the other 40% profit. Find the difference in the cost prices of the two televisions if he made an overall profit of 32%?
A.21000
B.21007
C.21004
D.21009
Answer: A.21000
Explanation: Let the cost prices of the colour television sold at 30% profit and 40% profit be Rs. x and Rs. (35000 - x) respectively.
Total selling price of televisions = x + 30/100 x + (35000 - x) + 40/100 (35000 - x)
=> 130/100 x + 140/100 (35000 - x) = 35000 + 32/100 (35000)
x = 28000
35000 - x = 7000
Difference in the cost prices of televisions = Rs. 21000
Answer:A
Question: Bradley owns b video game cartridges. If Bradley’s total is one-seventh the total owned by Andrew and four times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?
A.27b / 4
B.29b / 4
C.31b / 4
D.33b / 4
Answer: D.33b / 4
Explanation: b = Bradley’s total
7b = Andrew’s total
b/4 = Charlie’s total
The total number of cartridges is:
b + 7b+ b/4 = (4b + 28b + b) / 4 = 33b / 4
The answer is D.
Question: Tom purchased 8kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 45 per kg. How much amount did he pay to the shopkeeper?
A.A)1040
B.B)1045
C.C)965
D.D)1060
Answer: C.C)965
Explanation: Cost of 8 kg apples= 70 × 8 = 560.
Cost of 9 kg of mangoes = 45 × 9 = 405.
Total cost he has to pay = 560 + 405 = 965.
C)
Question: A single letter is selected at random from the word 'PROBABILITY'. The probability that it is a vowel is..??
A.2/11
B.3/11
C.4/11
D.0
Answer: C.4/11
Explanation: total vowels = 4, total number of letters = 11
so probability = 4/11
ANSWER:C
Question: The average number of shirts with Salman, Ambani and Dalmiya is 60, if all of them reached a shopping mall in Delhi and purchased 4 shirts each of them then average number of shirt each of them now has
A.66
B.63
C.62
D.64
Answer: D.64
Explanation: Required average
= Old average + New average
= 60 + 4 = 64
answer :D
Question: Ifaequals the sum of the even integers from 2 to 20, inclusive, andbequals the sum of the odd integers from 1 to 19, inclusive, what is the value of a * b ?
A.10000
B.11000
C.19000
D.20000
Answer: B.11000
Explanation: Yes! there is really a faster way to solve it.
Sum of consecutive odd or even integers = (no. of odd or even ints) * (first int + last int) / 2
Here A = sum of even ints from 2 to 20, inclusive
number of even ints = 10,
first int + last int = 2+20 = 22
A = 10*22 / 2 = 110
B = sum of odd ints from 1 to 19, inclusive
number of odd ints = 10,
first int + last int = 1+19 = 20
A = 10*20 / 2 = 100
A*B = 110 * 100 = 11000
Ans : B
Question: If two numbers are in the ratio 2:5. If 10 is added to both of the numbers then the ratio becomes 3:7 then find the smallest number?
A.40
B.80
C.60
D.20
Answer: B.80
Explanation: Given ratio - 2:5
2x + 10 : 5x + 10 = 3 : 7
7[2x + 10] = 3[5x + 10]
14x + 70 = 15x + 30
15x - 14x = 70 - 30
x = 40
Then smallest number is = 2
2x = 80
ANS - B
Question: Claire has 3 books. She averages the amount of pages of each book to have 305 pages. If her mom buys her a new book which has 400 pages, what will the new average be?
A.342.5
B.328.75
C.330.87
D.342.75
Answer: B.328.75
Explanation: (sum of the pages of the 3 books)/3 = 305
sum of the pages of the 3 books = 915
new sum = 915+400 = 1315
new average = 1315/4 = 328.75
ans: B
Question: Visitors to show were charged Rs.15 each on the first day. Rs.7.50 on the second day, Rs.2.50 on the third day and total attendance on the three days were in ratio 2:5:13 respectively. The average charge per person for the whole show is?
A.6
B.9
C.5
D.3
Answer: C.5
Explanation: 2: 5: 13
2x 5x 13x
15 7.5 2.5
30x + 37.5x + 32.5x = 100x/20x
Average = 5
Answer: C
Question: Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one green marble. Suppose we are going to put them into three cups: a black cup, a white cup, and a purple cup. The only restriction is that the two red marbles can’t be in the same cup. We could put as many as five (all except one of the reds) in any cup. We could leave one cup empty, or put some in each of the three cups. All combinations are allowed that don’t involve the two red marbles in the same cup. How many combinations are possible?
A.90
B.180
C.360
D.540
Answer: B.180
Explanation: 3 Blue Marble:
Different distribution : (1) All 3 in the same cup (2) Split 2-1 in two cups (3) Split 1-1-1
Case (1) 3 possibilities
Case (2) 6 possibilities ,
Case (3) 1 possibility
tot. 10 possibilities.
One Green Marble :
3 possibilities (one for each cup at the time)
First Red marble:
3 possibilities (one for each cup at the time)
Second Red marble:
2 possibilities ( because can't go in the same cup with the other Red marble)
TOTAL:
10*3*3*2 = 180 , answer, B .