RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Otto and Han are driving at constant speeds in opposite directions on a straight highway. At a certain time they are driving toward each other and are 40 miles apart. One and a half hours later, they are again 40 miles apart, driving away from each other. If Otto drives at a speed of x miles per hour, then, in terms of x, Han drives at a speed of how many miles per hour?
A.a) 80-x
B.b) 53.33-x
C.c) 80-2x
D.d) 120-x
Answer: B.b) 53.33-x
Explanation: Let's say the two cars have speeds V1 and V2. The fact that they are moving in opposite direction means that their relative speed is (V1 + V2). In other words, any gap between them will be changing in size at a rate of (V1 + V2). It doesn't matter whether they are moving toward each other or away from each other. If they are approaching each other, the gap between them is decreasing at a rate of (V1 + V2). If they are moving away from each other, the gap between them is increasing at a rate of (V1 + V2). Either way, the number for the rate of change remains the same.
Here, the two cars approach a distance 40 mi, then move away from each other another distance of 40 miles. That's a total distance of 80 miles in 1.5 hr, which gives a rate of:
R = (80 mi)/(1.5) = 53.33 mph
That's the rate of change of the gap, so it must equal the sum of the speeds of the two cars.
One of the speeds is x, and let's call the other y. We want y.
x + y = 53.33
y = 53.33 - x
Answer =(B)
Question: A jeep takes 4 hours to cover a distance of 620 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
A.148 Kmph
B.152 Kmph
C.106 Kmph
D.103 Kmph
Answer: D.103 Kmph
Explanation: Time = 4
Distance = 620
3/2 of 4 hours = 4 * 3/2 = 6 Hours
Required speed = 620/6 = 103 Kmph
D)
Question: Find at what time between 8 and 9 o'clock will the hands of a clock be in the same straight line but not together.
A.10x11/10
B.10x10/11
C.11x10/11
D.12x10/11
Answer: B.10x10/11
Explanation: Solution
At 8 o'clock, the hour is at 8 and the minute hand is at 12,i.e. the two hands are 20 min. Spaces apart.
So, the minute hand gain	= (30 - 20)minute
55 minutes will be gained in 60 min.
10 minutes spaces will be gained in (60/55 x10) min.	= 10x10/11 min.
The hands will be in the same straight line but not together at 10x10/11 min.past 8.
Answer B
Question: On Sunday morning, Pugsley and Wednesday are trading pet spiders. If Pugsley were to give Wednesday four of his spiders, Wednesday would then have four times as many spiders as Pugsley does. But, if Wednesday were to give Pugsley five of her spiders, Pugsley would now have five fewer spiders than Wednesday had before they traded. How many pet spiders does Pugsley have before the trading game commences?
A.6
B.7
C.8
D.10
Answer: D.10
Explanation: If Pugsley were to give Wednesday four of his spiders, Wednesday would then have five times as many spiders as Pugsley does:
(w + 4) = 4(p - 4)
If Wednesday were to give Pugsley five of her spiders, Pugsley would now have five fewer spiders than Wednesday had before they traded:
p + 5 = w - 5
Solving gives p = 10 and w = 20.
Answer: D.
Question: To apply for the position of photographer at a local magazine, a photographer needs to include two or three photos in an envelope accompanying the application. If the photographer has pre-selected six photos representative of her work, how many choices does she have to provide the photos for the magazine?
A.32
B.35
C.36
D.40
Answer: B.35
Explanation: 6C2 + 6C3 = 15 + 20 = 35
The answer is B.
Question: If x is an integer and y = 3x + 2, which of the following CANNOT be a divisor of y?
A.4
B.5
C.6
D.7
Answer: C.6
Explanation: Just to add some more to Bunuel's explanation, if a number is a multiple of 3, it will be in a form:
n = 3*k, where k is an integer
And if a number is a multiple of 6, it will be in a form :
m = 6*l, where l is an integer
so m = 2 * 3 * l = (2*l) * 3 = 3 * p, where p is an integer.
In other words, the prime factorization of m must have 3 as a factor, if it's a multiple of 6, but the expression can't have that (as explained by Bunuel), so it can't be a multiple of 6 either
ANSWER:C
Question: A book store bought copies of a new book by a popular author, in anticipation of robust sales. The store bought 400 copies from their supplier, each copy at wholesale price W. The store sold the first 150 copies in the first week at 80% more than W, and then over the next month, sold a 100 more at 20% more than W. Finally, to clear shelf space, the store sold the remaining copies to a bargain retailer at 40% less than W. What was the bookstore’s net percent profit or loss on the entire lot of 400 books?
A.30% loss
B.10% loss
C.10% profit
D.20% profit
Answer: D.20% profit
Explanation: C.P. = 400W
S.P. = 1.8W*150 + 1.2W*100 + 0.6W*150 = 480W
Since, S.P. > C.P., there is net profit.
Profit = S.P. - C.P. = 480W - 400W = 80W
Profit % = (Profit/C.P.)*100 = (80W/400W)*100 = 20%
So, the correct answer is D.
Question: A committee of 2 people is to be selected out of 3 teachers and 4 preachers. If the committee is selected at random, what is the probability that the committee will be composed of at least 1 preacher?
A.1/4
B.1/3
C.2/3
D.6/7
Answer: D.6/7
Explanation: Total no of ways in which you can select a committee of 2 people out of 7 people is 7C2 ways= 21 ways
Requirement is at-least 1 preacher= 4C1*3C1+4C2 or 7C2-3C2=18 ways
Probability= 18/21 = 6/7
ANSWER:D
Question: If 73! has 16 zeroes at the end, how many zeroes will 80! have at the end?
A.16
B.17
C.18
D.19
Answer: D.19
Explanation: Prime Factoring: you need a 2 and a 5 to make a 10 (a "zero"), and there are TONS of 2's so let's skip these and focus on the (rarer) 5s:
80! = 1*2*3*4*5*6...*78*79*80
Since there are 80 consecutive numbers, there are 16 multiples of 5 in there, but if we're prime factoring, we need to remember that SOME multiples of 5 actually contain more than just one 5. Which? 25 comes to mind -- it's got two of them! So all the multiples of 25 actually contain two 5's (ie: 50 and 75)
So, to recap, we have 16 of them, plus 3 more (the additional 5's in 25, 50, and 75), so that makes 19, and since we have more than enough 2's, we know our number will have exactly 19 zeros at the end.
ANSWER:D
Question: Mary's income is 60 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. What percent of Juan's income is Mary's income?
A.124%
B.120%
C.96%
D.80%
Answer: C.96%
Explanation: Juan's income = 100 (assume);
Tim's income = 60 (40 percent less than Juan's income);
Mary's income = 96 (60 percent more than Tim's income).
Thus, Mary's income (96) is 96% of Juan's income (100).
Answer: C
Question: P is two years older than Q who is twice as old as R. The total of the ages of P, Q and R is 25. How old is Q?
A.7.2 years
B.8.2 years
C.9.8 years
D.9.2 years
Answer: D.9.2 years
Explanation: Let age of R =x. Then,
Age of Q =2x
Age of P =2+2x
Total age of P,Q and R =25
⇒(2+2x)+2x+x=25
⇒5x=23
⇒x=23/5=4.6 years
B's age =2x=2×4.6=9.2 years
ANSWER:D
Question: A man can row with a speed of 20 kmph in still water. If the stream flows at 7 kmph, then the speed in downstream is?
A.27
B.23
C.20
D.27
Answer: D.27
Explanation: M = 20
S = 7
DS = 20 + 7 = 27
Answer: D
Question: A theater box office sold an average (arithmetic mean) of 65 tickets per staff member to a particular movie. Among the daytime staff, the average number sold per member was 75, and among the evening staff, the average number sold was 60. If there are no other employees, what was the ratio of the number of daytime staff members to the number of evening staff members?
A.1:2
B.1:4
C.5:11
D.1:3
Answer: A.1:2
Explanation: Deviation from the mean for the daytime staff = 75 - 65 = 10.
Deviation from the mean for the evening staff = 65 - 60 = 5.
Thus, the ratio of the number of daytime staff members to the number of evening staff members is 5:10 = 1:2.
The answer is A.
Question: Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Four years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
A.A)24
B.B)89
C.C)67
D.D)32
Answer: D.D)32
Explanation: Let the present ages of Sameer and Anand be 5x years and 4x years respectively.
Then,	(5x + 4/4x + 4)=11/9
9(5x + 4) = 11(4x + 4)
45x + 36 = 44x + 44
45x - 44x = 44 - 36
x = 8.
Anand's present age = 4x = 32 years.
Answer:D
Question: How many meaningful English words can be formed with the letters ESRO using each letter only once in each word?
A.1
B.3
C.4
D.8
Answer: B.3
Explanation: Explanation:
Meaningful words are ROSE, SORE and EROS.
Note the meaning of the words SORE and EROS with the help of dictionary.
Answer: B) Three
Question: If S is the product of all positive integers less than 31, than what is the greatest integer k for which S/18^k is an integer?
A.3
B.6
C.7
D.14
Answer: C.7
Explanation: 30! S must be divisible by (3*3*2)^k.
As I will find a lot of 2's among 30!'s factors I will focus on the 3's (that also occurs twice instead of only once as a factor in 18).
Every multiple of 3 will provide me with atleast one factor of 3. There aren't that many so I list them quickly.
3 6 9*
12 15 18*
21 24 27**
30
The stars are marked as they are multiples of 9* or 27** and thus provides two or three 3's respectively.
3=3 (occurs 10 times) +10
3*3=9 (occurs 3 times) +3(adding just one additional three each as they were not counted for in the multiples of 3)
3*3*3=27 (occurs 1 time) +1 (again, adding just one as they were previously not counted)
Total: 14.
For every k we add two 3's. So we must divide 14 by 2 to get the highest integer K before we receive a non-integer result.
Answer: 7 -> Answer choice: C.
Question: What is the ratio between perimeters of two squares one having 3 times the diagonal then the other?
A.3: 8
B.3: 6
C.3: 7
D.3: 1
Answer: D.3: 1
Explanation: d = 3d d = d
a√2 = 3d a√2 = d
a = 3d/√2 a = d/√2 => 3: 1
Answer:D
Question: Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?
A.22
B.72
C.37
D.16
Answer: D.16
Explanation: Explanation:
L.C.M. of 2, 4, 6, 8, 10, 12 is 120.
So, the bells will toll together after every 120 seconds(2 minutes).
In 30 minutes,they will together (30/2)+1=16 times
Answer: D) 16
Question: A train of length 150 metres takes 40.5 seconds to cross a tunnel of length 300 metres. What is the speed of the train in km/hr ?
A.13.33
B.26.67
C.40
D.66.67
Answer: C.40
Explanation: Explanation:
Speed = 150+300/40.5m/sec
=450/40.5=18/5km/hr = 40 km/hr.
ANSWER IS C
Question: Three numbers are in the ratio 1 : 2 : 3 and their H.C.F is 3. The numbers are
A.12, 24, 30
B.12, 24, 38
C.12, 24, 362
D.3, 6, 9
Answer: D.3, 6, 9
Explanation: Explanation:
Let the required numbers be x, 2x, 3x. Then, their H.C.F =x. so, x= 3
\inline \fn_jvn \therefore The numbers are 3, 6, 9
Answer: D) 3, 6, 9
Question: A miniature roulette wheel is divided into 10 equal sectors, each bearing a distinct integer from 1 to 10, inclusive. Each time the wheel is spun, a ball randomly determines the winning sector by settling in that sector. If the wheel is spun two times, approximately what is the probability that the product of the two winning sectors’ integers will be even?
A.88%
B.75%
C.67%
D.63%
Answer: B.75%
Explanation: The only way to have an odd product is if both integers are odd.
P(odd product) = 1/2*1/2 = 1/4
P(even product) = 1 - 1/4 = 3/4 = 75%
The answer is B.
Question: What is the lowest positive integer that is divisible by each of the integers 1 through 8, inclusive?
A.420
B.560
C.840
D.960
Answer: C.840
Explanation: The integers are 1 , 2 , 3 , 4 , 5 , 6 , 7 and 8
Lowest positive integer that is is divisible by each of the integers 1 through 8
= 2^3 * 3 * 5 * 7
=8*3 *5 *7
=24 * 35
= 840
Answer C
Question: There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one liter every hour in A, it gets filled up like 10, 20, 40, 80, 160 in tank B. (At the end of first hour, B has 10 liters, second hour it has 20, third hour it has 40 and so on). If tank B is 1/32 filled after 21 hours, what is the total duration required to fill it completely?
A.22
B.28
C.269
D.26
Answer: D.26
Explanation: The data related to the first tank A is not necessary. As you can see, the capacity that gets filled in the tank B after each hour is doubled. So If the tank is 1/32nd part is full after 21 hours, it is 1/16th part full after 22 hours, 1/8th part full after 23 hours, 1/4th part full after 24 hours, 1/2 full after 25 hours, completely full after 26 hours.
Answer:D
Question: Find the sum of first 30 natural numbers
A.470
B.468
C.465
D.463
Answer: C.465
Explanation: Explanation:
Sum of n natural numbers
=n(n+1) / 2
=30(30+1) / 2=30(31) / 2=465
Option C
Question: A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A?
A.298
B.608
C.279
D.280
Answer: D.280
Explanation: 80* 7: x* 3 = 1:1 1/2
560: 3x = 2: 3
x = 280
Answer:D
Question: John takes a trip and drives 9 hours from Town X to Town Z at a rate of 60 miles per hour. On his way back, John drives 85 miles per hour and stops in Town Y which is midway between Town X and Town Z. How many hours does it take Scott to drive from Town Z to Town Y?
A.1.75
B.1.25
C.1.45
D.4.15
Answer: D.4.15
Explanation: distance from X to Z =9 hr* 60 mph= 540 miles
hence distance from Y to Z= 1/2*540=270
time=270/85=4.15 hrs
IMO: D
Question: A company has 100 employees, 40% of whom are employed part time. If it hires 25 new employees, 40% of whom are employed part time, what will be the percent increase in part time employees?
A.1 2/3 %
B.2 2/3 %
C.4 %
D.25 %
Answer: D.25 %
Explanation: Total employee = 100
Part time Empl = 40
New part time empl = 25 * (40/100)
= 10
Total new part time Emp = 10+40= 50
Old part time Emp = 40
% increase = (new - old)*100/old
=10*100/40
= 25%
Ans-D
Question: In a class of 60 students, the number of boys and girls participating in the annual sports is in the ratio 3 : 2 respectively. The number of girls not participating in the sports is 5 more than the number of boys not participating in the sports. If the number of boys participating in the sports is 15, then how many girls are there in the class ?
A.22
B.32
C.30
D.28
Answer: C.30
Explanation: Let the number of boys and girls participating in sports be 3x and 2x respectively.
Then, 3x = 15 or x = 5.
So, number of girls participating in sports = 2x = 10.
Number of students not participating in sports = 60 - (15 + 10) = 35.
Let number of boys not participating in sports be y.
Then, number of girls not participating in sports = (35 -y).
Therefore (35 - y) = y + 5 2y 30 y = 15.
So, number of girls not participating in sports = (35 - 15) = 20.
Hence, total number of girls in the class = (10 + 20) = 30.
Answer:C
Question: To furnish a room in a model home an interior decorator is to select 4 chairs and 4 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 75 different combinations are possible, how many tables are there in the warehouse?
A.A)6
B.B)8
C.C)10
D.D)15
Answer: A.A)6
Explanation: Total number of ways to choose 4 chairs from 5= 5C4=5
Total number of combination=75
That means we need get 15 combinations from the selection of tables....
Screening through the answers.... 6C4=15..... 15*5=75
Answer is 6... A
Question: A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
A.66 km/hr
B.72 km/hr
C.78 km/hr
D.81 km/hr
Answer: D.81 km/hr
Explanation: Explanation:
4.5 km/hr =(4.5 x	5/18)m/sec =	5/4m/sec = 1.25 m/sec, and
5.4 km/hr =(5.4 x5/18)m/sec =3/2m/sec = 1.5 m/sec.
Let the speed of the train be x m/sec.
Then, (x - 1.25) x 8.4 = (x - 1.5) x 8.5
=> 8.4x - 10.5 = 8.5x - 12.75
=> 0.1x = 2.25
=> x = 22.5
Speed of the train =(22.5 x	18/5)km/hr = 81 km/hr.
ANSWER IS D
Question: 160 is what percent of 50 ?
A. 5%
B. 20%
C. 320%
D. 200%
Answer: C. 320%
Explanation: 50*x=160 --> x=3.2 --> 3.2 expressed as percent is 320%.
Answer: C.
Question: What will come in place of the x in the following Number series? 46080, 3840, ?, 48, 8, 2, 1
A.1
B.384
C.5
D.7
Answer: B.384
Explanation: 46080 /12 = 3840
3840 /10 = 384
384 /8 = 48
48 /6 = 8
8/4 = 2
2 /2 = 1
B
Question: The length of a rectangle is reduced by 20%. By what % would the width have to be increased to maintainthe original area?
A.10%
B.20%
C.25%
D.30%
Answer: C.25%
Explanation: Sol. Required change = (20*100)/(100-20)=25%
C
Question: Find the average of first 20 natural numbers?
A.5.5
B.7.2
C.10.5
D.12.3
Answer: C.10.5
Explanation: Sum of first n natural numbers = n(n+1)/2
sum of first 20 natural numbers = 20*21/2 =210
average = 210/20 = 10.5
Answer is C
Question: The inverse ratio of 4: 2: 1 is?
A.2:4:8
B.2:3:9
C.2:3:2
D.2:3:6
Answer: A.2:4:8
Explanation: 1/4: 1/2: 1/1 = 2:4:8
Answer:A
Question: If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
A.3
B.8
C.9
D.6
Answer: B.8
Explanation: 96% ---- 12
144% ---- ?
96/144 * 12 = 8
Answer: B
Question: NHAI employs 100 men to build a highway of 2km in 50 days working 8 hours a day. If in 25 days they completed 1/3 part of work .than how many more employees should NHAI hire to finish it in time working 10 hours a day?
A.22
B.60
C.28
D.11
Answer: B.60
Explanation: Here 2km is immaterial. The given problem can be written in a tabular form like below.
We can apply chain rule now.
Total men required to complete the remaining work = 100×2525×810×2313100×2525×810×2313 = 160
So additional men required = 160 - 100 = 60
Answer:B
Question: A train 500 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
A.277 m
B.700 m
C.800 m
D.187 m
Answer: C.800 m
Explanation: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (500 + x)/60 = 65/3
x = 800 m.
Answer:C
Question: The price of a radio was increased by 25 percent. The new price was then increased by 40 percent. A single increase of what percent is equivalent to these two successive increases?
A.80%
B.75%
C.65%
D.50%
Answer: B.75%
Explanation: consider base price - $100
25% increase = 1.25*100 = $125
another 40% increase on new price = 1.4* 125 = $175
so final price of radio - $175
therefore a 75% increase
correct option - B
Question: Two trains start from P and Q respectively and travel towards each other at a speed of 50 km/hr and 40 km/hr respectively. By the time they meet, the first train has travelled 100 km more than the second. The distance between P and Q is :
A.500 km
B.630 km
C.900 km
D.660 km
Answer: C.900 km
Explanation: Sol.
At the time of meeting, let the distane travelled byb the second train be x km. Then,
distance covered by the first train is (x + 100) km
∴ x/40 = (x+100)/50 ⇔ 50x = 40x 4000 ⇔ x = 400.
So, distance between P and Q = (x+x+100) km = 900 km.
Answer C
Question: What is the investment made if one invests in 15% stock at 50 and earns Rs.2000?
A.5000
B.2767
C.2697
D.126967
Answer: A.5000
Explanation: Explanation:
To earn Rs.15, investment = Rs.50.
Hence, to earn Rs.1500, investment = (1500*50)/15
= Rs.5000
ANSWER: A
Question: The seating chart of an airplane shows 30 rows of seats. Each row has 3 seats on each side of the center aisle, and one of the seats on each side is a window saet. The view from the window seats in 25 of the rows is obscured by the wings of the airplane. If the first person to be assigned a seat is assigned a window seat and thw window seat is assigned randomly, what is the probability that the person will get a seat with an unobscured view?
A.1/6
B.1/3
C.2/3
D.5/6
Answer: A.1/6
Explanation: priyalr
6 seats per row, think of a boeing 737. We have 30 rows, therefore window 30 seats one one side and 30 window seats on the other, totaling 60 window seats on the whole plane.
the view of the window of 25 rows is blocked. two wings, therefore 50 window seats are blocked.
Total window seats = 60
Total blocked window seats = 50
Total unblocked seats = 10
We know that a window seat was given, therefore probability for not window seat is 10/60 =1/6
ANS A
Question: Krishan and Nandan jointly started a business. Krishan invested three times as Nandan did and invested his money for double time as compared to Nandan. If the gain is proportional to the money invested and the time for which the money is invested and the total gain was Rs. 28000, find the earning of Nandan.
A.Rs.7000
B.Rs.5000
C.Rs.6000
D.Rs.Rs.4000
Answer: D.Rs.Rs.4000
Explanation: 3:1
2:1
------
6:1
7 ----- Rs.28000
1 ----- ? => Rs.28,000/7=Rs. 4000
Answer: D
Question: A certain bakery sells six different-sized wedding cakes. Each cake costs x dollars more than the next one below it in size, and the price of the largest cake is $24.50. If the sum of the prices of the six different cakes is $109.50, what is the value of x?
A. 1.50
B. 1.75
C. 2.00
D. 2.50
Answer: D. 2.50
Explanation: Since the price of the largest cake (6th) is $24.50, then the price of the smallest cake (1st) is $(24.50-5x). Now, the prices of the cakes are evenly spaced so the sum of the prices is (average price)*(# of cakes)=(first+last)/2*(# of cakes). So, (24.50-5x+24.50)/2*6= 109.50 --> x=2.5.
Answer: D.
Question: Three bells chime at intervals of 18 min., 24 min. and 32 min. respectively. At a certain time they begin together. What length Z of time will elapse before they chime together again?
A.2 hr. and 24 min.
B.4 hr. and 48 min.
C.1 hr. and 36 min.
D.5 hr.
Answer: B.4 hr. and 48 min.
Explanation: It should be simple. All the three bells will chime again together whenver their time intervals intersect eachother.
So the LCM of the three time intervals (18, 24,32) would be the answer.
LCM (18, 24, 32) Z= 288 => 4 hours 48 mins.B
Question: A man can row downstream at 25 kmph and upstream at 15 kmph. Find the time to reach a destination point at a distance of 50km along the downstream.
A.4 hrs.
B.1 hrs.
C.3 hrs.
D.2 hrs.
Answer: D.2 hrs.
Explanation: Let the speed of the man in downstream=25 kmph. distance to be covered along the stream=50kmph
=>time taken =D/S =50/25 =2 Hrs.
Answer:D
Question: Find the number that fits somewhere into the middle of the series. Some of the items involve both numbers and letters
Look at this series: C19, E21, __, I25, K27, ... What number should fill the blank?
A.D20
B.E21
C.F22
D.G23
Answer: B.E21
Explanation: B
G23
In this series, the letters progress by 2, and the numbers increase by 2.
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
A.276m
B.180m
C.286m
D.288m
Answer: B.180m
Explanation: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer:B
Question: For any real number x, the operatoris defined as:
(x) = x(2 − x)
If p + 2 =(p + 2), then p =
A.1
B.0
C.1
D.-2
Answer: D.-2
Explanation: (x) = x(2 − x)
(p + 2) = (p + 2)(2 - p - 2) = -p(p+1)
We are given that p + 2 =(p + 2)
Therefore -p(p+2) = (p + 2)
Or (p + 2) + p(p+2) = 0
(p + 2)(p+1) = 0
p = -1,p=-2
Option D
Question: The average age of five persons is 40 years while the average age of some other 10 persons is 25 years. The average age of all the 15 persons is:
A.27 Years
B.32 Years
C.37 Years
D.30 Years
Answer: D.30 Years
Explanation: x/5==40
x==200
after 10 person
x/10==25
x==250
so avg btwn 15 person is,,
(250+200) / 15==30 ans
ANSWER:D