RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Points A, B, and, C have xy-coordinates (2,0), (8,12), and (14,0), respectively. Points X, Y, and Z have xy-coordinates (6,0), (8,4), and (10,0), respectively. What fraction D of the area of triangle ABC is the area of triangle XYZ?
A. 1/9
B. 1/8
C. 1/6
D. 1/5
Answer: A. 1/9
Explanation: If you notice, both triangles ABC and XYZ have a side on X axis. we can take these sides as bases for each triangle, therefore
Area of ABC is 1/2*12*12 (Height of ABC is the y coordinate of the third point (8,12))
similarly Area of XYZ is 1/2*4*4
dividing area of XYZ with that of ABC gives D=1/9.A
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
A.229
B.240
C.288
D.277
Answer: B.240
Explanation: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x = 240 m.
Answer: B
Question: The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is?
A.24 kg
B.62 kg
C.34 kg
D.31 kg
Answer: D.31 kg
Explanation: Let A, B, C represent their respective weights.
Then, we have:
A + B + C = (45 * 3) = 135 --- (i)
A + B = (40 * 2) = 80 --- (ii)
B + C = (43 * 2) = 86 --- (iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 --- (iv)
Subtracting (i) from (iv), we get: B = 31
B's weight = 31 kg.
Answer:D
Question: A jar contains only three types of objects: red, blue, and silver paper clips. The probability of selecting a red paper clip is 1/3, and the probability of selecting a blue paper clip is 3/5. What is the probability of selecting a silver paper clip?
A. 1/12
B. 2/15
C. 7/15
D. 3/4
Answer: B. 2/15
Explanation: Prob of Red = 1/3
Prob of Blue = 3/5
Prob of Silver = ?
P(Silver) = 1 - P(Red) - P(Blue) ==> 1-1/3-3/5 = 1/15
Ans: B
Question: A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 2x km.
A.16kmph
B.20kmph
C.25kmph
D.30kmph
Answer: A.16kmph
Explanation: Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 2x/(x/8)
= 16 kmph
Answer:A
Question: A1, A2 and A3 enter into a partnership in the ratio 7/2 : 4/3 : 6/5 . After 4 months, A1 increases his share 50%. If the total profit at the end of one year be Rs. 21,600, then A2's share in the profit is:
A.3000
B.3200
C.3450
D.4000
Answer: D.4000
Explanation: Ratio of initial investments = 7/2 : 4/3 : 6/5
= 105 : 40 : 36.
Let the initial investments be 105x, 40x and 36x.
=> A1 : A2 : A3 = 105x x 4 + 150/100 x 105x x 8 : (40x x 12) : (36x x 12)
= 1680x : 480x : 432x
= 35 : 10 : 9.
Hence, A2's share = Rs. 21600 x 10/54
= Rs. 4000. Answer : D
Question: A lady builds 10cm length, 18cm width, and 4cm height box using 12cubic cm cubes. What is the minimum number of cubes required to build the box?
A.107
B.70
C.78
D.60
Answer: D.60
Explanation: Number of cubes required = Volume of box/Volume of cube
= 10*18*4/12
=60 cubes
ANSWER:D
Question: At a local supermarket, a box of cereal usually costs 18 dollars. This week, the supermarket sells the box of cereal for 12 dollars. How much money will you save if you buy this cereal at this supermarket?
A.5 dollars
B.3 dollars
C.6 dollars
D.2 dollars
Answer: C.6 dollars
Explanation: Solution:
In this situation, there is a decrease in the price.
Saving = 18 - 12 = 6 dollars
Option C
Question: A person covered one-fourth of the total distance at 20 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?
A.21 (6/7)kmph
B.22 (6/7)kmph
C.21 (7/3)kmph
D.27 (6/7)kmph
Answer: B.22 (6/7)kmph
Explanation: Let the total distance be x km
total time taken = (x/4)/20 + (3x/4)/24 = x/80 + x/32 = 7x/160
Average speed = x/(7x/160) = 160/7kmph
= 22 (6/7)kmph.
Answer:B
Question: 3 Years ago, the average age of a family of 5 members was 16 years. A baby having been born, the average age of the family is the same today. The present age of the baby is
A.1 year.
B.1.5 Years.
C.2 Years.
D.3 Years.
Answer: A.1 year.
Explanation: We're told that 3 YEARS AGO, the average age of a family of 5 members was 16 years.
This means that the SUM of their ages was (5)(16) = 80 years.
A baby was born (meaning that there are now 6 family members). We're told that the PRESENT average age of the family members is the SAME.
This means that the sum of the ages is (6)(16) = 96 years.
We're asked for the PRESENT age of the baby.
Since each of the original 5 family members has aged 3 years since the initial average was calculated, the sum of their PRESENT ages is...
80 + (5)(3) = 95.
A
Question: After spending 40 percent machinery, 25 percent inbuilding , 15 percent in raw material and 5 percent on furniture. John had a balance of Rs.1305. Total money with him was?
A.7600
B.8700
C.9000
D.9200
Answer: B.8700
Explanation: [100 - (40+25+5+15)] % of x = 1305
\inline \Rightarrow 15% of x =1305
\inline \Rightarrow \frac{15}{100}\times x=1305
\inline \therefore x=\frac{1305\times 100}{15}=8700
B
Question: Last year, sales at Company Zora were 12% greater in February than in January, 15% less in March than in Feb, 30% greater in April than in March, 10% less in May than in April, and 5% greater in June than in May. In which month were sales closest to Jan?
A.April
B.March
C.May
D.Feb
Answer: B.March
Explanation: Jan = $100
12% greater in February than in January ---> Feb = $112
15% less in March than in Feb ---> Mar = $95.2
30% greater in April than in March ---> Apr = $123.76
10% less in May than in April ---> May $111.38
5% greater in June than in May --->Jun = $116.95
Answer : B
Question: From 6 officers and 10 clerks in how many can 5 be chosen to include exactly one officer?
A.1452
B.1562
C.2456
D.1260
Answer: D.1260
Explanation: Required number of ways = 6C1 * 10C4 = 1260
Answer is D
Question: Sally, Mark, Sarah, Steve and Jim are inheriting the money from their grandmother. She left them $527,500 to split equally between all of them. If the money is split equally, how much money will each person receive?
A.$135,875
B.$52,700
C.$127,900
D.$105,500
Answer: D.$105,500
Explanation: There are 5 people inheriting the money.
We have to take the total of the inheritance and divide it by 5 for each person receiving money.
$527,500 / 5 = $105,500.
Therefore the correct answer is D.
Question: When positive integer N is divided by positive integer D, the quotient is 16, with a remainder of 7. When N is divided by (D + 2), the quotient is 15 and the remainder is 1. What is the value of N?
A.151
B.391
C.511
D.691
Answer: B.391
Explanation: N/D=16 7/D= 16D+7
N/(D+2)=15 1/(D+2)=15D+30+1
solving these two equations
we get D=24 N= 391 answer is B.
Question: If f(2, 4) = 24 and f(1, 5) = 26, what is the value of f(2, 10)?
A.107
B.127
C.147
D.108
Answer: D.108
Explanation: Solution:
The function f(a, b) = a3 + b2
f(2, 4) therefore is = 8 + 16 = 24 and
f(1,5) = 1 + 25 = 26
Therefore, f(2, 10) = 8 + 100 = 108
Answer D
Question: In a college, the ratio of the number of boys to girls is 8 : 5. If there are 300 girls, the total number of
students in the college is
A.420
B.520
C.780
D.620
Answer: C.780
Explanation: Explanation:
Let the boy are 8x and Girls are 5x
=> 5x = 300
=> x = 60
Total students = 8x+5x = 13x = 13(60) = 780
Answer: C
Question: What is the least number of digits (including repetitions) needed to express 10^400 in decimal notation?
A.a) 401
B.b) 100
C.c) 101
D.d) 1000
Answer: A.a) 401
Explanation: 10^n is a decimal number with a 1 followed by n zeros.
So 10^100 will include 400 0's + 1 digit for 1 = 401
So the answer is A
Question: A can give B 50 meters start and C 100 meters start in a kilometer race. How much start can B give C in a kilometer race?
A.111.12
B.111.67
C.111.64
D.52.63
Answer: D.52.63
Explanation: A runs 1000 m while B runs 950 m and C runs 900 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 900)/950 =947.37 m.
B can give C = 1000 - 947.37= 52.63m.
Answer:D
Question: A powder tin has a square base with side 8 cm and height 14 cm. Another tin has a circular base with diameter 8 cm and height 14 cm. The difference in their capacities is :
A.168 cm³
B.192 cm³
C.228 cm³
D.236 cm³
Answer: B.192 cm³
Explanation: Sol.
Difference in capacities = [8 * 8 * 14 - 22/7 * 4 * 4 * 14] cm³
= 192cm³
Answer B
Question: The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?
A.8
B.2
C.9
D.4
Answer: A.8
Explanation: Explanation:
[15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 96
15000[(1 + R/100)2 - 1 - 2R/100] = 96
15000[(100 + R)2 - 10000 - 200R]/10000 = 96
R2 = (96 * 2)/3 = 64 => R = 8
Rate = 8%
Answer: Option A
Question: 0, 1, 4, 15, 64, ____
A.225
B.325
C.125
D.145
Answer: B.325
Explanation: 0,1,4,15,64.....
0*1+1=1
1*2+2=4
4*3+3=15
15*4+4=64
64*5+5=325
ANSWER:B
Question: Mangala completes a piece of work in 14 days, Raju completes the same work in 30 days. If both of them work together, then the number of days required to complete the work is?
A.8 3/4 days
B.10 1/2 days
C.9 1/2 days
D.12 1/4 days
Answer: C.9 1/2 days
Explanation: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 14 × 30/44 = 9 1/2 days
C)
Question: A 4" cube is painted in all its faces and then it is cut down into 1" blocks. How many 1" blocks
are there even without a single face being painted?
A.7 blocks
B.8 blocks
C.9 blocks
D.10 blocks
Answer: B.8 blocks
Explanation: 4" cube is painted in all its faces and then it is cut down into 1" blocks.
Totally, 64 - 1" blocks
3 sides Painted are - 8 blocks
2 sides Painted are - 24 blocks
1 sides Painted are - 24 blocks
without a single face being Painted are - 8 blocks
ANSWER:B
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
A.1000
B.2090
C.2882
D.2770
Answer: A.1000
Explanation: 90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000
Answer: A
Question: Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 570 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)
A.8/3
B.3/8
C.38/15
D.5/8
Answer: C.38/15
Explanation: Distance traveled by Eddy = 570 km
Time taken by Eddy = 3 hours
Average speed of Eddy = 570/3 = 190 km/hour
Distance traveled by Freddy = 300 km
Time taken by Freddy = 4 hours
Average speed of Freddy = 300/4 = 75 km/hour
Ratio of average speed of Eddy to Freddy = 190/75 = 38/15
Answer C
Question: ?% of 360 = 180
A.277
B.36
C.50
D.72
Answer: C.50
Explanation: ?% of 360 = 180
or, ? = 180×100/360=50
Answer C
Question: Every year Taylor goes to the same carnival, and he attempts to shoot a basketball into a small hoop, hoping that he will win a ten-foot tall teddy bear. If the probability that Taylor does not make a basket is 8/15, what is the probability that Taylor makes exactly one basket in three tries?
A.45/120
B.45/113
C.45/130
D.35/130
Answer: B.45/113
Explanation: Probability of basket = 7/15
Probability of no basket = 8/15
Required probability= 3* 7/15*8/15*8/15=45/113
B is the answer .
Question: What least number should be added to 1536, so that the sum is completely divisible by 21?
A.16
B.17
C.18
D.19
Answer: C.18
Explanation: 1536÷21=73 Reminder -3
3+18 =21
Hence 18 should be added to 1536 so that the sum will be divisible by 21
answer :C
Question: A factory produces 5505 toys per week. If the workers at this factory work 5 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?
A.4436 toys
B.5487 toys
C.1101 toys
D.2354 toys
Answer: C.1101 toys
Explanation: To find the number of toys produced every day, we divide the total number of toys produced in one week (of 5 days) by 5.
5505 /5 = 1101 toys
correct answer C
Question: If A:B = 1/2: 1/3 B:C = 1/2:1/3 then A:B:C?
A.9:6:6
B.9:6:8
C.9:6:2
D.9:6:4
Answer: D.9:6:4
Explanation: A:B = 1/2:1/3 = 3:2
B:C = 1/2:1/3 = 3:2
--------------------
A:B:C = 9:6:4
Answer:D:
Question: How much time will it take for an amount of Rs. 600 to yield Rs. 12 as interest at 2% per annum of simple interest?
A.8 years
B.4 years
C.7 years
D.1 years
Answer: D.1 years
Explanation: Explanation:
Time = (100 x 12)/(600 x 2) years
= 1 years.
Answer: D
Question: In the following questions, the following letters indicate mathematical operations as indicated below:
A: Addition; V: Equal to; S: Subtraction; W:Greater than; M: Multiplication; X: Less than; D: Division
Find Out of the four alternatives given in these questions, only one is correct according to the above letter symbols. Identify the correct one.
A.6 S 7 A 2 M 3 W 0 D 7
B.6 A 7 S 2 M 3 W 0 A 7
C.6 S 7 M 2 S 3 W 0 M 7
D.6 M 7 S 2 A 3 X 0 D
Answer: A.6 S 7 A 2 M 3 W 0 D 7
Explanation: Explanation:By BODMAS rule
6 – 7 + 3 × 2 > 0/7
Answer: A
Question: A furniture manufacturer has two machines, but only one can be used at a time. Machine S is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine S can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule?
A.14
B.13
C.11
D.9
Answer: D.9
Explanation: 'Approximately' could actually make such a question ambiguous. Not this one though but a similar question with the answer as 9.2 days. You round off 8.89 days as 9 days and everything is fine in this question. What do you do when you get 9.2 days? Do you need 9 days or 10 days? Can you round off 9.2 as 9 even though that is what you do with numbers? No, because in 9 days your work is not over. You do need 10 days.
To finish a work say Machine S you need to work full 9 days and a part of the 10th day. If I ask you how many days do you need to complete the work, will you say 9 or 10? You will say 10 even if you don't use the 10th day fully=D
Question: Lorna invests $5000, with some at 6% annual interest and some at 11% annual interest. If she receives a total of $580 from these investments at the end of a year, how much was invested at the 6% interest rate?
A.$1,000
B.$1,600
C.$2,200
D.$4,400
Answer: A.$1,000
Explanation: We have that 'x' invested at 6%
We also have that '6000-x' invested at 11%
Now then 580/5000 is approx 10%
Therefore, -4x+5000-x=0
5x=5000
x=1000 approximately. Probably higher
Only A matches
Question: The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 300,000 bacteria
A.10
B.12
C.14
D.16
Answer: D.16
Explanation: The question basically asks how many minutes it takes for a population to increase by factor 300 (300,000 / 1,000 = 300).
Now you know that every two minutes the population doubles, i.e. is multiplied by 2. So the equation becomes:
2^x >= 300, where x represents the number of times the population doubles. A lot of people remember that 2^10 = 1,024. Hence, 2^8 = 256, i.e. the population has to double 8 times.
Since it takes the population 2 minutes to double once it takes 8*2 minutes = 16 minutes to double 8 times.
Thus, solution D = 16 is correct.
Question: In what time will a train 90 meters long cross an electric pole, if its speed is 124 km/hr
A.5 seconds
B.4.5 seconds
C.3 seconds
D.2.6 seconds
Answer: D.2.6 seconds
Explanation: Explanation:
First convert speed into m/sec
Speed = 124*(5/18) = 34 m/sec
Time = Distance/speed
= 90/34 = 2.6 seconds
Option D
Question: Find the number which when multiplied by 15 is increased by 196
A.10
B.12
C.14
D.16
Answer: C.14
Explanation: Explanation:
Let the number be x.
Then, 15x = x + 196
=› 14 x= 196
=› x = 14.
Option C
Question: Company C produces toy trucks at a cost of $5.00 each for the first 100 trucks and $3.50 for each additional truck. If 500 toy trucks were produced by Company C and sold for $9.00 each, what was Company C’s gross profit?
A. $2,250
B. $2,900
C. $2,600
D. $3,250
Answer: C. $2,600
Explanation: Cost of 500 trucks: (100 * 5 ) + (400 * 3.5) = 500 + 1400 =$ 1900
Revenue : 500 * 9 = $4500
Profit: 4500 - 1900 = $ 2600
Option C is correct
Question: A tank holds x gallons of a saltwater solution that is 20% salt by volume. One Fourth of the water is evaporated, leaving all of the salt. When 7 Gallons of water and 14 gallons of salt are added, the resulting mixture is 33 1/3 % salt by volume. What is the value of x?
A.37.5
B.75
C.105
D.150
Answer: C.105
Explanation: Nope, 150. I can only get it by following PR's backsolving explanation. I hate that.
Original mixture has 20% salt and 80% water.
Total = x
Out of which Salt = 0.2x and water = 0.8x
Now, 1/4 water evaporates and all salt remains.
So what remains is 0.2x salt and 0.6x water.
Now 14 gallons salt is added and 7 gallons of water is added.
So salt now becomes -> (0.2x + 14) and water --> (0.6x+7)
Amount of salt is 33.33% of total. So amount of water is 66.66%. So salt is half of the volume of water.
So (0.2x+14) = (0.6x+7)/2 = > 0.2x = 21
Solving, x = 105
Answer : C
Question: Find the cost of fencing around a circular field of diameter 30m at the rate of Rs.1.50 a meter?
A.A)Rs.150
B.B)Rs.141.37
C.C)Rs.100
D.D)Rs.125
Answer: B.B)Rs.141.37
Explanation: 2 * 22/7 * 15 = 94.24
94.24 * 1 1/2 = Rs.141.37
ANSWER:B
Question: The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8450. If his salary for the month of May is Rs.6500, find his salary for the month of January?
A.2177
B.2876
C.4700
D.2981
Answer: C.4700
Explanation: Sum of the salaries of the person for the months of January, February, March and April = 4 * 8000 = 32000 ----(1)
Sum of the salaries of the person for the months of February, March, April and May = 4 * 8450 = 33800 ----(2)
(2)-(1) i.e. May - Jan = 1800
Salary of May is Rs.6500
Salary of January = Rs.4700.Answer: C
Question: What is the next number in the sequence below?
1 4 9 16 25 36 49 __ ?
A.64
B.46
C.47
D.48
Answer: A.64
Explanation: as the series of numbers are squares of numbers
1^2=1
2^2=4
3^2=9
and so on
therefore 8^2=64
ANSWER:A
Question: In a group of 6 boys&4 girls a Committee of 4 persons is to be formed. In how many different ways can it be done so that the committee has at least 1girl?
A.110
B.120
C.140
D.195
Answer: D.195
Explanation: The committee of 4 persons is to be so formed that it has at least 1 woman The different ways that we can choose to form such a committee are:
(i) lw. 3 m in t 6X5X4' x 6C3 = 4x — — 80 3X2X1
x 6c2 =42:: x 26:: = 90 (ii) 2w. 2 m in °C2 (iii) 3w. 1 m in 4C3 x 6C1 = 4 x 6 = 24 (iv) 4w in 6C4 = 1 Total no. of different ways in which a committee of 4 persons can be formed so that it has at least one woman. = 80 + 90 + 24 + 1 = 195
D
Question: Out of 19 students studying in a class, 7 are from Maharashtra, 5 are from Karnataka and 3 are from Goa. Four students are to be selected at random. What are the chances that at least one is from Karnataka?
A.12â„13
B.11â„13
C.10â„15
D.23/31
Answer: D.23/31
Explanation: Total possible ways of selecting 4 students out of 19 students = 19C4 = 3876
The no. of ways of selecting 4 students in which no student belongs to Karnataka = 14C4=1001
âˆ´ Hence no. of ways of selecting at least one student from Karnataka = 19C4 â€“ 14C4 = 2875
âˆ´ Probability = 2875â„3876 = 23/31
Answer D
Question: For the real value of x what is the maximum value of |x+2|+|x-1|-|2x-4|=?
A.2
B.3
C.4
D.5
Answer: D.5
Explanation: value of expression will be maximum if mod(2x-4) will give minimum value
so 2x-4=0
x=2
maximum value=mod(2+2)+mod(2-1)-0=5
ANSWER:D
Question: In order to obtain an income of Rs. 650 from 10% stock at Rs. 96, one must make an investment of:
A.3100
B.6240
C.6500
D.9600
Answer: B.6240
Explanation: To obtain Rs. 10, investment = Rs. 96.
To obtain Rs. 650, investment = Rs. (96X650)/10 =6240 Answer: B
Question: Ram professes to sell his goods at the cost price but he made use of 900 grms instead of a kg, what is the gain percent?
A.11 1/5%
B.11 1/4%
C.11 1/9%
D.11 8/9%
Answer: C.11 1/9%
Explanation: 900 --- 100
100 --- ? => 11 1/9%
Answer: C
Question: -45*29+108=?
A.1197
B.1897
C.-1197
D.-1900
Answer: C.-1197
Explanation: => -45*(30-1)+108;
=> -(45*30)+45+108;
=> -1350+153=-1197.
Correct Option: C
Question: Farm Tax is levied on the 40% of the cultivated Land. The tax department collected total $ 3840 through the farm Tax from the village of Mr. willam. Mr. willam paid only $ 480 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is :
A.31.25%
B.25%
C.12.5%
D.0.2083%
Answer: A.31.25%
Explanation: Only trick n this question is to ignore 40% information as farm tax is levied uniformly in the village and that includes Mr William's land.
What percentage of tax Mr William paid ? 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 (100/40) = 31.25% and the answer is not there in the options.
The correct answer is (A).
Question: You have a flashlight that takes 2 working batteries. You have 8 batteries but only 4 of them work.
What is the fewest number of pairs you need to test to guarantee you can get the flashlight on?
A.5
B.8
C.7
D.6
Answer: C.7
Explanation: If you break the batteries into 3 groups: Two groups of 3 and one group of 2. By doing this you guarantee that one of the groups has 2 working batteries. Both of the groups of 3 have 3 possible combinations of 2 batteries and the group of 2 only has 1 combination. So, 3 + 3 + 1 = 7 tries at most to find two working batteries.
Question: What is the sum of all the composite numbers up to 20?
A.130
B.132
C.124
D.145
Answer: B.132
Explanation: 4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 = 132
ANSWER B
Question: A certain music store stocks 800 cellos and 600 violas. Of these instruments, there are 120 cello-viola pairs, such that a cello and a viola were both made with wood from the same tree (each tree can make at most one viola and one cello, so there are no pairs other than these 90). If one viola and one cello are chosen at random, what is the probability that the two instruments are made with wood from the same tree?
A.3/16,000
B.1/8,000
C.3/1,600
D.1/90
Answer: B.1/8,000
Explanation: Solution provided by stanford2012 is correct: 120/800 choosing one of the cellos which has a pair viola, 1/600 choosing the viola which is the pair of chosen cello --> P=120/800*1/600=1/8,000.
Answer: B.
Question: 1,000^2 + 1,001^2 +1,002^2 =
A.6,030,053
B.6,030,054
C.6,006,005
D.6,030,056
Answer: C.6,006,005
Explanation: Interesting problem.
I think key is to notice that all the given answer choices differs in last two digits. Therefore, our entire focus should be to figure out how the given terms contribute to last two digits of total.
1000^2 -> 00
1001^1 -> 01
.
.
.
1002^2 -> 5
Total -> *5
Answer C.
Question: f two positive numbers are in the ratio 1/8 : 1/5, then by what percent is the second number more than the first?
A.50%
B.80%
C.60%
D.84%
Answer: C.60%
Explanation: Given ratio = 1/8 : 1/5 = 5 : 8
Let first number be 5x and the second number be 8x.
The second number is more than first number by 3x.
Required percentage = 3x/5x * 100 = 60%.
Answer:C
Question: How many 3-digit numbers are completely divisible 6 ?
A.149
B.150
C.151
D.166
Answer: B.150
Explanation: 3-digit number divisible by 6 are: 102, 108, 114,... , 996
This is an A.P. in which a = 102, d = 6 and l = 996
Let the number of terms be n. Then tn = 996.
a + (n - 1)d = 996
102 + (n - 1) x 6 = 996
6 x (n - 1) = 894
(n - 1) = 149
n = 150
Number of terms = 150.
Answer: B