RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The arithmetic mean of 5 negative integers is -100. If the average of 3 of these integers is -90, what is the least possible value that one of the other 2 integers can have?
A.229
B.-1
C.-229
D.90
Answer: C.-229
Explanation: The Arithmetic Mean of 5 negative integers is (a+b+c+d+e)/5=-100
So, The sum of 5 negative integers would be a+b+c+d+e=-100*5 = -500
Similarly, The sum of 3 negative integers would be a+b+c= -90*3 = -270
Thus, the sum of the other 2 integers is -500 + 270= -230. Since we know that the integers are negative then the least one from these two can be -229, the other one being -1.
Hence, the correct ans is C
Question: For every positive integer n, the nth term of sequence is given by an= 1/n - 1/(n+1). What is the sum of the first 75 terms?
A.25/26
B.40/41
C.75/76
D.150/151
Answer: C.75/76
Explanation: a1 = 1 - 1/2
a2 = 1/2 - 1/3
a3 = 1/3 - 1/4
etc...
a75 = 1/75 - 1/76
The sum of these terms is 1-1/76 = 75/76
The answer is C.
Question: A wheel rotates 20 times every minute and moves 30 cm during each rotation. How many metres does the wheel move in one hour?
A.360 metre
B.12 metre
C.320 metre
D.1200 metre
Answer: A.360 metre
Explanation: Number of times wheel moves in 1 hour = 20 * 30 = 1200
:. Distance moves = (1200*30) cms = 36000 cms
In metres = 360 metre
ANSWER:A
Question: In a one km race A gives B a start of 100m and in a one km race B gives a start of 80 m to C. In a 1 km race who will win and by how much distance from the worst performer between two losers?
A.172 m
B.372 m
C.172 m
D.772 m
Answer: A.172 m
Explanation: Ratio of speeds of A:B = 1000:900 = 100:90
Ratio of speeds of B:C = 1000:920 = 100:92
Therefore, when A moves 1000m , B moves 900 m and when B moves 900m, C moves 828m
Thus,
Since , C moves 8 % less than B in the same time . Thus, C is the worst performer and A will win by him by 172 m
ANSWER=A
Question: How many 4-digit numbers contain no.2?
A.22
B.98
C.28
D.29
Answer: B.98
Explanation: Answer:B
Question: If you divide 7^84 by 5, which remainder do you get?
A.0
B.1
C.2
D.3
Answer: B.1
Explanation: The units digit of 7^1 is 7.
The units digit of 7^2 is 9.
The units digit of 7^3 is 3.
The units digit of 7^4 is 1.
The units digit of 7^5 is 7.
etc...
The units digit of 7^n repeats in blocks of 4: {7, 9, 3, 1}
The remainder of 84/4 is 0.
So the units digit of 7^84 is 1.
The remainder of 7^84 / 5 is 1.
The answer is B.
Question: In how many ways can 4 boys and 2 girls sit around a table in such a way that no two girls sit together?
A.74
B.72
C.78
D.82
Answer: B.72
Explanation: The 4 boys can be seated around a table in 3! Ways. In between them there are 4 places.
The 2 girls can be placed in the 4 places in 4P2 ways.
Therefore, Required number of ways= 3!* 4P2
=6*12
=72
ANSWER:B
Question: The sum of three consecutive even numbers is 20 more than the first of these numbers. What is the middle number?
A.7
B.9
C.11
D.Cannot be determined
Answer: B.9
Explanation: Solution
Let the numbers be x, x + 2 and x + 4.
Then, x + (x + 2) + (x + 4) = x + 20 ⇔ 2x = 14 ⇔ x = 7.
∴ Middle number = x + 2 = 9.
Answer B
Question: In how many ways can a committee consisting of 4 men and 5 women be formed from a group of 9 men and 9 women?
A.9C4 9C5
B.4C9 5C9
C.7C5 9C4
D.9C4 7C5
Answer: A.9C4 9C5
Explanation: Group consisting of 9 men and 9 women
4 men can be selected from 9 men in 9C4 ways
5 women can be selected from 9 women in 9C5 ways
Therefore, Total number of ways= 9C4 9C5
ANSWER:A
Question: a number when divided by 899 gives a remainder 63. what remainder will be obtained by dividing the same number by 29
A.8
B.5
C.7
D.6
Answer: B.5
Explanation: 63 / 29, thereforerequired number is: 5, correct answer (B)
Question: For the integer n, if n*n*n is odd, then what is true
A.n is odd and n*n is even
B.n*n is odd
C.n is even
D.n*n is odd
Answer: A.n is odd and n*n is even
Explanation: Option A
Question: How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 5, and the digit 2 can be used only once?
A.20
B.150
C.225
D.300
Answer: B.150
Explanation: 4 options for the first digit: 2, 4, 6, 8;
5 options for the second digit: 1, 3, 5, 7, 9;
4 options for the third digit: 2, 3, 5, 7;
4 options for the fourth digit: 0, 5.
Four digit # possible without the restriction (about the digit 2): 4*5*4*2=160
Numbers with two 2-s, 2X2X 1*5*1*2=10.
Thus there are 160-10=150 such numbers.
Answer: B.
Question: A fellow borrowed a certain sum of money at 6% per annum at simple interest and in 6 years the interest amounted to Rs.672 less than the sum lent. What was the sum lent?
A.1050
B.1220
C.1250
D.1060
Answer: A.1050
Explanation: P - 672 = (P*6*6)/100
P = 1050
Answer: A
Question: The H.C.F of two numbers is 23 and the other two factors of their L.C.M are 13 and 14. The larger of the two numbers is:
A.338
B.278
C.322
D.231
Answer: C.322
Explanation: Clearly, the numbers are (23 * 13) and (23 * 14). Larger number
= (23 * 14) = 322.
Answer: C
Question: In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?
A.7:3
B.3:7
C.4:6
D.5:7
Answer: A.7:3
Explanation: Required rate = 3.50 : 1.50 = 7 : 3.
ANSWER A
Question: The reflex angle between the hands of a clock at 10.25 is
A.180°
B.192 ½°
C.195°
D.197 ½°
Answer: D.197 ½°
Explanation: Solution
Angle traced by hour hand in 125 / 12 hrs.	=[360/12 x 125/12]°
= 312½°.
Angle traced by minute hand in 25 min.	= [360/60 x 25]°
=150°.
Reflex angle	= 360 - (312½ -150)°
=360° - 162 ½°
= 197½°.
Answer D
Question: During a certain week, a seal ate 55% of the first 80 smelt it came across, and 30% of the remaining smelt it came across. If the seal ate 40% of the smelt it came across during the entire week, how many smelt did it eat?
A.32
B.80
C.55
D.64
Answer: B.80
Explanation: Total smelt = x.
Then, 0.55*80+0.3(x-80)=0.4*x --> x=200 --> 0.4*x=80.
Answer: B.
Question: The breadth of a rectangular field is 60% of its length. If the perimeter of the field is 800 m.What is the area of the field?
A.18750 sq.m
B.37500 sq.m
C.40000 sq.m
D.48000 sq.m
Answer: B.37500 sq.m
Explanation: Solution
So length =250 m; breadth=150m
Area	= (250 x 150)m²
= 37500 m²
Answer B
Question: By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?
A.42 6/4%
B.42 9/7%
C.42 2/7%
D.42 6/7%
Answer: D.42 6/7%
Explanation: SP = CP + g
50 SP = 50 CP + 15 SP
35 SP = 50 CP
35 --- 15 CP gain
100 --- ? => 42 6/7%
Answer: D
Question: Two vessels having volumes in the ratio 3:5 are filled with water and milk solutions. The ratio of milk and water in the two vessels are 3:1 and 6:4 respectively. If the contents of both the vessel are empties into a larger vessel, find the ratio of milk and water in the larger vessel.
A.26:11
B.23:11
C.21:11
D.24:11
Answer: C.21:11
Explanation: Vessel A = 300 gallons --> milk = 225, water = 75;
Vessel B = 500 gallons --> milk = 300, water = 200;
Vessel A + B = 800 gallons --> milk = 525, water 275
The ratio =525/275 -->21:11
Answer: C
Question: The G.C.D. of 1.08, 0.36 and 0.9 is:
A.0.03
B.0.9
C.0.18
D.0.2
Answer: C.0.18
Explanation: Given numbers are 1.08, 0.36 and 0.90.
H.C.F. of 108, 36 and 90 is 18,
H.C.F. of given numbers = 0.18.
Answer: Option C
Question: There are 12 pieces of radioactive metal K that look identical. 11 of the pieces give the same radiation count when measured, the 12th piece is a counterfeit and gives a different radiation level, which may be more or less than the other 11. We are given a radiation scale, which can take 2 sets of samples and compare their added up radiation levels to tell us if the sums are the same or if different, which set has the higher level of radiation. What is the minimum number of comparisons we need on this scale to identify the counterfeit sample and to also determine whether it has more or less radiation than the other samples ?
A.2
B.3
C.4
D.5
Answer: B.3
Explanation: First of all if you are down to just 3 pieces and you know that if the offending piece is less or more active, then it takes exactly 1 measurement to find out the offending piece. So you know you have to reduce the problem to three.
Now when you are down to either A or B after measurement 1, you need the next measurement to (a) reduce the problem set to 3 and (b) to know whether anser is more or less. Now you cannot compare a group of 4 to 4, as in the best case it will only reduce the problem to 4 elements which is not good enough.
If you have to choose a set of 3 to compare, you cannot pick any 3 on the same side from the same set (A or B) because if you do this, a quick check will show you that in every choice there is a case where you can only get down to 4 elements. Eg. If you weighed {1,2,3} v/s {5,9,10} and they were equal you're problem would only reduce to {4,6,7,8}
The easiest way to solve this then is to compare 3 to 3, and make sure each side has elements from both AB such that whatever the measurement outcome in the worst case the problem reduces to 3 elements only. Which is why the sets {1,5,9} and {2,6,7} OR {A,B,C}{A,B,B}. The extra element from C is just taken to make the problem symmetric so to say, we have 8 elements and we make it 9, to compose 3 sets of 3 each.=B
Question: The unit digit in the product 1457*7863*4575*9719 is?
A.5
B.1
C.2
D.3
Answer: A.5
Explanation: Unit digit in the given product = unit digit in 7*3*5*9 = 5
Answer is A
Question: The average temperature for Monday, Tuesday, Wednesday and Thursday was 48 degrees and for Tuesday, Wednesday, Thursday and Friday was 46 degrees. If the temperature on Monday was 39 degrees. Find the temperature on Friday?
A.65 degrees
B.73 degrees
C.31 degrees
D.34 degrees
Answer: C.31 degrees
Explanation: M + Tu + W + Th = 4 * 48 = 192
Tu + W + Th + F = 4 * 46 = 184
M = 39
Tu + W + Th = 192 -39 = 153
F = 184 – 153 = 31
Answer:C
Question: The distance from City A to City B is 150 miles. While driving from City A to City B, Cara drives at a constant speed of 30 miles per hour. Dan leaves City A 90 minutes after Cara. What is the minimum constant speed in miles per hour that Dan must exceed in order to arrive in City B before Cara?
A.42.85
B.44
C.46
D.48
Answer: A.42.85
Explanation: The time it takes Cara to drive to City B is 150 / 30 = 5 hours.
Dan needs to take less than 3.5 hours for the trip.
Dan needs to exceed a constant speed of 150 / 3.5 = 42.85 miles per hour.
The answer is A.
Question: Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
A.17 min
B.10 min
C.90 min
D.18 min
Answer: B.10 min
Explanation: 4/12 + x/15 = 1
x = 10
Answer: B
Question: There were 36,000 hardback copies of a certain novel sold before the paperback version was issued. From the time the first paperback copy was sold until the last copy of the novel was sold 7 times as many paperback copies as hardback copies were sold. If a total of 441,000 copies of the novel were sold in all, how many paperback copies were sold?
A.45,000
B.360,000
C.354,300
D.392,000
Answer: C.354,300
Explanation: Say x was the # of hardback copies sold from the time the first paperback copy was sold.
Then the total # of paperback copies sold was 9x;
Hence the total # of copies sold was (hardback)+(paperback)=(36+x)+(7x)=441 --> x=50.6.
So, the total # of paperback copies sold was 7x=7*50.6=354.3 or 354,300.
Answer: C.
Question: Anil can do a work in 15 days while Sunil can do it in 25 days. How long will they take if both work together?
A.9 3/9
B.9 3/7
C.9 3/8
D.9 3/2
Answer: C.9 3/8
Explanation: 1/15 + 1/25 = 8/75
75/8 = 9 3/8 days
Answer:C
Question: A glass was filled with 24 ounces of water, and 0.06 ounce of the water evaporated each day during a 12-day period. What percent of the original amount of water evaporated during this period?
A.0.003%
B.0.03%
C.3%
D.2%
Answer: C.3%
Explanation: In 12 days 12*0.06=0.72 ounces of water evaporated, which is 0.72/24âˆ—100=3 of the original amount of water.
Answer: C.
Question: Tom reads at an average rate of 30 pages per hour, while Jan reads at an average rate of 40 pages per hour. If Tom starts reading a novel at 4:30, and Jan begins reading an identical copy of the same book at 5:20, at what time will they be reading the same page?
A.9:30
B.9:00
C.8:40
D.7:50
Answer: D.7:50
Explanation: Relative speed =jan - Tom =10 pages per hour = 1/6 page per minute
time diff =50 minutes
by the time Jan started ToM already finished (30/60)*50 = 25 pages
time taken = 25 /(1/6) =25*6= 150 minutes=7:50
ANSWER:D
Question: If the sum of the 4th term and the 12th term of an arithmetic progression is 30, what is the sum of the first 15 terms of the progression?
A.250
B.275
C.260
D.225
Answer: D.225
Explanation: 4th term + 12th term = 30
i.e., (a+3d)+(a+11d) = 30
Now, Sum of first 15 terms = (15/2) * [2a + (15-1)d]
= (15/2) * [2a + 14d]
= (15/2) * 30 --------------- From (1)
=225
Answer : D
Question: four children, Arya, Betsy, Chen, Daniel, Emily, and Franco, are to be seated in a single row of six chairs. If Betsy cannot sit next to Emily, how many different arrangements of the six children are possible?
A.24
B.480
C.540
D.720
Answer: A.24
Explanation: Since it is more time consuming and error prone to find ways Betsy and E not sitting together, It is better we find ways in which they will be together and then subtract from total ways..
total ways = 6!..
ways B and E will be sitting together..
take both B and E as one, then these two together with other 4 can sit in 5! ways ...
Also B and E can sit within themselves in 2! ways..
so the answer required = 6!-2*5!=24..
ans A
Question: An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 20-meter platform and caught it after it had traveled 59.4 meters. How many times did the ball bounce?
A.5
B.6
C.7
D.8
Answer: B.6
Explanation: Ans: 6
Division of total diatance travelled will be 20+20+10+5+2.5+1.25+0.6 ANS B
Question: Jonathan’s grandparents lend $20,000 to Jonathan at a simple annual interest rate of 10%. He pays them back 5 years later. How much do they receive?
A.20,000∗0.1^5
B.20,000∗1.5
C.20,000∗0.5
D.20,000∗1.1^5
Answer: B.20,000∗1.5
Explanation: if you are like me and have used S.I = P x R x T formula in school, then while the question is asking for Amount in 5 years. so (B) 20,000∗ 1.5
Ans : B
Question: Find the ratio of the curved surfaces of two cylinders of same heights if their radii are in the ratio 1:2?
A.1:2
B.2:3
C.2:9
D.2:1
Answer: A.1:2
Explanation: 1:2
Answer: A
Question: Look at this series: 42, 36, 39, __, 42, 45, 42, 48, ... What number should fill the blank?
A.40
B.48
C.46
D.42
Answer: D.42
Explanation: D
42
In this series, 3 is added to the previous number; the number 42 is inserted as every third number.
Question: A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
A.126 ways
B.516 ways
C.154 ways
D.108 ways
Answer: D.108 ways
Explanation: The boy can select one trouser in nine ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 12
= 108 ways.
Answer: D
Question: A sum of Rs. 2665 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
A.2888
B.2677
C.2998
D.1640
Answer: D.1640
Explanation: (x*8*3)/100 = ((2665 - x)*3*5)/100
24x/100 = 39975/100 - 15x/100
39x = 39975 => x = 1025
Second sum = 2665 – 1025 = 1640
Answer:D
Question: A pharmaceutical company received $5 million in royalties on the first $25 million in sales of generic equivalent of one of its products and then $10 million in royalties on the next $100 million in sales. By approximately what percent did the ratio of royalties to sales decrease from the first $25 million in sales to the next $100 million in sales?
A.50%
B.65%
C.70%
D.75%
Answer: A.50%
Explanation: change in ratio of royalties to sales = 5/25 -10/100 = 1/10
% decrease = (1/10)/(5/25) *100 = 50%
Answer: A)
Question: If the annual rate of simple interest increases from 10% to 12 1/2 %, a man's yearly income increases by Rs. 1250. His principal in Rs. is?
A.34377
B.50000
C.777768
D.2777
Answer: B.50000
Explanation: Let the sum be Rs. x. Then,
(x * 25/2 * 1/100) - (x * 10 * 1)/100 = 1250
25x - 20x = 250000
x = 50000
Answer: B
Question: How many cuboids of length 5 m, width 3 m and height 2 m can be farmed from a cuboid of 12 m length, 14 m width and 10 m height.
A.82
B.56
C.80
D.56
Answer: B.56
Explanation: (12 Ã— 14 Ã— 10)/(5 Ã— 3 Ã— 2) = 56
Answer is B.
Question: The length of rectangle is thrice its breadth and its perimeter is 104 m, find the area of the rectangle?
A.507 sq m
B.356 sq m
C.452 sq m
D.428 sq m
Answer: A.507 sq m
Explanation: 2(3x + x) = 104
l = 39 b = 13
lb = 39 * 13 = 507
ANSWER:A
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 180 m and they cross each other in 12 sec, then the speed of each train is?
A.54
B.26
C.36
D.99
Answer: A.54
Explanation: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (180 + 180)/12 => x = 15
Speed of each train = 15 m/sec.
= 15 * 18/5 =54 km/hr.
Answer: A
Question: Which of the following numbers has more than two distinct prime factors?
A.385
B.422
C.425
D.471
Answer: A.385
Explanation: 385=5*7*11
422=2*211
425=5^2*17
471=3*157
500=2^2 * 5^3
385 has 3 distinct prime factors
Answer A
Question: A certain lab experiments with white and brown mice only. In one experiment, 2/3 of the mice are white. If there are 7 brown mice in the experiment, how many mice in total are in the experiment?
A.39
B.33
C.26
D.21
Answer: D.21
Explanation: Let total number of mice = M
Number of white mice = 2/3 M
Number of brown mice = 1/3 M = 7
=> M = 21
Answer D
Question: If 2x + 3y = 37; 2y + z = 19 and x + 2z = 29, what is the value of x + y + z ?
A.18
B.32
C.25
D.22
Answer: C.25
Explanation: On solving equation we get
x = 11, y = 5, z = 9
Answer C
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 23 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
A.37
B.240
C.288
D.195
Answer: D.195
Explanation: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 23)m = 345 m. Let the length of the platform be x meters. Then, (x + 345)/36 = 15 ==> x + 345 = 540 ==> x = 195 m.Answer: D
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 2 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
A.s.4528
B.s.1812
C.s.4527
D.s.4530
Answer: B.s.1812
Explanation: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls
= 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3)
= 906 sq.ft.
Total cost = 906 * 2
= Rs.1812
Answer:B
Question: Large, medium and small ships are used to bring water. 4 large ships carry as much water as 7 small ships; 3 medium ships carry as much water as 2 large ships and 1 small ship. If 15 large, 7 medium and 14 small ships, each made 36 journeys to bring a certain quantity of water , then in how many journeys will 12 large, 14 medium and 21 small ships bring the same quantity of water?
A.29 journeys
B.30
C.20
D.50
Answer: A.29 journeys
Explanation: Explanation :
Here, Large, Medium and Small ships are denoted by the symbol L, M and S.
Now, according to the question,
4L = 7S. ------(i)
3M = 2L + S. ------(ii)
Using above equations, the ratios of the capacity of the Large, Medium and Small ships are :-
7: 6 : 4.
Let, the number of journeys required be x. Since, quantity of water remains the same, so :-
=((15×7+7×6+14×4)36) = x (12×7+14×6+21×4).
=>((15×7+7×6+14×4)36) / (12×7+14×6+21×4)= x
=>x=7308/252
=>x=29.
Answer : A
Question: A mixed doubles tennis game is to be played between two teams. There are four married couples. No team is to consist of a husband and his wife. What is the maximum number of games that can be played.
A.12
B.21
C.36
D.42
Answer: D.42
Explanation: Let's denote the four couples by (A,a), (B,b), (C,c), and (D,d) where A,B,C,D are the husbands and a,b,c,d are the wives.
For a games, let's choose first the husbands. We have 4C2=4*3/2=6 possibilities. Now we know that the final number of games will be a multiple of 6, so we are down to two choices, C and D.
Once husbands were chosen, say A and B, let's count how many possibilities we have to choose their partners under the given restrictions.
We can choose a and b and we have to pair them as (A,b) and (B,a) - 1 possibility.
We can choose one of the wives, a or b, but we have to pair her with the other husband and in addition, we have to choose another partner for the second husband.
This we can do in 2*2 = 4 ways, as there are two possibilities to choose from a and b, then we have 2 possibilities to choose the other wife, c or d - 4 possibilities
Finally, we can choose the other two wives, c and d, and we have two possibilities to team them up with the men, (A,c), (B,d) or (A,d), (B,c) - 2 possibilities.
In conclusion, for every pair of husbands, we have 1 + 4 + 2 = 7 possibilities to choose their partners for the game.
Total number of possibilities 6 * 7 = 42.
Answer D.
Question: A triangle has a perimeter 14. The two shorter sides have integer lengths equal to x and x + 1. Which of the following could be the length of the other side?
A.6
B.7
C.8
D.9
Answer: A.6
Explanation: The SHORTER sides have integral lengths equal to x and x + 1
Let the longest side be 'a'
So, a + x + (x +1) = 14
a + 2x = 13.......eqn (1)
We know that the sum of the lengths of the shorter sides has to be more than the length of the longer one. i.e 2x+1> a
a =6
A
Question: If a mixture is 1⁄2 alcohol by volume and 3⁄2 water by volume, what is the ratio of the volume of alcohol to the volume of water in this mixture?
A.3⁄7
B.4⁄7
C.3⁄4
D.4⁄3
Answer: C.3⁄4
Explanation: Should be a sub-600 level Q..
volume= {1/2}/{3/2}=1/3
C
Question: David has d books, which is 3 times as many as Jeff and 3/2 as many as Paula. How many books do the three of them have altogether, in terms of d?
A. 2*d
B. 7/3*d
C. 10/3*d
D. 7/2*d
Answer: A. 2*d
Explanation: Although we could plug in a real value for d, the problem can be just as easily solved by setting up equations. However, let’s start by defining some variables. Since we are given that David has d books, we can use variable d to represent how many books David has.
number of books David has = d
number of books Jeff has = j
number of books Paula has = p
We are given that David has 3 times as many books as Jeff. We can now express this in an equation.
d = 3j
d/3 = j
We are also given that David has ½ as many books as Paula. We can also express this in an equation.
d = (3/2)p
2d/3 = p
Notice that we immediately solved forj in terms of d and p in terms of d. Getting j and p in terms of d is useful when setting up our final expression. We need to determine, in terms of d, the sum of the number of books for David, Jeff, and Paula. Thus, we have:
d + d/3 + 2d/3
=2d
The answer is A
Question: Johnny bought six peanut butter cans at an average price (arithmetic mean) of 38.0¢. If Johnny returned two cans to the retailer, and the average price of the remaining cans was 31¢, then what is the average price, in cents, of the two returned peanut butter cans?
A.5.5
B.11
C.52
D.66
Answer: C.52
Explanation: Total price of six cans = 6*38.0 = 228
Total price of 4 cans = 4*31 = 124
Total rice of two cans = 228 - 124 = 104
Average price of two cans = 104/2 = 52 c
Another way to do it is this:
Assume that the four leftover cans were of 31c each. The avg was 38c initially because the two cans were 38c each and were providing another 7c of cost to other 4 cans.
So cost of the two cans = 2*38 + 4*7 = 104
Avg cost of the two cans = 104/2 = 52c
Answer (C)