RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A hollow cube of size 5 cm is taken, with a thickness of 1 cm. It is made of smaller cubes of size 1 cm. If 4 faces of the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted?
A.488
B.269
C.299
D.266
Answer: A.488
Explanation: The Hallow cube volume = n3−(n−2)2n3−(n−2)2, Here n is the number of small cubes lie on the big cube edge.
Now n = 5 so Hallow cube volume = 53−(5−2)2=125−27=9853−(5−2)2=125−27=98
So 98 small cubes required to make a hallow cube of size 5 cm. Now total surfaces = 6 x 98 = 588
Now if the bigger cube is painted 4 sides, total 4 x 25 small faces got paint. So remaining small faces which does not have paint after cutting is 588 - 100 = 488
Answer:A
Question: A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 7 with 2 students left over. What is the sum of the two smallest possible values of n?
A.42.
B.46.
C.50.
D.54.
Answer: B.46.
Explanation: n = 4k+1 = 7j+2
Let's start at 1 = 4(0)+1 and keep adding 4 until we find a number in the form 7j+2.
1, 5, 9 = 7(1)+ 2
The next such number is 9 + 4*7 = 37.
9+37 = 46
The answer is B.
Question: If −y ≥ x, and −x < −4, then which of the following must be true?
A.y = −4
B.y > −4
C.−y > 4
D.y ≤ −4
Answer: C.−y > 4
Explanation: −y ≥ x, and −x < −4
y <= -x < -4
As '-x' is less than '-4' and Y is less than or equal to '-x'
we have y < -4 which is similar to -y > 4.
C) -y >4
Question: The average of six numbers is 3.95. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers ?
A.4.7
B.4.6
C.4.2
D.4.1
Answer: B.4.6
Explanation: Explanation:
Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)]
= 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20.
Required average = (9.2 / 2) = 4.6.
Answer: B) 4.6
Question: A man can row 7 ½ kmph in still water.if in a river running at 1.5 km/hr an hour,it takes him 50 minutes to row to a place and back,how far off is the place?
A.4km
B.2km
C.5km
D.3km
Answer: D.3km
Explanation: Speed downstream =(7.5+1.5)km/hr=9 km/hr;
Speed upstream=(7.5-1.5)kmph=6kmph.
Let the required distance be x km.then,
x/9+x/6=50/60.
2x+3x=(5/6*18)
5x=15
x=3.
Hence,the required distance is 3km
ANSWER D 3km
Question: Which of the following is a prime number ?
A.33
B.81
C.93
D.97
Answer: D.97
Explanation: Clearly, 97 is a prime number.
answer -Option D
Question: A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it?
A.23 days
B.16 days
C.11 days
D.24 days
Answer: D.24 days
Explanation: D
24 days
2c = ¼ + 1/6 – 1/3 = 1/12
c = 1/24 => 24 days
Question: If n is an integer, f(n) = f(n-1) - n and f(4)=15. What is the value of f(6)?
A.4
B.0
C.1
D.2
Answer: A.4
Explanation: Since f(n)=f(n-1)-n then: f(6)=f(5)-6 and f(5)=f(4)-5.
As given that f(4)=15 then f(5)=15-5=10 --> substitute the value of f(5) back into the first equation: f(6)=f(5)-6=10-6=4.
Answer: A.
Questions on funtions to practice:
Question: There are 21 students in a class. In how many different ways can a committee of 3 students be formed?
A.1180
B.1330
C.1540
D.1760
Answer: B.1330
Explanation: 21C3 = 21*20*19 / 6 = 1330
The answer is B.
Question: Tough and Tricky questions: Exponents.
If 7^(3x-1)*3^(4y-3) = 49^x*27^y, then x + y =
A.3
B.4
C.2
D.1
Answer: B.4
Explanation: Here is my solution.
7^(3x-1)*3^(4y-3) = 49^x*27^y
Here RHS 49^x*27^y= 7^(2x)*3^(3y)
Equating powers on both sides-->
3x-1=2x , thus x=1 and
4y-3=3y giving y=3
So, x+y=4
Option: B
Question: An error 3% in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square?
A.9.09%
B.4.02%
C.4%
D.3%
Answer: A.9.09%
Explanation: Percentage error in calculated area
=(3+3+(3Ã—3)/100)%
=9.09%
ANSWER:A
Question: The CI on Rs 30000 at 7% per annum for a certain period is 4347.The period is ?
A.2
B.3
C.1
D.6
Answer: A.2
Explanation: I year 2100II year 2100+147=22472100+2247=4347So 2 YearsAnswer A
Question: The temperature of a certain cup of coffee 6 minutes after it was poured was 120 degrees Fahrenheit. If the temperature F of the coffee t minutes after it was poured can be determined by the formula F = 120*2^(-at) + 60, where F is in degrees Fahrenheit and a is a constant. Then the temperature of the coffee 30 minutes after it was poured was how many degrees Fahrenheit?
A.65
B.63.75
C.80
D.85
Answer: B.63.75
Explanation: First, we have to find a.
We know that after t=6 minutes the temperature F=120 degrees.
Hence:
120 = 120*(2^-6a)+60
60 = 120*(2^-6a)
60/120 = 2^-6a
1/2 = 2^-6a
2^-1 = 2^-6a
-1 = -6a
1/6 = a
Now we need to find F after t=30 minutes:
F = 120*(2^-1/6*30)+60
F = 120* (2^-5) +60
F = 120* (1/2^5) +60
F = 120*1/32 +60
F = 3.75+60 = 63.75
Answer B!
Question: A committee of 5 people is to be selected from 7 people. How many different committees are possible?
A.21
B.40
C.56
D.D.168
Answer: A.21
Explanation: Because the order does not matter in selecting 5 people for the committee, this is a combination question.
The number of ways to select 5 people from 7 = 7C5 = 7!/5!*2! = 21. Hence A
Question: Difference of two numbers is 1860. If 7.5% of the number is 12.5% of the other number , find the number ?
A.2660, 1000
B.3660, 2000
C.3000, 4160
D.2790, 4650
Answer: D.2790, 4650
Explanation: Let the numbers be x and y. Then, 7.5 % of x =12.5% of y
X = 125*y/75 = 5*y/3.
Now, x-y =1860
5*y/3 –y =1860
2*y/3= 1860
y =[ (1860*3)/2] =2790.
One number = 2790, Second number =5*y/3 =4650.
Answer D.
Question: A and B are partners in a business. A contributes 1/4 of the capital for 15 months and B received 2/3 of the profit. For how long B's money was used ?
A.11 months
B.17 months
C.10 months
D.19 months
Answer: C.10 months
Explanation: Let the total profit be Rs. z. Then,
B's share = Rs. 2z/3, A's share = Rs. ( z - 2z/3 ) = Rs. z/3.
A : B = z/3 : 2z/3 = 1:2
Let the total capital be Rs, X and suppose B's money was used for x months. Then.
(1(x) / 4 * 15) / (3x) / 4 * y) = 1/2 <=> y = (15 * 2 / 3) = 10 .
Thus, B's money was used for 10 months.
Answer: C
Question: If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value S of z - x?
A.6
B.7
C.8
D.9
Answer: D.9
Explanation: x<y<z
To find the least possible value for z-x; we need to find the values for z and x that can be closest to each other. If x is some even number, then what could be minimum possible odd z.
If x is some even number
y-x>5; y>x+5; minimum value for y=x+5+2=x+7[Note: x+5 is as even+odd=odd and nearest odd greater than x+5 is x+5+2]
Minimum value for z=y+2=x+7+2=x+9 [Note: z=y+2 because both z and y are odd. Difference between two odd numbers is 2]
S=z-x = x+9-x= 9
Ans:D
Question: A is a working partner and B is a sleeping partner in the business. A puts in Rs.15000 and B Rs.25000, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is?
A.Rs.3240
B.Rs.3600
C.Rs.3800
D.Rs.4200
Answer: D.Rs.4200
Explanation: 15:25 => 3:5
9600*10/100 = 960
9600 - 960 = 8640
8640*3/8 = 3240 + 960
= 4200
ANSWER:D
Question: What is the place value of 7 in the numeral 2734?
A.450
B.500
C.700
D.800
Answer: C.700
Explanation: Option 'C'
7 * 100 = 700
Question: A bowl was half full of water. 4 cups of water were then added to the bowl, filling the bowl to 70% of its capacity. How many cups of water are now in the bowl?
A.14 cups
B.15
C.16
D.17
Answer: A.14 cups
Explanation: lets say total volume of the container = V
Initial water content is half of total volume = V/2
Then 4 cups of water were added.
Current water content = (V/2) + 4 cups = (70/100)V
=> V = 20 cups
=> current water content is equivalent to = V/2+ 4 cups = 20/2 + 4 = 14 cups; ANSWER:A
Question: Last month, John rejected 0.5% of the products that he inspected and Jane rejected 1.00 percent of the products that she inspected. If total of 0.75 percent of the products produced last month were rejected, what fraction of the products did Jane inspect?
A.1/6
B.1/2
C.5/8
D.5/4
Answer: D.5/4
Explanation: X - fraction of products Jane inspected
(1 - X) - fraction of products John inspected
0.8(X) + 1.00(1-X) = 0.75
0.2X = 1.00 - 0.75
X = 0.25/0.2
X = 5/4
Therefore the answer is D: 5/6.
Question: What is the greatest value of n such that 17^n is a factor of 17! ?
A.1
B.2
C.3
D.4
Answer: B.2
Explanation: Another way to solve this question :
We know that 18 = 2 *3^2.
Hence, we need to find total number of 3s in 18! ( As out of 3 and 2 , we will have count of 3 least)
No. of 3s = 18/3 =6/3 =2.
Add the numbers in Bold, you will get total number of 3s = 8.
Hence, total number of 2^2 = 4/2 = 2.
Hence, answer is 2. B
Question: In the biology lab of "Jefferson" High School there are 2.16*10^6 germs, equally divided among 10,800 Petri dishes. How many germs live happily in a single dish?
A.100
B.200
C.500
D.1000
Answer: B.200
Explanation: 2.16*10^6/ 10800==> 21.6*10^3/108==> 21600/108= 200
ANSWER:B
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?
A.3/8
B.3/2
C.3/5
D.3/9
Answer: B.3/2
Explanation: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train
= 17 y meters. (27 x + 17 y) / (x + y)
= 23 ==> 27 x + 17 y
= 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2
Answer: B:
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
A.6.24 km
B.6 km
C.5.76 km
D.5.66 km
Answer: C.5.76 km
Explanation: M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2 = 5.76
ANSWER:C
Question: If r = 199,999 and s = 991,999, which of the following is the units digit of r^2 + s^3?
A.0
B.1
C.3
D.9
Answer: A.0
Explanation: Using cyclicity rule of number 9
199,999^2 will have units digit as 1
991,999^3 will have units digit as 9
Thus r2 + s3 = 1 + 9 = 0
Thus answer will be (A)
Question: A profit of Rs. 900 is divided between X and Y in the ratio of 1/2:1/3 . What is the difference between their profit shares ?
A.s. 280
B.s. 180
C.s. 380
D.s. 50
Answer: B.s. 180
Explanation: A profit of Rs. 900 is divided between X and Y in the ratio of 1/2 : 1/3 or 3:2.
so profits are 540 and 360.
difference in profit share = 540-360=180
ANSWER:B
Question: A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
A.155 m
B.150 m
C.187 m
D.177 m
Answer: B.150 m
Explanation: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y
= x/15
(x + 100)/25
= x/15
=> x = 150 m.
Answer: B
Question: What will come in place of the x in the following Number series? 6, 12, 21, x , 48
A.33
B.36
C.45
D.50
Answer: A.33
Explanation: (A)
The pattern is + 6, + 9, + 12, +15 ………..
So the missing term is = 21 + 12 = 33
Question: An investor bought two shares of stock, which he sold for $48 each. If he had a profit of 20% on one of the shares and a loss of 20% on the other share, then on the sale of both shares combined, the investor had:
A.a profit of $10
B.a profit of $4
C.a loss of $4
D.a loss of $10
Answer: C.a loss of $4
Explanation: The cost of the first stock was 48/1.2=40, so the profit from it is 8.
The cost of the second stock was 48/0.8=60, so loss from it is 12.
Overall the loss is $4.
The answer is C.
Question: How many times are the hands of a clock at right angle in a day?
A.22
B.24
C.44
D.46
Answer: C.44
Explanation: In 12 hours, they are at right angles 22 times.
In 24 hours, they are at right angles 44 times. Answer: Option C
Question: If k and w are the dimensions of a rectangle that has area 21, and if k and w are integers such that k > w, what is the total number of possible values of k?
A. Two
B. Three
C. Four
D. Five
Answer: A. Two
Explanation: kw=21=21*1=7*3--> k can take 2 values,
Answer: A
Question: Find the invalid no.from the following series 2,3,12,37,86,166,288
A.2
B.3
C.166
D.37
Answer: C.166
Explanation: 3-2=1
12-3=9
37-12=25
86-37=49
166-86=80(this must be 81=167-86=81)
so wrong number in the sequence is 166
difference between two sucessive numbers sequence would be
1,9,25,49,81,121(square of 1,3,5,7,9,11)
C
Question: An empty fuel tank with a capacity of 200 gallons was filled partially with fuel A and then to capacity with fuel B. Fuel A contains 12% ethanol by volume and fuel B contains 16% ethanol by volume. If the full fuel tank contains 20 gallons of ethanol, how many gallons of fuel A were added?
A.300
B.150
C.100
D.80
Answer: A.300
Explanation: Say there are A gallons of fuel A in the tank, then there would be 200-A gallons of fuel B.
The amount of ethanol in A gallons of fuel A is 0.12A;
The amount of ethanol in 200-A gallons of fuel B is 0.16(200-A);
Since the total amount of ethanol is 20 gallons then 0.12A+0.16(200-A)=20 --> A=300.
Answer: A.
Question: When 2/9 of the votes on a certain resolution have been counted, 3/4 of those counted are in favor of the resolution. What fraction e of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution?
A.11/14
B.13/18
C.4/7
D.3/7
Answer: A.11/14
Explanation: If we use variable for total votes there will be too many fractions to manipulate with, so pick some smart #: let set total # of votes is 18.
2/9 of the votes on a certain resolution have been counted--> 4 counted and 18-4=14 votes left to be counted;
3/4 of those counted are in favor of the resolution--> 3 in favor and 1 against;
Ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18*2/3=12 people who voted against, so in the remaining 14 votes there should be 12-1=11 people who voted against. Thus e=11/14 of the remaining votes must be against.
Answer: A.
Question: Of 60 children, 30 are happy, 10 are sad, and 20 are neither happy nor sad. There are 18 boys and 42 girls. If there are 6 happy boys and 4 sad girls, how many boys are neither happy nor sad?
A.2
B.4
C.6
D.8
Answer: C.6
Explanation: Venn diagrams are useful for multiple values of a single variable e.g. State of mind - happy/sad/neither. When you have two or more variables such as here where you have gender - boy/girl too, it becomes unwieldy. In this case, either use the table or logic.
Table method is shown above; here is how you will use logic:
There are 6 happy boys.
There are 4 sad girls but total 10 sad children. So rest 6 sad children must be sad boys.
We have 6 happy boys and 6 sad boys. Total we have 18 boys. So 18 - 6 - 6 = 6 boys must be neither happy nor sad.
Answer (C)
Question: A man can row 4.5 km/hr in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of the stream.
A.2
B.2.5
C.1.5
D.1
Answer: C.1.5
Explanation: Speed - x
upward speed (4.5-x)
downward = 4.5+x
distance => y
time rowing upwards = 2 * time rowing upwards
y/4.5-x = 2*y/4.5+x
x =1.5 km/hr
ANSWER C
Question: Which of the following is closest to (7!-6!)/(7!+6!)?
A.0.75
B.1.25
C.0.92
D.0.86
Answer: A.0.75
Explanation: (7!-6!)/(7!+6!)
6! (7-1)/6! (7+1)
6/8 = 3/4 = 0.75
A is the answer
Question: Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.?
A.10
B.12
C.14
D.17
Answer: B.12
Explanation: Let the numbers be x, x+2 and x+4 then
x + x+2 + x+4 = x+26
3x + 6 = x + 26
2x = 20
\inline \therefore x = 10
\inline \therefore Middle number = x + 2 = 10+2 = 12
B
Question: One year ago the ratio between Laxman's and Gopal's salary was 3:4. The ratio's of their individual salaries between last year's and this year's salaries are 4:5 and 2:3 respectively. At present the total of their salary is Rs.4290. The salary of Laxman now is :
A.Rs.1040
B.Rs.1650
C.Rs.2560
D.Rs.3120
Answer: B.Rs.1650
Explanation: Explanation:
Let the salaries of Laxman and Gopal one yer before be 12x and 16x.
Given that laxman's last year and present year salary are in the ratio 4 : 5 so his present salary = 5/4(12x) = 15x
Also Gopal's last year and present year salary are in the ratio 2 : 3 so his present salary = 3/2(16x) = 24x
But given that sum of the salaries 15x + 24x = 39x = 4290 ⇒⇒ x = 110
Laxman's present salary = 15x = 15 x 110 = 1650
Correct Option: B
Question: The distance between 2 cities A and B is 1000km. A train starts from A at 9 a.m. and travels towards B at 100 km/hr. Another starts from B at 10 a.m. and travels towards A at 150 km/hr. At what time do they meet?
A.11am.
B.12p.m.
C.3pm.
D.2p.m.
Answer: D.2p.m.
Explanation: Suppose they meet x hrs after 9 a.m.
Distance moved by first in x hrs + Distance moved by second in (x-1)hrs = 1000
100x + 150 (x-1) = 1000
x = 4.60 = 5 hrs
They meet at 9+5 = 2 p.m.
Answer is D
Question: To mail a package, the rate is 10 cents for the first pound and 5 cents for each additional pound. Two packages weighing 3 pounds and 5 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?
A.Combined, with a saving of 5 cents
B.Combined, with a saving of 10 cents
C.Combined, with a saving of 15 cents
D.Separately, with a saving of 5 cents
Answer: A.Combined, with a saving of 5 cents
Explanation: 3 pounds cost = 10+2*5 = 20
5 pounds cost = 10+4*5 = 30
Total = 50
8 pounds cost = 10+ 7*5 =45
Answer : A
Question: From the given equation find the value of z: zÂ² + 5z + 6
A.2
B.1
C.-1
D.-3
Answer: D.-3
Explanation: (z + 2)(z + 3)
Z = -2 or -3
Answer is D
Question: A Bell Curve (Normal Distribution) has a mean of − 1 and a standard deviation of 1/8 . How many integer values Z are within three standard deviations of the mean?
A.0
B.1
C.3
D.6
Answer: B.1
Explanation: Got the question correctly -- the second item -- [highlight]bthe list of elements in the set is required.[/highlight] is not required.
With the new information, there is only one integer value (-1) that is between (-1.375, -0.625) i.e., falls within the three 3 SD range. B
Question: In 10 years, A will be twice as old5as B was 10 years ago. If A is now 9 years older than B, the present age of B is
A.35
B.37
C.39
D.41
Answer: C.39
Explanation: Explanation:
Let B's age = x years.
Then, As age = (x+ 9) years.
(x+9+10)=2(x—10)
hence x=39.
Present age of B = 39 years
Answer: Option C
Question: In Smithtown, the ratio of right-handed people to left-handed people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of right-handed men is maximized, then what percent Z of all the people in Smithtown are left-handed women?
A. 50%
B. 40%
C. 25%
D. 20%
Answer: C. 25%
Explanation: looking at the ratio we can take total number of people=20..
ans 5/20 or 25% C
Question: The average age of 11 boys is 50, if the average age of first six boys is 49 and that of the last six is 52. Find the boy age?
A.48
B.50
C.56
D.62
Answer: C.56
Explanation: 1 to 11 = 11 * 50 = 550
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 – 550 = 56
C
Question: in how many ways can six members be selected from a group of ten members?
A.10C6
B.10C4
C.10C9
D.10C2
Answer: B.10C4
Explanation: Six members can be selected from ten members in
10C6 = 10C4 ways.
Answer: B
Question: A rectangular room has the rectangular shaped rug shown as above figure such that the rug’s area is 220 square feet and its length is 12 feet longer than its width. If the uniform width between the rug and room is 12 feet, what is the area of the region uncovered by the rug (shaded region), in square feet?
A.32
B.1136
C.40
D.1344
Answer: D.1344
Explanation: Rug's area = 220
which is (x) x (12+x) = 220
so x= 10
rug maintains a uniform distance of 12 feet
so room has dimension 10+24 and 22+24 i.e. 34 and 46
area of room 34x46 = 1564
area covered is 120
so uncovered area is 1564-220=1344 (ANSWER D)
Question: A bank offers 5% C.I. calculated on half-yearly basis . A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is?
A.288
B.121
C.772
D.992
Answer: B.121
Explanation: Amount = [1600 * (1 + 5/(2 * 100)2 + 1600 * (1 + 5/(2 * 100)]
= [1600 * 41/40(41/40 + 1)
= [(1600 * 41 * 81)/(40 * 40)] = Rs. 3321.
C.I. = 3321 - 3200 = Rs. 121.
Answer: B
Question: If x + (1/x) = 5, what is the value of T= x^2 + (1/x)^2?
A.T=21
B.T=22
C.T=23
D.24
Answer: C.T=23
Explanation: Squaring on both sides,
x^2 + (1/x)^2 + 2(x)(1/x) = 5^2
x^2 + (1/x)^2 = 23
Answer: C
Question: In how many ways can an answer key for a quiz be written if the quiz contains 4 true-false questions followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same?
A.120
B.190
C.224
D.298
Answer: C.224
Explanation: There are 2^4 = 16 possibilities for the true-false answers.
However we need to remove two cases for TTTT and FFFF.
There are 4*4 = 16 possibilities for the multiple choice questions.
The total number of possibilities is 14*16 = 224.
The answer is C.
Question: If the product of two positive integers is 50, which of the following could be the LCM and HCF of the two numbers?
1. LCM 10 : HCF 5
2. LCM 25 : HCF 2
3. LCM 18 : HCF 4
A.II only
B.I only
C.III only
D.II,III only
Answer: B.I only
Explanation: Answer : 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 3x km.
A.28 kmph
B.26 kmph
C.24 kmph
D.84 kmph
Answer: C.24 kmph
Explanation: Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 3x/(x/8)
= 24 kmph
Answer:C
Question: In a dairy farm, 20 cows eat 10 bags of husk in 40 days. In how many days one cow will eat one bag of husk?
A.20
B.40
C.80
D.30
Answer: C.80
Explanation: One cow eats 10/20=0.5 bags of husk in 40 days. Then, it eats 1 bag in 40/0.5=80 days
Answer: C
Question: At a certain laboratory, chemical substance are identified by an unordered combination of three different colors. If no chemical may be assigned the same three colors as any other, what is the maximum number of substances that can be identified using nine colors?
A.21
B.35
C.84
D.135
Answer: C.84
Explanation: The prompt tells us that substance is identified by an UNORDERED combination of 3 colors and that no chemical may be assigned the same 3 colors as any other chemical.
As an example, a chemical with the colors A/B/C means that the following combinations CANNOT be used by any other chemical:
ABC
ACB
BAC
BCA
CAB
CBA
By extension, the first part of your calculation would be the number of possible substances that could be identified with 9 colors: 9c3 = 84 possible substances
C
Question: HCF of two numbers is 15 and their LCM is 180. If their sum is 105, then the numbers are
A.30 and 75
B.35 and 70
C.40 and 65
D.45 and 60
Answer: D.45 and 60
Explanation: Explanation:
Let the numbers be 15a and 15b. Then,
15a + 15b = 105 or a+ b = 7 .. (i)
LCM = 15ab = 180
ab = 12..(ii)
Solving equations (i) and (ii), we get a=4, b=3
So, the numbers are 15 ×4 and 15 ×3, i.e., 60 and 45
Answer: D
Question: Anna and Carol buy CDs and tapes at a music store that sells each of its CDs for a certain price and each of its tapes for a certain price. Anna spends twice as much as Carol spends, buying three times as many CDs and the same number of tapes. If Carol spends $60.00 on four CDs and five tapes, how much does one tape cost?
A.$5.00
B.$6.00
C.$12.00
D.$25.00
Answer: B.$6.00
Explanation: CD => C
Type => T
Carol: 4C+5T=60
Anna: 12C+5T=120
12C-4C=60
8C=60
C=7.5
4C+5T=60
30+5T=60
5T=30
T=6
Answer is B
Question: A certain stock exchange designates each stock with a 1, 2 or 3 letter code, where each letter is selected from the 12 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order, constitute a different code, how many diff stocks is it possible to designate with these codes?
A.2000
B.1900
C.1800
D.1884
Answer: D.1884
Explanation: Pretty simple actually
Number of 1 letter symbols = 12
Number of 2 letter symbols = 12*12
Number of 3 letter symbols = 12*12*12
The answer is sum of the 3. = 12 +12*12 + 12*12*12 = 12*(1+12+144) =12*157=1884
So the answer is D.