RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: 894.7 – 573.07 – 95.007 = ?
A.226.623
B.224.777
C.233.523
D.414.637
Answer: A.226.623
Explanation: Solution
Given expression = 894.7 - (573.07 + 95.007) = 894.7 - 668.077 = 226.623. Answer A
Question: A train when moves at an average speed of 60 kmph, reaches its destination on time. When its average speed becomes 45 kmph, then it reaches its destination 30 minutes late. Find the length of journey.
A.70 km
B.76 km
C.85 km
D.90 km
Answer: D.90 km
Explanation: Explanation :
Solution: Difference between timings = 30 min. = 30/60 hr = 1/2 hr.
Let the length of the journey be x km.
Then, x/45 - x/60 = 1/2
=> 4x -3x = 180/2
=> x = 90 km.
Answer : D
Question: A certain sum of money is divided among A, B and C so that for each Rs. A has, B has 65 paisa and C 40 paisa. If C's share is Rs.40, find the sum of money?
A.782
B.276
C.727
D.205
Answer: D.205
Explanation: A:B:C = 100:65:40
= 20:13:8
8 ---- 40
41 ---- ? => Rs.205
Answer:D
Question: In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?
A.8 sec
B.7 sec
C.2 sec
D.6 sec
Answer: D.6 sec
Explanation: T = 60/36 * 18/5
= 6 sec
Answer:D
Question: Camel and carriage for Rs. 5000. He SP the camel at a gain of 20% and the carriage at a loss of 10%. If he gains 3% on the whole, then find the CP of the camel?
A.Rs.2166.67
B.Rs.2224
C.Rs.2270.72
D.Rs.2145
Answer: A.Rs.2166.67
Explanation: Now, in this numerical, there is no common loss and gain %.
Hence, solve it making equations.
Let cost price of camel be x.
As cost of camel and carriage = Rs 5000
Cost of carriage = Rs. (5000 – x)
After selling camel he gains 20% and on carriage a loss of 10%. But on the whole he gains 3%.
Therefore,
20% of x – 10 % of (5000 – x) = 3 % of 5000
20 × x – 10 × (5000 – x) = 3 × 5000
100 100 100
x – (5000 – x) = 150
5 10
10x – (5000 – x) × 10 = 150 × 10
5 10
2x-5000+x=1500
3x=1500+5000
x=2166.67
The cost of camel = Rs.2166.67
Option (A) is the correct answer
Question: The roots of the equation axpower2 + bx + c =0 will be reciprocal if:
A.a=b
B.a-bc
C.c=a
D.c=b
Answer: C.c=a
Explanation: based on the problem 1/k will be the other root of the given equation. root equation = c/a. k*1/k=c/a. c/a= 1 or a = c[multiplying on both sides].
the roots of the equation axsquared + bc + c= 0 will be reciprocal if a= c. correct answer: (C)
Question: a plane travelled k miles in 1st 96 miles of flight time.if it completed remaining 300 miles of the trip in 1 minute what is its average speed in miles/hr for entire trip ?
A.396/60+k
B.376/60+k
C.386/60+k
D.366/60+k
Answer: A.396/60+k
Explanation: k=96+300
tot distance= 396 miles
tot time= 1min + k
avg speed= 396/60+k
ANSWER:A
Question: In a function they are distributing noble prize. In how many ways can 2 prizes be distributed among 5 boys when a boy gets any no. of prizes?
A.25
B.30
C.64
D.70
Answer: A.25
Explanation: Ans.(A)
Sol. In this case, repetitions are allowed, so all the two prizes can be given in 5 ways, i.e. (5 x 5) ways = 52 ways = 25 ways Or nr ways = 52 ways = 25 ways
Question: The speed of a boat in upstream is 40 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
A.20 kmph
B.13 kmph
C.65 kmph
D.55 kmph
Answer: A.20 kmph
Explanation: Speed of the boat in still water
= (40+80)/2
= 60 kmph. Speed of the stream
= (80-40)/2
= 20 kmph.
Answer: A
Question: There are 12 intermediate stations between two places A and B. Find the number of ways in which a train can be made to stop at 4 of these intermediate stations so that no two stopping stations are consecutive?
A.108
B.112
C.126
D.140
Answer: C.126
Explanation: Explanation :
Initially, let's remove the 4 stopping stations
Then we are left with 8 non-stopping stations (=12-4) as shown below
(non-stopping stations are marked as 1,2 ... 8)
Now there are 9 positions (as marked by * in the above figure) to place the 4 stopping stations
such that no two stopping stations are consecutive
This can be done in 9C4 ways
Hence, required number of ways = 9C4
=((9)(8)(7)(6)/(4)(3)(2)(1))=126
Answer C
Question: If,
1 * 3 * 5 = 16
3 * 5 * 7 = 38
Then find,
5 * 6 * 9 =?
A.65
B.59
C.72
D.80
Answer: B.59
Explanation: (9 * 6) + 5 = 59
B
Question: Some numbers are very mysterious. They are all integers. They have more than one digit. If you multiply them with 2 their digits may shift ,but no new digit will include or no digit will disappear. Example: 12 is not such a number. Because if you multiply 2 with 12, it will become 24. And 24 includes a new digit 4 ,and fails to obtain the previous digit 1. Can you find one of them?
A.138687
B.142587
C.144487
D.142667
Answer: B.142587
Explanation: B
142587
142587*2=285174
These type of numbers are called cyclic numbers where a number multiplied by any digit the result will contain all the digit in the original number and no other digit.
cyclic numbers are generated by full reptend prime 7,17,19,23 etc.
where 1/7=0.142857……
1/17=0.058823529411764
Question: Find the lowest common multiple of 25, 35 and 50.
A.350
B.420
C.510
D.320
Answer: A.350
Explanation: LCM=2*5*5*7=350.
Answer is A
Question: Two pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
A.20 hours
B.15 hours
C.10 hours
D.12 hours
Answer: A.20 hours
Explanation: Part filled by A in 1 hour = 1/36
Part filled by B in 1 hour = 1/45
Part filled by (A+B) in 1 hour = 1/36 + 1/45 = 9/180 = 1/20
Both the pipes together fill the tank in 20 hours
Answer is A
Question: A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount was offered?
A.60%
B.37%
C.30%
D.80%
Answer: C.30%
Explanation: Let C.P. be Rs. 100.
Then, S.P. = Rs. 123.50
Let marked price be Rs. x. Then, 95/100 x = 123.50
x = 12350/95 = Rs. 130
Now, S.P. = Rs. 130, C.P. = Rs. 100
Profit % = 30%.
Answer & Answer:C
Question: Two mechanics were working on your car. One can complete the given job in 5 hours, but the new guy takes eight hours. They worked together for the first two hours, but then the first guy left to help another mechanic on a different job. How long will it take the new guy to finish your car?
A.7/4
B.4/3
C.14/5
D.10/3
Answer: C.14/5
Explanation: Rate(1)=1/5
Rate(2)=1/8
Combined = 13/40
Work done in 2 days=13/20
Work left = 7/20
Rate * Time = Work left
1/8 * Time = 7/20
Time=14/5
C
Question: An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week she sold 5 more pairs of soft lenses than hard lenses. If her total sales for pairs of contact lenses last week were $1,455, what was the total number of pairs of contact lenses that she sold?
A. 11
B. 13
C. 15
D. 17
Answer: A. 11
Explanation: (x+5)*150 +x*85=1455
=>x=3
total lens=3+(3+5)= 11
Answer A
Question: What would be the compound interest on an amount of Rs.5500 at the rate of 5 p.c. per annum after 2 years?
A.610.25
B.573.85
C.563.75
D.420.5
Answer: C.563.75
Explanation: CI=P[(1+(R/100))^T-1]
=5500*[(1+(5/100))^2-1]
=5500*[(1.05)^2-1]
=5500*0.1025
=Rs.563.75
Option C
Question: Eight percent of the programmers in a startup company weigh 200 pounds or more. Twenty-five percent of the programmers that are under 200 pounds in that same company weigh 100 pounds or less. What percent of the programmers in the startup company weigh between 100 and 200 pounds?
A.15%
B.20%
C.25%
D.69%
Answer: D.69%
Explanation: Initially 92% and 8% split
80% is further divided as 25% and 75%
Q is asking about that 75%
let total be '100' then that 75% is (3/4)∗92
so, the required % is [(3/4)∗92/100]∗100 = 69%
ANSWER:D
Question: A water tank is one-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how many minutes will it take to empty or fill the tank completely?
A.3
B.6
C.9
D.12
Answer: A.3
Explanation: The combined rate of filling/emptying the tank = 1/10 - 1/6 = -1/15
Since the rate is negative, the tank will be emptied.
A full tank would take 15 minutes to empty.
Since the tank is only one-fifth full, the time is (1/5) * 15 = 3 minutes
The answer is A.
Question: The price of 3 pants and 6 t-shirts is Rs. 2250. With the same money one can buy 1 pant and 12 t-shirts. If one wants to buy 8 t-shirts, how much shall she have to pay ?
A.1300
B.1100
C.1000
D.1200
Answer: D.1200
Explanation: Let the price of a pant and a t-shirt be Rs. x and Rs. y respectively.
Then, 3x + 6y = 2250 .... (i)
and x + 12y = 2250 .... (ii)
Divide equation (i) by 3, we get the below equation.
= x + 2y = 750. --- (iii)
Now subtract (iii) from (ii)
x + 12y = 2250 (-)
x + 2y = 750
----------------
10y = 1500
----------------
y= 150
cost of 8 t-shirts = 8*150 = 1200
Answer : D
Question: When the price of an article was reduced by 30% its sale increased by 80%. What was the net effect on the sale?
A.26% increase
B.44% decrease
C.60% increase
D.66% increase
Answer: A.26% increase
Explanation: if n items are sold for $p each, revenue is $np. If we reduce the price by 30%, the new price is 0.7p. If we increase the number sold by 80%, the new number sold is 1.8n. So the new revenue is (0.7p)(1.8n) = 1.26np, which is 1.26 times the old revenue, so is 26% greater.
ANSWER:A
Question: The average expenditure of a labourer for 10 months was 85 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income is
A.180
B.100
C.112
D.110
Answer: C.112
Explanation: Income of 10 months = (10 × 85) – debt
= 850 – debt
Income of the man for next 4 months
= 4 × 60 + debt + 30
= 270 + debt
∴ Income of 10 months = 1120
Average monthly income = 1120 ÷ 10 = 112
Answer C
Question: How many terms are there in 2, 4, 8, 16,..., 512?
A.14
B.11
C.12
D.9
Answer: D.9
Explanation: 2, 4, 8, 16, ..., 512 is a G.P with a =2
and r =4/2 =2
Let the number of terms be n. Then
2 x 2 ^n-1 = 512
or 2^n-1 = 256 = 2^8
Thus n - 1 =8
n= 9
ANSWER:D
Question: The speed of a bus increases by 2 km after every one hour. If the distance travelling in the first one hour was 35 km. what was the total distance travelled in 12 hours?
A.233
B.552
C.376
D.287
Answer: B.552
Explanation: Given that distance travelled in 1st hour = 35 km
and speed of the bus increases by 2 km after every one hour
Hence distance travelled in 2nd hour = 37 km
Hence distance travelled in 3rd hour = 39 km
...
Total Distance Travelled = [35 + 37 + 39 + ... (12 terms)]
This is an Arithmetic Progression(AP) with
first term, a=35, number of terms,n = 12 and common difference, d=2.
The sequence a , (a + d), (a + 2d), (a + 3d), (a + 4d), . . . is called an Arithmetic Progression(AP)where a is the first term and d is the common difference of the AP
Sum of the first n terms of an Arithmetic Progression(AP),Sn=n2[2a+(n−1)d]where n = number of terms
Hence, [35+37+39+... (12 terms)]=S12=122[2×35+(12−1)2]=6[70+22]=6×92=552
Hence the total distance travelled = 552 km
Answer :B
Question: The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
A.2:5
B.2:6
C.2:3
D.2:4
Answer: A.2:5
Explanation: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2
=> h1/h2 = 2/5
i.e. h1 : h2
=2:5
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.120
B.130
C.150
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: When positive integer r is divided by 13, the remainder is 2. When n is divided by 8, the remainder is 5. How many such values are less than 180?
A. 0
B. 1
C. 2
D. 3
Answer: B. 1
Explanation: the equation that can be formed r is 13x+2=8y+5..
13x-3=8y...
as we can see x can take only odd values as the RHS will always be even..
Also x can take values till 13 as 13*14>180..
now we have to substitue x as 1,3,5,7,9,11,13...
once we find 7 fitting in , any other value need not be checked as every 4th value will give us answer so next value will be 15..
ans 1.. B
Question: Torry has submitted 2/5 of his homework assignments, and he received an average grade of 75 for those assignments. If he wishes to receive an average grade of 105 for all his homework assignments, the average grade for Torry's remaining homework assignments must be what percent greater than the average grade for the assignments he has already submitted?
A.15%
B.20%
C.25%
D.66 2/3%
Answer: D.66 2/3%
Explanation: 0.4*75 + 0.6x = 105
30 + 0.6x=107
0.6x = 75
x= 125
125/75= 1.66666...
Ans:D
Question: A block of wood has dimensions 10cm x 10cm x 50cm. The block is painted red and then cut evenly at the 25 cm mark, parallel to the sides, to form two rectangular solids of equal volume. What percentage of the surface area of each of the new solids is not painted red?
A.5.5%
B.8.3%
C.11.6%
D.14.2%
Answer: B.8.3%
Explanation: The area of each half is 100+4(250)+100 = 1200
The area that is not painted is 100.
The fraction that is not painted is 100/1200 = 1/12 = 8.3%
The answer is B.
Question: A board 7ft. 9 inches long is divided into 3 equal parts . What is the length of each part?
A.2 FT 7 IN
B.1 FT 7 IN
C.2 FT 6 IN
D.3 FT 7 IN
Answer: A.2 FT 7 IN
Explanation: Length of board=7ft. 9 inches=(7*12+9)inches=93 inches.
Length of each part = (93/3) inches = 31 inches = 2ft. 7 inches
ANSWER A
Question: In an office, 20 percent of the workers have at least 5 years of service, and a total of 16 workers have at least 10 years of service. If 90 percent of the workers have fewer than 10 years of service, how many of the workers have at least 5 but fewer than 10 years of service?
A. 32
B. 64
C. 50
D. 144
Answer: A. 32
Explanation: (10/100)Workers = 16 = > number of workers = 160
(20/100)*Workers = x+16 = > x = 32
Answer A
Question: a and b are positive integers less than or equal to 8. If a and b are assembled into the six-digit number ababab, which of the following must be a factor of ababab?
A.3
B.4
C.5
D.6
Answer: B.4
Explanation: 484848 when divided by 4 gives the result 121212
CONCEPT: Rule of Divisibility of 4 isIf sum of the digits of the Number is divisible by 4 then the number will be divisible by 2
SUm of the digits of No. which is divisible by 4 hence the Number 121212 will be divisible by 4
B
Question: A right triangle has sides of a, b, and 9, respectively, where a and b are both integers. What is the value of (a + b)?
A.64
B.49
C.96
D.81
Answer: D.81
Explanation: LET a= hypotenuse , b =base ,9 = perpendicular . therefore a^2 -b^2 =9^2 or (a+b)(a-b) = 81
a+b =81/a-b ' a-b cannot be zero ..therefore a+ b =81 where a-b is equal to 1
D
Question: In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?
A.10 sec
B.8 sec
C.5 sec
D.6 sec
Answer: D.6 sec
Explanation: T = 60/36 * 18/5 = 6 sec
ANSWER D
Question: In the graduating class of a certain college, 48 percent of the students are male and 52 percent are female. In this class 40 percent of the male and 30 percent of the female students are 25 years old or older. If one student in the class is randomly selected, approximately what is the probability that he or she will be less than 25 years old?
A.A)0.9
B.B)0.6
C.C)0.45
D.D)0.3
Answer: B.B)0.6
Explanation: Percent of students who are 25 years old or older is 0.4*48+0.3*52=~34, so percent of people who are less than 25 years old is 100-34=66.
Answer: B.
Question: How many integers V are prime numbers in the range 200 < V < 220?
A. 1
B. 2
C. 3
D. 4
Answer: A. 1
Explanation: My friend, every single odd number greater than can be written either as 4V+1 or as 4V+3. If you divide any odd number by 4, you will get a remainder of either 1 or 3. That's not a rule unique to prime numbers at all.
The 6V+1 or 6V-1 rule is basically every odd number that is not divisible by three, so it narrows the search a little.
Here's how I thought about the problem. First, eliminate all the even numbers and the odd multiples of 5 in that range. That leaves us with:
{201, 203, 207, 209, 211, 213, 217, 219}
Eliminate the four multiples of 3. Notice that 21 is a multiple of 3, so 210 is also a multiple of 3. If we add or subtract 3 or 9, we get more multiples of three. When we eliminate those, we are left with.
{203, 209, 211, 217}
Now, notice that a cool thing about this range is that 210 is also a multiple 7 (again, because 21 is a multiple of 7). This means that
210 - 7 = 203
210 + 7 = 217
Those two numbers are also multiples of 7, so eliminate them from the list. Now, we are left with
{209, 211}.
We've already checked all the prime numbers less than 10, so we know that neither of these numbers is divisible by anything less than 10. We have to check 11 now. We know that 22 is a multiple of 11, so 220 is also a multiple of 11. This means that
220 - 11 = 209
is also a multiple of 11. We can eliminate this from the list also.
That leaves us with just 211. There's no zero option in the question, so this must be a prime number.
Answer = (A)
Question: Carol spends 1/3 of her savings on a stereo and 1/3 less than she spent on the stereo for a television. What fraction of her savings did she spend on the stereo and television?
A.1/4
B.2/7
C.5/9
D.1/2
Answer: C.5/9
Explanation: Total Savings = S
Amount spent on stereo = (1/3)S
Amount spent on television = (1-1/3)(1/3)S = (2/3)*(1/3)*S = (2/9)S
(Stereo + TV)/Total Savings = S(1/3 + 2/9)/S = 5/9
Answer: C
Question: Find √? /13 = 4 ?
A.76
B.5776
C.304
D.2704
Answer: D.2704
Explanation: Answer
Let √N/13= 4
Then √N = 13 x 4 = 52
∴ N = 52 x 52 = 2704.
Correct Option: D
Question: As part of her MBA program, Karen applied for three different Spring Break outreach projects, each of which selects its students by a random lottery of its applicants. If the probability of her being accepted to each individual project is 50%, what is the probability that Karen will be accepted to at least one project?
A.1/2
B.3/4
C.5/8
D.7/8
Answer: D.7/8
Explanation: Since the probability of Karen's being accepted to each individual project is 50%, the probability of her not being accepted to each project is 50%. The probability that she will be accepted to none is, therefore, (1/2)*(1/2)*(1/2)=1/8.
P(Karen will be accepted to at least one project) = 1 - (1/8) = 7/8.
The answer is D.
Question: At the end of the day, February 14th, a florist had 120 roses left in his shop, all of which were red, white or pink in color and either long or short-stemmed. A third of the roses were short-stemmed, 15 of which were white and 15 of which were pink. The percentage of pink roses that were short-stemmed equaled the percentage of red roses that were short-stemmed. If none of the long-stemmed roses were white, what percentage of the long-stemmed roses were red?
A.20%
B.25%
C.62.5%
D.75%
Answer: C.62.5%
Explanation: R + W + P = 120
S + L = 120
1/3 * 120 = 40
Short-Stemmed White = 15
Short-Stemmed Pink = 15
=> Short-Stemmed Red = 10
15/P =10/R
=> R = 2R/3
So Total Long Stemmed = 80
And Long Stemmed Red + Long Stemmed Pink = 80
So Long Stemmed Red/Long Stemmed = ?
Total White = 20 (As no Long stemmed white)
=> R + 2R/3 + 20 = 120
=> 5R = 300 and R = 60
Long Stemmed R = 60 - 10 = 50
So Long Stemmed Red/R = 50/80 = 62.5%
Answer - C
Question: Prizes totaling $24,000 were awarded unequally between 3 contestants. Which of the following choices could be the highest prize?
A.(a) $5,000
B.(b) $7,000
C.(c) $15,000
D.(d) $25,000
Answer: C.(c) $15,000
Explanation: The highest prize cannot possibly be less than 1/3rd of 24,000 (because in this case the sum of 3 prizes would be less than 24,000) and cannot be more than 24,000.
Answer: C.
Question: 385, 462, 572, 396, 429, 671, 264
A.385
B.429
C.671
D.264
Answer: B.429
Explanation: Solution
In each number except 429,the middle digit is the sum of the other two. Answer B
Question: A sum of money becomes double itself in 8 years at simple interest. How many times will it become 24 years at the same rate?
A.2
B.4
C.6
D.8
Answer: C.6
Explanation: P ---- 2P ---- 8 years6P ---- 24 years Answer: C
Question: What is the difference between the place values of two sevens in the numeral 54179759 ?
A.699990
B.99990
C.99980
D.69300
Answer: D.69300
Explanation: Explanation:
Required Difference
= 70000 - 700 = 69300
Answer is D
Question: Out of a total of 1,000 employees at a certain corporation, 52 percent are female and 40 percent of these females work in research. If 40 percent of the total number of employees work in research, how many male employees do NOT work in research?
A. 520
B. 480
C. 392
D. 288
Answer: D. 288
Explanation: total number of female employees =52% =520
female employees working in research =(2/5)*520=208
Total no of employees working in research =40% =400
Total male employees =48%=480
male employees working in research =400-208=192
male employees not working in research =480-192=288
Answer D
Question: What is the greatest power that 9 can be raised to so that the resulting number is a factor of 18!?
A.2
B.3
C.4
D.5
Answer: A.2
Explanation: the number of 9s in 18!= 18/9=2..
ans A
Question: A train 145 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
A.13 km/hr
B.57.2 km/hr
C.17 km/hr
D.18 km/hr
Answer: B.57.2 km/hr
Explanation: Speed of the train relative to man = (145/10) m/sec
= (14.5) m/sec. [(14.5) * (18/5)] km/hr
= 52.2 km/hr. Let the speed of the train be x km/hr. Then, relative speed
= (x - 5) km/hr. x - 5 = 52.2 ==> x
= 57.2 km/hr.
Answer:B
Question: What is the volume of an tetrahedron with edge length of 1?
A.3.11545466
B.0.76678113
C.0.11785113
D.2.11785113
Answer: C.0.11785113
Explanation: The answer is sqr(2)/12 = 0.11785113
The following can be derived using the Pythagorean theorem:
The height of a face is 3.5/2.
The area of any face is 3.5/4.
The distance from any corner to the center of a joining face is 1/3.5.
The height of the tetrahedron is (2/3).5
The area is 1/3*base*height =
(1/3) * 3.5/4 * (2/3).5 = 21/2/12.
The above cube has sides of length 1/sqr(2). The area formed by the diagonals along four of the faces as shown in the diagram is a tetrahedrom. Left over are four pyramids. The base of each pyramid is half of the side of the cube and the height is the height of the cube. Thus the area of each pyramid is: 1/2*(1/sqr(2))2 * 1/sqr(2) * 1/3 = (12*sqr(2))-1
The total area of the cube is (1/sqr(2))3 = (2*sqr(2))-1
The area of the tetrahedrom is thus (2*sqr(2))-1 - 4*(12*sqr(2))-1 =
3/(6*sqr(2)) - 2/(6*sqr(2)) = 1/(6*sqr(2)) = sqr(2)/12
correct answer C
Question: A can contains a mixture of liquids A and B is the ratio 7:5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many liter T of liquid A was contained by the can initially?
A.10
B.20
C.21
D.25
Answer: C.21
Explanation: As A:B::7:5 ---> only option C is a multiple of 7 and hence it is a good place to start. Also A:B::7:5 means that , A = (712)*Total and B = (5/12)*Total
If A = 21 , B = 15 ---> remove 9 litres ---> you remove (7/12)*9 of A ---> A remaining = 21-(7/12)*9 = 63/4
Similarly, for B, you remove (5/12)*9 ---> B remaining = 15 - (5/12)*9 = 45/4 and then add 9 more litres of B ---> 9+45/4 = 81/4
Thus A/B (final ratio) = (45/4)/(81/4) = 7:9 , the same as the final ratio mentioned in the question.
Hence C is the correct answer.
A/B = 7/9 = (7x-(7/12)*9)/ (5x-(5/12)*9+9), where 7x and 5x are initial quantities of A and B respectively.
Thus, 7/9 = (7x-(7/12)*9)/ (5x-(5/12)*9+9) ---> giving you x=3. Thus A (original) T= 7*3 = 21.C
Question: If x^2=x+2, then x^3=?
A.3x+2
B.3x-2
C.2x+1
D.2x-3
Answer: A.3x+2
Explanation: Given X^2 = X+2
X^3 = X*X^2 = x*(X+2)-- Substituted from above.
= X^2 + 2X = X+2+2X = 3X+2.
Hence A.