RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If a and b are the two values of t that satisfy
the equation t^2 â€“ 8t + 12 = 0, with a > b, what is the value of a â€“ b?
A.2
B.4
C.6
D.8
Answer: B.4
Explanation: Factor the left side of the equation:
t^2 â€“ 8t + 12 = 0
(t â€“ 2)(t â€“ 6) = 0
t = 2, t = 6
Thus, a = 6 and b = 2. So a â€“ b = 6 â€“ 2 = 4.
The answer is B.
Question: Statements: Population increase coupled with depleting resources is going to be the scenario of many developing countries in days to come.
Conclusions:
1) The population of developing countries will not continue to increase in future.
2) It will be very difficult for the governments of developing countries to provide its people decent quality of life.
A.Only conclusion I follows
B.Only conclusion II follows
C.Either I or II follows
D.Neither I nor II follows
Answer: B.Only conclusion II follows
Explanation: The fact given in I is quite contrary to the given statement. So, I does not follow. II mentions the direct implications of the state discussed in the statement. Thus, II follows.
B
Question: In a school of 450 boys, 44% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
A.72
B.75
C.80
D.81
Answer: D.81
Explanation: 44 + 28 + 10 = 82%
100 – 82 = 18%
450 * 18/100 = 81
ANSWER:D
Question: An bus covers a certain distance at a speed of 230 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?
A.690 km/hr
B.720 km/hr
C.730 km/hr
D.750 km/hr
Answer: A.690 km/hr
Explanation: Distance = (230 x 5) = 1150 km.
Speed = Distance/Time
Speed = 1150/(5/3) km/hr. [We can write 1 hours as 5/3 hours]
Required speed = 1150 x 3 km/hr = 690 km/hr.
A
Question: For any non-zero a and b that satisfy |ab| = ab and |a| = -a
|b - 4| + |ab + b| = ?
A.a) ab - 4
B.b) 2b - ab - 4
C.c) ab + 4
D.d) ab - 2b + 4
Answer: C.c) ab + 4
Explanation: |a| = -a Suggests that 'a' is Negative
|ab| = ab Suggests that 'ab' is Positive
'ab' is Positive Suggests that 'a' and 'b' have same Sign i.e. either both positive or both negative
But since 'a' is Negative therefore 'b' is Negative too.
Since b is negative so |b - 4| = -b+4
Since ab is Positive and b is Negative so |ab - b| = ab + b
i.e. |b - 4| + |ab - b| = -b+4 + ab + b =ab + 4
Answer: Option C
Question: The reduction in the speed of an engine is directly proportional to the square of the number of bogies attached to it. The speed of the train is 100 km/hr when there are 4 bogies and 55 km/hr when there are 5 bogies. What is the maximum number of bogies that can be attached to the train so that, even with those many numbers of bogies, it can just move?
A.3
B.4
C.5
D.6
Answer: C.5
Explanation: We know that S=Smax−K×(bogies)2
When there are 4 bogies speed of the train is 100km/hr 100=Smax−K×(4)2 ⇒100=Smax−K×16.......(1)
When there are 5 bogies speed of the train is 55km/hr
55=Smax−K×(5)2⇒ 55 = Smax−K×25 ........(2)
(2) - (1) gives 9K=45⇒K=5
By substituting K = 5 in either (1) or (2) we can find the maximum speed of the train = 180 km/hr
Assume, for N number of bogies the train does not move.
⇒0=180−5(N)2⇒N=6
If the engine is attached to 6 bogies, it does not move. If we want the train to move we need to attach maximum of 5 bogies
Answer C
Question: The greatest number of four digits which is divisible by 12, 20, 36 and 60 is:
A.9000
B.9900
C.9500
D.9800
Answer: B.9900
Explanation: Greatest number of 4-digits is 9999.
L.C.M. of 12, 20, 36 and 60 is 180.
On dividing 9999 by 180, the remainder is 99.
Required number (9999 - 99) = 9900.
Answer: Option B
Question: The amount of time that three people worked on a special project was in the ratio of 3 to 5 to 6. If the project took 140 hours, how many more hours did the hardest working person work than the person who worked the least?
A.32 hours
B.40 hours
C.35 hours
D.30 hours
Answer: D.30 hours
Explanation: Let the persons be A, B, C.
Hours worked:
A = 3*140/14 = 30 hours
B = 5*140/14 = 50 hours
C = 6*140/14 = 60 hours
C is the hardest worker and A worked for the least number of hours. So the difference is 60-30 = 30 hours.
Answer : D
Question: If n is the product of the first 10 prime numbers, which of the following is an integer?
I. n/7
II. n/4
III. n/143
A.I only
B.I and II only
C.I and III only
D.III only
Answer: C.I and III only
Explanation: The product of first 10 prime numbers is: 2*3*5*7*11*13*17*19*23*29 = n
I) n/7 is an integer --> Yes (It is a part of the product)
II) n/4 is an integer --> No (2 is present only once in the product, not twice)
III) n/143 is an integer --> Yes (Both 11 and 13 are a part of the product)
Answer: C
Question: A Flask contains a mixture of AB in the ratio 5:2. When 20 L of Mixture is replaced with liquid B, ratio becomes 4:1. How many liters of liquid A was present in mixture initially.
A.10
B.22
C.15
D.30
Answer: B.22
Explanation: Let the volume of the initial total mixture was V. When 20L of mixture is removed the volume becomes (V - 20). The concentration stays 5:2.
Next step, when you add 20 litres of B, the amount of A does not change.
So
Amount of A in original mix = Amount of A in final mix
C1 * V1 = C2 * V2
(5/7)*(V - 20) = (4/5)*V
V = 30.8
So volume of A in initial mixture was (5/7) * 30.8 = 22 litres
Answer B
Question: The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 16 terms of the arithmetic progression?
A.300
B.120
C.150
D.160
Answer: D.160
Explanation: n th term of A.P. is given by a+(n-1)d
4 th term = a+3d
12 th term = a+11d
Given a+3d+a+11d=20 --> 2a+14d=20 --> a+7d = 10
Sum of n term of A.P = n/2[2a+(n-1)d]
subsitiuing n = 16 ...we get 15/2[ 2a + 14d] = 16 [a+7d] = 16*10 = 160...
Answer is D...
Question: A piece of string is 40 centimeters long. It is cut into three pieces. The longest piece is 3 times as long as the middle-sized piece and the shortest piece is 23 centimeters shorter than the longest piece. Find the lengths of the three pieces.
A.27
B.5
C.4
D.9
Answer: C.4
Explanation: Explanation :
Let the largest piece = 3x.
Middle = x.
Shortest = 3x – 23.
or 3x + x + (3x – 23) = 40.
or x = 9
or the shortest piece = 3(9) – 23 = 4
Check choices:
The shortest piece has to be < 20 cm.
27 is wrong choice.
The largest piece is a multiple of 3.
Or (23 + Shortest) should be a multiple of 3.
Hence ,the answer = 4 cm.
Answer : C
Question: A sum is divided among W, X and Y in such a way that for each rupee W gets, X gets 30 paisa and Y gets 20 paisa. If the share of W is RS. 10, what is the total amount?
A.12
B.13
C.14
D.15
Answer: D.15
Explanation: w:x:y = 100:30:20
20:6:4
20 --- 10
30 --- ? => 15
Answer:D
Question: If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area?
A.120 cm2
B.197 cm2
C.876 cm2
D.267 cm2
Answer: A.120 cm2
Explanation: The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle
= 1/2 * 24 * 10
= 120 cm2
Answer: A
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 10 overs to reach the target of 282 runs?
A.6.25
B.5.5
C.25
D.15
Answer: C.25
Explanation: Explanation:
Runs scored in the first 10 overs = 10 × 3.2 = 32
Total runs = 282
Remaining runs to be scored = 282 - 32 = 250
Remaining overs = 10
Run rate needed = 250/10=25
Answer: Option C
Question: If the number 872,152,24x is divisible by 11, what must be the value of x?
A.1
B.2
C.3
D.4
Answer: C.3
Explanation: Multiplication rule of 11: (Sum of digits at odd places - Sum of digits at even places) should be divisible by 11
Given number: 872,152,24x
Sum of digits at odd places = 8 + 2 + 5 + 2 + x = 17 + x (i)
Sum of digits at even places = 7 + 1 + 2 + 4 = 14 (ii)
(i) - (ii) = 17 + x - 14 = x - 3
Hence x should be = 3 to make this a multiple of 11 (0) Option C
Question: What is the measure of the radius of the circle inscribed in a triangle whose sides measure 8, 15 and 21 units?
A.8.5 units
B.2.6 units
C.3 units
D.5 units
Answer: B.2.6 units
Explanation: Sides are 8, 15 and 21...thus it is right angle triangle Since 21^2 = 8^2 + 15^2
therefore, area = 1/2 * 15 * 8 = 60
We have to find in-radius
Therefore, area of triangle = S*r ....where S=semi-perimeter and r= in-radius
Now S=semi-perimeter = 21+15+8 /2 = 22
Thus , 60 =22*r
and hence r=in-radius= 2.6
Option B
Question: Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.5400. How much third person will get?
A.2400
B.2429
C.2980
D.2707
Answer: A.2400
Explanation: First persons investment = x
Second persons investment = x + 1000
Third persons investments = x + 2000
x + x + 1000 + x + 2000 = 9000
3x = 6000
x = 2000
Ratio = 2000 : 3000 : 4000
2:3:4
4/9 * 54000 = 2400
Answer:A
Question: 400 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees
A.10
B.12
C.14
D.16
Answer: D.16
Explanation: 26 trees have 25 gaps between them,
Required distance (400/25) = 16
D
Question: Two trains are traveling on a collision course. If train A is traveling at a speed of 350 mph and train B is traveling 28% slower, how much time will it take the trains to collide if the initial distance between the two is 1505 miles?
A.Two hours and 30 minutes
B.One hour and 10 minutes
C.Two hours and 25 minutes.
D.Three hours and 15 minutes
Answer: C.Two hours and 25 minutes.
Explanation: let S1 and S2 be the speeds of train A and B
S1 is 350 and S2=28% less = 252
time taken = S1+S2/1505
which is
1505/602 =x
where 2<x<3
therefore C !!
Question: The average of first nine prime numbers:
A.5.6
B.11.1
C.12.9
D.6.3
Answer: B.11.1
Explanation: Explanation:
The first ten prime numbers is 2, 3, 5, 7, 11, 13, 17, 19, 23
Average = 100/9 = 11.11
Answer: Option B
Question: How many two-element subsets of <1, 2,3,4,5,6,7,8,9> are there that do not contain the pair of elements 2 and 4?
A.21
B.22
C.24
D.35
Answer: D.35
Explanation: 9C2 - 1 = 35 Answer is D
Question: John makes $60 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase?
A.16%
B.16.66%
C.18%
D.19%
Answer: B.16.66%
Explanation: Increase = (10/60)*100 = (1/6)*100 = 16.66%.
B
Question: One ton has 2600 pounds, and one pound has 16 ounces. How many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons?
A. 2080
B. 1700
C. 2350
D. 2500
Answer: A. 2080
Explanation: 16 pounds and 4 ounces= 16*16 + 4 = 260 ounces.
13 tons = 13*2600 pound = 13*2600*16 ounces.
Hence the answer is (13*2600*16)/260 = 2080.
Answer: A.
Question: When the price of a pressure cooker was increased by 15%, the sale of pressure cookers decreased by 15%. What was the net effect on the sales?
A.15% decrease
B.no effect
C.2.25% increase
D.2.25% decrease
Answer: D.2.25% decrease
Explanation: Net effect on sale = −(common%change)2/100
= −(15)2/100= 2.25% decrease
Answer D
Question: There are 43 stations between Ernakulam and Chennai. How many second class tickets have to be printed, so that a passenger can travel from one station to any other station?
A.1980
B.1920
C.1990
D.1890
Answer: A.1980
Explanation: The total number of stations= 45
From 45 Stations we have to choose any two stations and the direction of travel (Ernakulam to Chennai is different from Chennai to Ernakulam) in 45P2 ways.
45P2= 45*44= 870
ANSWER:A
Question: What is the average of 1200, 1300, 1400, 1510, 1520, 1530, 1115, 1120, and 1125?
A. 1345
B. 1334
C. 1313.33
D. 1350
Answer: C. 1313.33
Explanation: Add 1200, 1300, 1400, 1510, 1520, 1530, 1115, 1120, and 1125
Grouping numbers together may quicken the addition
sum = 11820
11820/9 =1313.33
C
Question: What no. should be subtracted from x^3+4x^2−7x+12x^3+4x^2−7x+12, if it is to be perfectly divisible by x+3x+3?
A.17
B.42
C.46
D.54
Answer: B.42
Explanation: According to remainder theorem when dfracf(x)x+adfracf(x)x+a, then the remainder is f(−a)f(−a).
In this case, as x+3x+3 divides x3+4x2−7x+12–kx3+4x2−7x+12–k perfectly (kk being the number to be subtracted), the remainder is 0 when the value of xx is substituted by -3.
i.e., (−3)3+4(−3)2−7(−3)+12−k=0(−3)3+4(−3)2−7(−3)+12−k=0
or −27+36+21+12=k−27+36+21+12=k
or k=k= 42
B
Question: It is required to fix a pipe such that water flowing through it at a speed of 7 metres per minute fills a tank of capacity 110 cubic metres in 10 minutes. The inner radius of the pipe should be :
A.√2 m
B.2 m
C.1⁄2 m
D.1⁄√2 m
Answer: D.1⁄√2 m
Explanation: Let inner radius of the pipe be r.
Then, 110 = 22⁄7 × r2 × 7 × 10
or r2=110/22×10=1/2
or r = 1/√2 m
Answer D
Question: The cost of a car is 400% greater than the cost of a bike. If there is an increase in the cost of the car is 15% and that of bike 20%. Then the total increase in the cost of the 5 cars and 10 bikes is:
A.17.5%
B.16(3/7)%
C.18.5%
D.18.25%
Answer: B.16(3/7)%
Explanation: Solution: Let the bike's initial cost be X and then car's initial cost be 5X.
After the increase,
Bike price = 1.2X
Car price = 5.75X
Initial total cost of 5 cars and 10 bikes,
= 25X+10X = 35X
New cost,
= 28.75X+12x = 40.75X
Change in cost = (40.75X-35X) = 5.75X
% change = (5.75X*100)/35 = 16(3/7)%.
Answer: Option B
Question: What is the area of square field whose side of length 17 m?
A.225
B.662
C.772
D.289
Answer: D.289
Explanation: 17 * 17
= 289 sq m
Answer:D
Question: Manoj borrowed Rs.3450 from Anwar at 6% p.a. simple interest for three years. He then added some more money to the borrowed sum and lent it to Ramu for the same time at 9% p.a. simple interest. If Manoj gains Rs.824.85 by way of interest on the borrowed sum as well as his own amount from the whole transaction, then what is the sum lent by him to Ramu?
A.5352
B.5355
C.5328
D.5312
Answer: B.5355
Explanation: Let the sum lent by Manoj to Ramu be Rs.P.
Amount gained by Manoj = P. 3.9 /100 = 3450.3.6/100 = Rs.824.85
27P = 62100 = 82485
P = (82485 + 62100)/27 = 3055 + 2300 = Rs.5355
Answer: B
Question: In a division sum, the quotient is 120, the divisor 456 and the remainder 333, find the dividend?
A.23504
B.34545
C.55053
D.23434
Answer: C.55053
Explanation: Explanation:
120 * 456 + 333 = 55053
C
Question: A cistern which could be filled in 9 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full in what time will the leak empty it?
A.27 hrs
B.29 hrs
C.28 hrs
D.90 hrs
Answer: D.90 hrs
Explanation: 1/9 - 1/x = 1/10
=> 90 hrs
Answer:D
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 50000, then the share of B is?
A.23077
B.24000
C.24005
D.24009
Answer: A.23077
Explanation: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 50000
Share of B = 6/13 (50000) = Rs. 23076.92~ 23077
Answer: A
Question: A, B and C completed a piece of work, A worked for 6 days, B for 9 days and C for 4 days. Their daily wages were in the ratio of 3:4:5. Find the daily wages of C, if their total earning was Rs.1628?
A.s.109
B.s.108
C.s.110
D.s.103
Answer: C.s.110
Explanation: 3x 4x 5x
6 9 4
18x + 36x + 20x = 1628
74x = 1628 => x = 22
5x = 110 Rs.
Answer:C
Question: In the line xy plane line m has the equation y = 3x - 9, then the line m passes through which of the following points?
A.(3, 1)
B.(3, 4)
C.(4, 2)
D.(6, 9)
Answer: D.(6, 9)
Explanation: Yes it is y=3x-8....extremely sorry for mistake....
IF that's the case then answer is D
y=3x-8
9=3X6-9
9=18-9
9=9 (satisfied)
Question: 10 men, working 6 hours a day can complete a work in 18 days. How many hours a day must 15 men work to complete the work in 12 days ?
A.4 hours a day
B.5 hours a day
C.6 hours a day
D.7 hours a day
Answer: C.6 hours a day
Explanation: Explanation:
More Men, Less Hours {Indirect Proportion}
Less Days, More Hours {Indirect Proportion}
[men 15 10
days 12 18] ::6:x
=>x∗15∗12=10∗18∗6
=>x=10∗18∗6/ 15∗12
=>x=6
Option C
Question: If p is an odd integer, which of the following must also be odd?
A.4p + 4
B.p + p
C.3p + 3
D.2p + p
Answer: D.2p + p
Explanation: Things to keep in mind:
Odd + odd = even
Odd + even = odd
Odd*odd = odd
Odd*even = even
On checking each option
A. 4p + 4
4p = even, 4p + 4 = even + even = even.
B. p + p
Odd + odd = even. This will be even
C. 3x + 3
3x = odd, 3x + 3 = odd + odd = even
D. 2p + p
2p = even, 2p + p = even + odd = odd
E. p^2 + 1
p^2 = odd, p^2 + 1 = odd + odd = even
Correct option: D
Question: In a LAB experiment, a 100 ml compound of element X and element Y needs to be increased to 240 ml by adding some quantity of element X, and some quantity of element Y. If the original compound contains 30% of element X, how much (in ml) of element Y must be added so that element X will be exactly one third of the resulting mixture ?
A.40 ml
B.100/3 ml
C.20 ml
D.90 ml
Answer: D.90 ml
Explanation: There are 0.3*100=30 ml of element X in the initial solution.
We need X to be 1/3rd of 240 ml in the resulting solution, so 80 ml. Thus out of 140 ml of solution added, 50 must be X (in order it to become 80 ml) ans the remaining 90 must be Y.
Answer: D
Question: The ratio of men to women in the Snyder community choir is 4 to 5. The ratio of men to women in the Leigh community choir is 5 to 6. If the two choirs merged, the ratio of men to women in the combined choir would be 22 to 27. If Snyder has 4 more men and 6 more women than Leigh, how many men's are in the Snyder choir?
A.20
B.25
C.30
D.33
Answer: A.20
Explanation: This question has a number of patterns in it that we can take advantage of. We can also TEST THE ANSWERS (but we can actually eliminate most of the answer choices rather quickly.
We're told that the ratio of the Men to Women in the Snyder choir is 4 to 5, so the number of men MUST be a multiple of 4 and the number of women MUST be a multiple of 4 The question asks how many MEN are in the SNYDER choir, so the answer MUST be a multiple of 4. We can eliminate Answers B,C, D and E (since they're NOT multiples of 4.
Answer A
Question: Joey is planning to throw a small party and for that he needs to do the following tasks:
I. Decide guest list
II. Send invites
III. Arrange catering
IV. Decide the venue
V. Rent a music system
The tasks can be done in any order as long as the invites are sent after the guest list is decided. In how many ways can Joey do the five tasks listed above?
A.24
B.48
C.60
D.120
Answer: C.60
Explanation: These 5 tasks can be arranged in 5! = 120 ways. In half of them invites are sentafterthe guest list is decided and in half of them before. So, there are total of 120/2 = 60 ways to arrange the task so that the invites are sent after the guest list is decided.
Answer: C.
Question: Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab for all non-negative integers. What is the value of (a + b) + 6, when a # b = 100?
A.5
B.8
C.10
D.11
Answer: D.11
Explanation: OFFICIAL SOLUTION:
(B) We know that a # b = 100 and a # b = 4a² + 4b² + 8ab. So
4a² + 4b² + 8ab = 100
We can see that 4a² + 4b² + 8ab is a well-known formula for (2a + 2b)². Therefore
(2a + 2b)² = 100.
(2a + 2b) is non-negative number, since both a and b are non-negative numbers. So we can conclude that 2(a + b) = 10. (a + b) + 6 = 10/2 + 6 = 11.
The correct answer is D.
Question: In a two-digit, if it is known that its unit’s digit exceeds its ten’s digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:
A.24
B.26
C.42
D.46
Answer: A.24
Explanation: EXPLANATION
Let the ten’s digit be x.
Then, unit’s digit = x + 2.
Number = 10x + (x + 2) = 11x + 2.
Sum of digits = x + (x + 2) = 2x + 2.
(11x + 2)(2x + 2) = 144
22x2 + 26x – 140 = 0
11x2 + 13x – 70 = 0
(x – 2)(11x + 35) = 0
x = 2.
Hence, required number = 11x + 2 = 24.
Answer A
Question: If a pipe can fill a tank in 6 hours, find the part of tank it fills in one hour.
A.1/6
B.2/3
C.1/2
D.None of these
Answer: A.1/6
Explanation: Explanation:
Let the capacity of the tank be C litres.
Time to fill the tank = 6 hours
Hence, in 1 hour C/6 litres gets filled.
Therefore, 1/6th part of the tank gets filled in one hour.
ANSWER A
Question: On the xy co-ordinate plane, point C is (5,-2) and point D is (-1,2). The point on line segment CD that is twice as far from C as from D is:
A.(1,-1)
B.(1,1)
C.(2,0.25)
D.(3,0.5)
Answer: D.(3,0.5)
Explanation: We want the point on the line that is twice as far from C as it is from D. We can examine the x and y coordinates separately since they are independent.
*It should be noted that there are two solutions to this problem, one point between C and D, and another point with D in the middle of C and the point. We can quickly look at the answer choices and see that all the points are between C and D, therefore we can search for that point using the following method:
Taking the x-coordinate first, the distance between C and D is |(x-coordinate of C) - (x-coordinate of D)|= |5 - (-1)| = 6
The x-coordinate that is twice as far from C as it is from D (and in between C and D) will be 4 units from C and 2 units from D. So the x coordinate of the point we're looking for is 5-4 = 1, or (-1)+2 = 1.
Now looking at the y-coordinate, we do the same thing. The distance between C and D is |(-2) - 2.5| = 4.5
The y-coordinate that is twice as far from C as it is from D (and in between C and D) will be 3 units from C and 1.5 units from D. So the y coordinate of the point we're looking for is (-2)+3 = 1, or 2.5-1.5 = 1.
So now we have our coordinates of the point on the line that is twice as far from C as it is from D: (3,1)
Answer: D
Question: The table below shows the enrollment in various classes at a certain college.
Class | Number of Students
Biology | 80
Physics | 35
Calculus | 40
Although no student is enrolled in all three classes, 15 are enrolled in both Biology and Physics, 10 are enrolled in both Biology and Calculus, and 12 are enrolled in both Physics and Calculus. How many different students are in the three classes?
A.118
B.88
C.90
D.125
Answer: A.118
Explanation: No. of total students = no of students of biology + no of students of physics but not biology + no of students of calculus but not biology and physics
No. of total students = 80 + (35-15) + (40-10-12) = 80+20+18 = 118
Hence, Answer will be A.
Question: If the integer n has exactly five positive divisors, including 1 and n, how many positive divisors does n^2 have?
A.5
B.7
C.9
D.10
Answer: C.9
Explanation: take the example of 16...
it has 5 positive divisors (1,2,4,8,16)
Now, take the example of 256...
it has only 9 divisors..
so C is the ans
Question: A man sitting in a train which is traveling at 56 kmph observes that a goods train, traveling in opposite direction, takes 15 seconds to pass him. If the goods train is 410 m long, find its speed
A.52 kmph
B.56 kmph
C.58 kmph
D.42 kmph
Answer: D.42 kmph
Explanation: Explanation:
Relative speed = 410/15 m / sec = ((410/15)×(18/5)) kmph = 98 kmph.
Speed of goods train = (98 - 56) kmph = 42 kmph
Answer: Option D
Question: The bus that travels from St. Louis to Chicago and back comes to St. Louis every 3 hours while the bus that travels from St. Louis to Springfield and back comes to St. Louis every 7 hours. If at 01:00 o'clock both bused arrived at St. Louis, at what time will they meet in St. Louis again?
A.16:00.
B.18:00.
C.20:00.
D.22:00.
Answer: D.22:00.
Explanation: Time taken by bus to travel from St. Louis to Chicago and back comes to St. Louis = 3 hours
Time taken by bus to travel from St. Louis to Springfield and back comes to St. Louis = 7 hours
Time taken by both buses to meet again in St. Louis will be LCM of 3 and 7 = 21
If the buses start at 01:00 o'clock from St. Louis , they will meet again in St. Louis at 22:00 hours
Answer D
Question: The average marks in mathematics scored by the pupils of a school at the public examination were 39. If four of these pupils who actually scored 25, 12, 15 and 19 marks at the examination had not been sent up, the average marks for the school would have been 44. Find the number of pupils sent up for examination from the school?
A.20
B.21
C.22
D.23
Answer: B.21
Explanation: 39x = 25 + 12 + 15 + 19 + (x – 4)44
39x = 71+44X-176
5X=105
X=21
ANSWER:B