RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: An empty wooden vessel weighs 12% of its total weight when filled with paint. If the weight of a partially filled vessel is one half that of a completely filled vessel, what fraction of the vessel is filled.
A.3/5
B.6/11
C.1/24
D.4/9
Answer: B.6/11
Explanation: An empty wooden vessel weighs 12% of its total weight when filled with paint:
Vessel = 0.12(Vessel + Paint);
12V = V + P (so the weight of completely filled vessel is 10V)
P = 11V (so the weight of the paint when the vessels is completely filled is 9V).
The weight of a partially filled vessel is one half that of a completely filled vessel:
V + P' = 1/2*12V;
P' = 6V (so the weight of the paint when the vessels is partially filled is 6V).
What fraction of the vessel is filled?
So, we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled:
P'/P = 6V/11V = 6/11.
Answer: B.
Question: By selling an article at Rs.800, a profit of 25% is made. Find its cost price?
A.s.486
B.s.455
C.s.640
D.s.480
Answer: C.s.640
Explanation: SP = 800
CP = (SP)*[100/(100+P)]
= 800* [100/(100+25)]
= 800* [100/125]
= Rs.640
Answer: C
Question: Envelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $8.10?
A.426
B.430
C.443
D.520
Answer: D.520
Explanation: I think first we should see in what group envelopes value less, so that we can buy as many as we can with a specific amount of money:
-the 100 pack costs 1.5$, meaning 0.015$ per envelope
-the 50 pack costs 1$, meaning 0.02$ per envelope
-the single envelope costs 0.03$ per envelope
Thus, we have to buy as many 100 packs as we can, then as meny of 50 packs as we can and the remaining envelopes are single ones.
Having 8.1$, we can buy as many as 5 packs of 100 (5 x 1.5$ = 7.5$). We then have 0.6 $ left. so we buy 20 individual envelopes. If we add up the numbers, we get 500+20=520 envelopes. Answer D
Question: If 23^3*19^4*14^2 = x, what is the units digit of x ?
A.2
B.3
C.6
D.7
Answer: A.2
Explanation: 23^3*19^4*14^2 = x
Units digit of x will be
3^3 * 9^4 * 4^2
=7* 1 *6
=42
Therefore , units digit of x = 2
Answer A
Question: A car takes 6 hours to cover a distance of 270 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
A.10Kmph
B.20Kmph
C.25Kmph
D.30Kmph
Answer: D.30Kmph
Explanation: Time = 6
Distence = 270
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 270/9 = 30 Kmph
D)
Question: What sum of money will produce Rs.70 as simple interest in 5 years at 3 1/2 percent?
A.400
B.500
C.367
D.368
Answer: A.400
Explanation: 70 = (P*5*7/2)/100
P = 400
Answer: A
Question: Jasmine has a toaster with two slots that toasts one side of each piece of bread at a time, and it takes one minute to do so.
If she wants to make 3 pieces of toast, what is the least amount of time she needs to toast them on both sides?
A.1
B.2
C.3 min
D.4
Answer: C.3 min
Explanation: 3 minutes. She puts two pieces in the toaster, toasting one side of each. Then she flips one of them, takes one out, and puts the completely untoasted piece into the toaster. Finally, she takes out the toasted piece and puts the two half-toasted pieces of bread into the toaster for a minute and she's done. C
Question: Adding two non multiples of Q always results in a multiple of Q; which of the following must be the value of Q ?
A.[A] two
B.[B] three
C.[C] five
D.[D] ten
Answer: A.[A] two
Explanation: NON- multiples of 2 would always be ODD and sum of two odd would be EVEN.
so irrespective of value of non-multiples, sum of two them would always be even and thus multiple of 2..
A
Question: A towel, when bleached, lost 30% of its length and 40% of its breadth. What is the percentage decrease in area?
A.24%
B.30 %
C.44%
D.58%
Answer: D.58%
Explanation: percentage change in area
=(−30−40+(30×40)/100)%=−58%
i.e., area is decreased by 58%
ANSWER:D
Question: A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is?
A.5
B.6
C.8
D.4
Answer: A.5
Explanation: US = 25
DS = 35
M = (35 - 25)/2 = 5 Answer:A
Question: in how many different ways can the letters of the word OPTICAL be arranged so that the vowels always come together
A.520
B.620
C.720
D.750
Answer: C.720
Explanation: The word 'OPTICAL' contains 7 different letters.
When the vowels OIA are always together, they can be supposed to form one letter.
Then, we have to arrange the letters PTCL (OIA).
Now, 5 letters can be arranged in 5! = 120 ways.
The vowels (OIA) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
ANSWER:C
Question: The price of rice falls by 20%. How much rice can be bought now with the money that was sufficient to buy 40 kg of rice previously?
A.5 kg
B.15 kg
C.25 kg
D.50 kg
Answer: D.50 kg
Explanation: Solution: Let Rs. 100 be spend on rice initially for 40 kg.
As the price falls by 20%, new price for 40 kg rice,
= (100 -20% of 100) = 80
New price of rice = 80/40 = Rs. 2 per kg.
Rice can bought now at = 100/2 = 50 kg.
Answer: Option D
Question: John has taken four (4) tests that have an average of 80. In order to bring his course grade up to a ‘B’, he will need to have a final average of 87. What will he need to average on his final two tests to achieve this grade?
A.87
B.101
C.92
D.94
Answer: B.101
Explanation: 87-80=7*4=28 points
2*87=174
174+28=202 points to be scored in the 2 tests.
Avg of 2 tests = 202/2=101
Answer: B
Traditional Method:
Total scored till now 80*4=320
Total score to avg 87 in 6 tests = 87*6=522
Total to be scored on 2 tests = 522-320=202
Avg on 2 tests = 202/2 = 101
Answer B
Question: Find the C.I. on Rs. 15,625 for 9 months at 16% per annum compounded quarterly?
A.19587
B.1987
C.1951
D.1998
Answer: C.1951
Explanation: P = Rs. 15625, n = 9 months = 3 quarters, R = 16% p.a. per quarter.
Amount = [15625 * (1 + 4/100)3]
= (15625 * 26/25 * 26/25 * 26/25) = Rs. 17576 C.I. = 17576 - 15625 = Rs. 1951.
Answer: C
Question: A large research project was scheduled over the course of a 30-month period, and a budget of $99,000 was allotted for the course of the entire project. After ten months, the project had spent $30,000. Was the project at this point over budget or under budget, and by how much?
A.under, $4200
B.under, $1200
C.under, $700
D.on bugdget
Answer: D.on bugdget
Explanation: cost per month = 99,000/30 = 3,000.
Now, multiply by seven months: 10*($3000) = $30,000. That would be the budgeted amount, the amount theoretically supplied to the project. The real amount spent is equal to this, so it is on budget.
$30,000 â€“ #30,000 = $0
Answer = (D)
Question: Directions : In questions no. 1 to 8, select the one which is different from other three alternatives.
A.Delegate
B.Person
C.Manager
D.Deputy
Answer: B.Person
Explanation: B
Except (B) all are designations.
Question: Mariah has decided to hire three workers. To determine whom she will hire, she has selected a group of 10 candidates. She plans to have one working interview with 3 of the 10 candidates every day to see how well they work together. How many days will it take her to have working interviews with all the different combinations of job candidates?
A.720
B.120
C.300
D.30
Answer: B.120
Explanation: There are C310=120 different groups of three possible out of 10 candidates and since each of these groups is interviewed every day then total of 120 days are needed.
Answer: B
Question: A constructor estimates that 3 people can paint Mr khans house in 4 days. If he uses 4 people instead of 3,how long will they take to complete the job?
A.2
B.8
C.1
D.3
Answer: D.3
Explanation: Explanation:
Use formula For a work Members × days = constant
3 × 4 = 4 × a
a = 3
so answer is 3 days
Answer: D
Question: John has on his shelf three books of poetry, five novels, and two reference works. Suppose from these ten books, we were to pick two books at random. What is the probability that we pick one novel and one reference work?
A.1/2
B.2/9
C.3/10
D.7/20
Answer: B.2/9
Explanation: When we are picking two books, one novel and one reference work, we could either pick a novel first and then a reference book or pick a reference book and then a novel. Therefore the answer is 5/10*2/9 + 2/10*5/9 = 2/9.
Answer: B.
Question: A boat M leaves shore A and at the same time boat B leaves shore B. They move across the river. They met at 500 yards away from A and after that they met 300 yards away from shore B without halting at shores. Find the distance between the shore A & B
A.1000 yards
B.1200 yards
C.1400 yards
D.1600 yards
Answer: B.1200 yards
Explanation: If X is the distance, a is speed of A and b is speed of B, then ;
500/a= (x-500)/b and (x+300)/a = (2x-300)/b , solving it, we get x=1200 yards
ANSWER:B
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.110
B.114
C.128
D.130
Answer: C.128
Explanation: First Purchased = 250 Wes= 128
C
Question: The sides of a triangle are in the ratio 5: 12: 13 and its perimeter is 360 m, its area is?
A.180
B.882
C.277
D.261
Answer: A.180
Explanation: 5x + 12x + 13x = 360 => x = 12
a = 60, b = 144, c = 156
S = (60 + 144 + 156)/2 = 180
Answer: A
Question: Find the area of a parallelogram with base 10 cm and height 20 cm.
A.200
B.384
C.200
D.244
Answer: C.200
Explanation: Area of a parallelogram = base * height = 10 * 20 = 200 cm2
Answer: Option C
Question: If the number 517 * 324 is completely divisible by 3, then the smallest whole number in the place of * will be:
A.1
B.2
C.3
D.4
Answer: B.2
Explanation: B
2
Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 3.
x = 2.
Question: In a rectangular coordinate system, if a line passes through the points (-17,-18), (13,22) and (x,2) then what is the value of x?
A.-2
B.-1
C.0
D.1
Answer: A.-2
Explanation: The slope of the line m is rise/run = 22-(-18) / 13-(-17) = 4/3
4/3 = 22-2 / 13-x
52-4x = 66-6
x = -2
The answer is A.
Question: A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in?
A.20 days
B.16 days
C.24 days
D.28 days
Answer: C.24 days
Explanation: Explanation:
B = 1/8 – 1/2 = 1/24 => 24 days
Answer: C
Question: If n is an integer and 5^n > 40,000,000,000, what is the least possible value of n?
A.16
B.8
C.9
D.10
Answer: A.16
Explanation: When you seperate the 40000000000 into factors of 5 and 2 you get - > 10^10 x 2^2 = 5^10 x 2^12
2 to the ^ 8 = 4096 so its4096 x 5^10
that means 5^10 x 5^x must be greater
5^x > 4096
5^1=5
5^2=25
5^3= 125
5^6= 15625 - > so x must be at least 6
5^(10+6)= 5^16
A
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 8 p.c?
A.28000
B.36800
C.37000
D.38000
Answer: B.36800
Explanation: Option B
Explanation:
CP + CP/8 = 45000
CP = 40000
SP = 40000*(92/100) = 36800
Option B
Question: Jason flips a coin three times. What is the probability Q that the coin will land on the same side in all three tosses?
A.1/16
B.1/8
C.1/4
D.1/3
Answer: C.1/4
Explanation: Total outcome is 2^3=8
Favorable cases HHH or TTT
Therefore, probability Q is 2/8 or 1/4=C
Question: A man can row with a speed of 20 kmph in still water. If the stream flows at 30 kmph, then the speed in downstream is?
A.27
B.41
C.20
D.50
Answer: D.50
Explanation: M = 20
S = 30
DS = 30+ 20 = 50
Answer:D
Question: The largest 4 digit number exactly divisible by 88 is:
A.9944
B.9768
C.9988
D.8888
Answer: A.9944
Explanation: Explanation:
Largest 4-digit number = 9999
88) 9999 (113
88
----
119
88
----
319
264
---
55
---
Required number = (9999 - 55)
= 9944.
ANSWER IS A
Question: The batting average of a particular batsman is 61 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, find his highest score.
A.179
B.202
C.210
D.223
Answer: B.202
Explanation: Explanation:
Total runs scored by the batsman = 61*46 = 2806 runs
Now excluding the two innings the runs scored = 58*44 = 2552 runs
Hence the runs scored in the two innings = 2806 – 2552 = 254 runs.
Let the highest score be x, hence the lowest score = x – 150
x + (x - 150) = 254
2x = 404
x = 202 runs
ANSWER B
Question: A contest will consist of n questions, each of which is to be answered wither "True" or "False". Anyone who answers all n questions correctly will be a winner. What is the least value of n for which the probability is less than 1/1000 that a person who randomly guesses the answer to each question will be a winner?
A.5
B.10
C.50
D.100
Answer: B.10
Explanation: (1/2)^n < 1/1000
(1/2)^n < (1/2)^3*(1/5)^3
Because 1/5 ~ (1/2)^2
n > 3 + 3*2 = 9
ANSWER: B
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 12 m wide at the top and 5 m wide at the bottom and the area of cross-section is 344 sq m, the depth of cannel is?
A.39
B.28
C.27
D.40
Answer: D.40
Explanation: 1/2 * d (12 + 5) = 344
d = 40
Answer: D
Question: Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. How many notebooks were distributed in all?
A.432
B.640
C.256
D.512
Answer: D.512
Explanation: In case I: Let the no. of children = x.
Hence, total no. of notebooks distributed
1⁄8x.x or x2⁄8.......(i)
In case II: no.of children = x⁄2
Now, the total no. of notebooks
= 16 × x⁄2 .......(ii)
Comparing (i) & (ii), we get
x2⁄8 = 8x
or, x = 64
Hence, total no. of notebooks
= 64×64/8=512
Answer D
Question: The height of a triangle is decreased by 25% and its base increased by 50%. Its area will
A.decrease by 12.5%
B.increase by 12.5%
C.decrease by 25%
D.Increase by 25%
Answer: B.increase by 12.5%
Explanation: Explanation :
Let the initial height be 100 and the base be 200 units.
∴ Area = 1/2 x 100 x 200 = 1000sq units
Now, height = 75 units and base = 300 units
∴ New area = 1/2 x 75 x 300 = 11250
∴ Area is increased by (11250 - 10000)/10000 x 10
= 12.5%
Answer : Option B
Question: How much is 80% of 40 is greater than 4/5 of 25?
A.22
B.67
C.88
D.12
Answer: D.12
Explanation: (80/100) * 40 – (4/5) * 25
32 - 20 = 12
Answer: D
Question: A and B can do a work in 5 days and 10 days respectively. A starts the work and B joins him after 4 days. In how many days can they complete the remaining work?
A.6 days
B.2/3 days
C.8 days
D.3 days
Answer: B.2/3 days
Explanation: Work done by A in 4 days = 4/5
Remaining work = 1/5
Work done by both A and B in one day = 1/5 + 1/10 = 3/10
Remaining work = 1/5 * 10/3 = 2/3 days.
Answer: B
Question: 1
11
21
1211
111221
??????
A.312211
B.312212
C.312221
D.312222
Answer: A.312211
Explanation: 1
11
111 as 21
1211
1112111 as 111221
11112211 as 312211
ans 312211
ANSWER:A
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?
A.40
B.41
C.48
D.67
Answer: C.48
Explanation: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.9 = 2 km = 2000 m.
Required time = 2000 * 3/125 = 48 sec.
Answer: Option C
Question: If population of certain city increases at the rate of 5%. If population in 1981 was 138915, then population in 1978 was?
A.120000
B.27778
C.27779
D.27767
Answer: A.120000
Explanation: X * (105/100) * (105/100) * (105/100) = 138915
X = 138915/1.157625
X = 120000
Answer: A
Question: Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 6, what is the probability that one of the two cards drawn is numbered 3 ?
A.1/3
B.1/2
C.1/5
D.3/5
Answer: C.1/5
Explanation: (5,1) (1,5) (4,2) (2,4) (3,3) – only 5 possible scenarios for sum to be 6. One from this 5 has already happened.
From this five cases, only in one we have 3. So, the probability is 1 chances out of 5 that the one that occurred had 3: P=1/5.
Answer: C.
Question: Three independent strategies A, B and C have been initiated for cost cutting in a company producing respectively 40%, 40% and 10% savings. Assuming that they operate independently, what is the net saving achieved?
A.56%
B.67.6%
C.62.2%
D.68%
Answer: B.67.6%
Explanation: If initial cost is Rs 100, then
Final cost will be 100*0.6*0.6*0.9 = Rs. 32.4
savings = 100-32.4=67.6
so 67.6%
ANSWER:B
Question: There are two names given JOHNSON and JONES. If one letter is picked from both simultaneously at random, then find the probability that the letter is same?
A.24/35
B.17/35
C.8/25
D.6/35
Answer: D.6/35
Explanation: This question can also be solved by using 'brute force' - you just have to 'map out' the possibilities.
The nameJohnsonhas 7 letters and the nameJoneshas 5 letters, so there are (7)(5) = 35 possible pairings of letters that can occur.
Of those 35, the pairings that include the SAME letter both times are:
J and J
1st O and O
1st N and N
S and S
2nd O and O
2nd N and N
Total: 6
So the probability that the two randomly selected letters will match is 6/35.
D
Question: the age of man is three time the sum of the age of his two sons. Five years hence, his age will be double of the sum of the ages of his sons. the father’s present age is :
A.40 year
B.45 year
C.50 year
D.55 year
Answer: B.45 year
Explanation: Solution
Let the sum of present ages of the two sons be x years.
Then, father's present age = 3x years.
∴ (3x + 5) = 2 (x + 10) ⇔ 3x + 5 = 2x + 20 ⇔ x = 15.
Hence, father's present age = 45 years. Answer B
Question: In a mixture of 60 liters, the ratio of milk and water is 2:1. What amount of water must be added to make the ratio of milk and water as 1:2?
A.76 liters
B.16 liters
C.60 liters
D.16 liters
Answer: C.60 liters
Explanation: 2:1 --- 60
1:2
2:4
---------------
3
3 ----------- 60
3 ----------- ? => 60 liters
Answer: C
Question: The S.I. on a certain sum of money for 3 years at 8% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is?
A.Rs.1718
B.Rs.1729
C.Rs.1750
D.Rs.1724
Answer: C.Rs.1750
Explanation: C.I. = [4000 * (1 + 10/100)2 - 4000]
= (4000 * 11/10 * 11/10 - 4000) = Rs. 840.
Sum = (420 * 100)/(3 * 8) = Rs.1750
Answer:C
Question: Three workers have a productivity ratio of 1 to 2 to 4. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 9th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest?
A.12 to 1
B.6 to 1
C.5 to 1
D.20 to 3
Answer: D.20 to 3
Explanation: The fastest worker who does 4 units of job worked for all 10 hours, so he did 4*10=40 units of job;
The slowest worker who does 1 unit of job worked for only 4+2=6 hours (first 4 hours and last 2 hours), so he did 1*6=6 units of job;
The ratio thus is 40 to 6, or 20 to 3.
Answer: D
Question: In a hostel there were 100 students. To accommodate 10 more students the average is decreased by rupees 5. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?
A.A)Rs.5800
B.B)Rs.9900
C.C)Rs.5400
D.D)Rs.5900
Answer: B.B)Rs.9900
Explanation: 100x + 400
= 110(x – 5)
x = 95
100 * 95 + 400
= 9900
Answer:B
Question: A person incurs 5% loss by selling a watch for $1140. At what price should the watch be sold to earn 5% profit?
A.$1260
B.$1200
C.$1150
D.$1320
Answer: A.$1260
Explanation: Let the new S.P. = x
then (100-loss%): (1st S.P.) = (100+gain%): (2nd S.P.)
(100-5)/1140 = (100+5)/x
x=105*1140/95 = 1260
new price = $1260
correct option is A
Question: An escalator moves towards the top level at the rate of 15 ft.sec and its length is 200 feet. If a person walks on the moving escalator at the rate of 5 feet per second towards the top level, how much time does he take to cover the entire length.
A.5sec
B.10sec
C.20sec
D.15sec
Answer: B.10sec
Explanation: Explanation :
Time taken to cover the entire length = tot.dist/resultant speed = 200/ (15+5) = 10sec
Answer : B
Question: There are 7 red shoes & 3 green shoes . If two of red shoes are drawn what is the probability of getting red shoes
A.1/13
B.1/14
C.1/15
D.7/15
Answer: D.7/15
Explanation: taking 2 red shoe the probablity is 7C2
from 10 shoes probablity of taking 2 red shoe is 7C2/10C2=7/15
ANSWER:D
Question: A shipment of 230 smartphones contains 84 that are defective. If a customer buys two smartphones at random from the shipment, what is the approximate probability that both phones are defective?
A.1/250
B.1/84
C.1/11
D.9/68
Answer: D.9/68
Explanation: Probability of chosing one defective phone from a lot of 230 which ontains 84 defective phones is = (84/230)
Probability of chosing one defective phone from a lot of 229(we already picked one) which ontains 83(we already picked one) defective phones is = (83/229)
Combined probability of series of events = product of the probabilities = (84/230)*(83/229)
84/230 is close to (23/63) and (83/229)= (29/80)
so answer is (23/63)*(29/80) = (9/68)
So, answer will be D
Question: John and Jane went out for a dinner and they ordered the same dish. Both used a 10% discount coupon. John paid a 15% tip over the original price of the dish, while Jane paid the tip over the discounted price for the coupon. If John paid $0.54 more than Jane, what was the original price of the dish?
A. 24
B. 34.8
C. 36
D. 42
Answer: C. 36
Explanation: The difference between the amounts John paid and Jane paid is the deference between 15% of p and 15% of 0.9p:
0.15p - 0.15*0.9p = 0.54 --> 15p - 13.5p = 54 --> p = 36.
Answer: C.
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
A.372
B.375
C.278
D.267
Answer: B.375
Explanation: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
75 ----- ? => 375
Answer:B
Question: Mixture A is 25 percent milk, and mixture B is 65 percent milk. If the two are poured together to create a 4-gallon mixture that contains 40 percent milk, approximately how many gallons of mixture A are in the mixture?
A.1.5
B.1.75
C.2.85
D.2.5
Answer: C.2.85
Explanation: (65-40)/(40-25) = Qa/Qb
25/15 = Qa/Qb
5/3 = Qa/Qb
Qa = (5/7) * 4 = 20/7 = 2.85 approx
Answer : C
Question: In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible score K that Lindsey could have received on her midterm exam?
A.52%
B.64%
C.72%
D.76%
Answer: A.52%
Explanation: If the midterm counts for 25% of the total grade, then the final exam must count for the remaining 75%, meaning that in this weighted average problem the final is weighted 3 times as much as the midterm. Using the weighted average mapping strategy, then, and maximizing her final exam score so that you minimize her midterm score, you have:
100-------------88----------------------------x
And you know that the ratio is 3:1. Since the final exam score of 100 is weighted heavier, then the difference of 12 between 100 and 88 is the1part of the ratio, meaning that 3(12) is the 3 portion. That equals 36, so the midterm score (x) is 36 less than the weighted average of 88. 88 - 36 = 52, sothe correct answer is 52%.
Question: There are 11 dozen mangoes in a box. If there are 16
such boxes, how many mangoes are there in all the
boxes together?
A.2112
B.3096
C.6192
D.628
Answer: A.2112
Explanation: Number of mangoes = 11 dozens
= 11 × 12 = 132
∴ Number of mangoes in 16 boxes
= 16 × 132 = 2112
Answer A