divelab/Sys2Bench huggingface dataset:
Question: An equity analyst needs to select 4 stocks for the upcoming year and rank these securities in terms of their investment potential. If the analyst has narrowed down the list of potential stocks to 8, in how many ways can she choose and rank her top 4 picks?
Options:
A)1200
B)1680
C)2102
D)4020
E)1840
Rationale: Number of ways of choosing 4 stocks = 8C4
Number of ways of ranking the chosen stocks = 4!
Hence total ways of chosing and ranking = 8C4 * 4! = 1680
Correct Option: B
Answer: B
Question: A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
Options:
A)118
B)110
C)112
D)113
E)115
Rationale: Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
Answer: C
Answer: C
Question: Today John is 3 times older than Mark. If in 13 years, John will be one year younger than twice the age of Mark on that day, how old is Mark today?
Options:
A)12
B)33
C)36
D)38
E)39
Rationale: today +13yrs
J =3M 3M+13
M M+13
Given after 13yrs john will be 1 year younger than twice mark's age
i.e 3M+13 = 2(M+13)-1
M=12
Answer is A.
Answer: A
Question: A train moves fast a telegraph post and a bridge 245 m long in 8 sec and 20 sec respectively. What is the speed of the train?
Options:
A)73.5
B)39.5
C)79.9
D)79.2
E)79.1
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 245)/20 = y
y = 20.42
Speed = 20.42 m/sec = 20.42 * 18/5 = 73.5 km/hr.
Answer:A
Answer: A
Question: The side of a square is increased by 25% then how much % does its area increases?
Options:
A)52.65
B)56.25
C)50.75
D)42.75
E)52.75
Rationale: a = 100 a2 = 10000
a = 125 a2 = 15625
----------------
10000 --------- 5625
100 -------? => 56.25 %
ANSWER:B
Answer: B
Question: Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is?
Options:
A)1:7
B)2:15
C)9:31
D)8:17
E)9:19
Rationale: 1/4 : 3/4 = (1:3)5 = 5:15
1/5 : 4/5 = (1:4)4 = 4:16
------
9:31
C
Answer: C
Question: How much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 11 inches than that of a rectangular sheet of paper measuring 5.5 inches by 11 inches?
Options:
A)50%
B)87%
C)100%
D)187%
E)200%
Rationale: Let's just look at the dimensions (no calculation needed).
With dimension 11 the same, the other dimension 11 is twice 5.5
Then the area will be double which means 100% greater.
The answer is C.
Answer: C
Question: To mail a package, the rate is 20 cents for the first pound and 5 cents for each additional pound. Two packages weighing 5 pounds and 10 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?
Options:
A)Combined, with a saving of 10 cents
B)Separately, with a saving of 10 cents
C)Combined, with a saving of 15 cents
D)Separately, with a saving of 15 cents
E)Combined, with a saving of 5 cents
Rationale: 5 pounds = 1*20+4*5 = 40
10 pounds = 1*20+9*5 =65
total = 105
15 pound = 1*20+14*5 = 90
dif. 15
Answer : C
Answer: C
Question: An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.2800, what will be the difference between Q and R's share?
Options:
A)2788
B)3500
C)7282
D)2782
E)2729
Rationale: 4 --- 2800
5 --- ? => 3500
Answer:B
Answer: B
Question: A father was as old as his son's present at the time of your birth. If the father's age is 38 years now, the son's age 5years back was?
Options:
A)10 years
B)12 years
C)14 years
D)16 years
E)20 years
Rationale: Let the son's present age be x years. Then, (38 - x) = x
2x = 38.
x = 19.
Son's age 5 years back (19 - 5) = 14 years.
C
Answer: C
Question: On average, the bottle-nosed dolphin comes up for air once every four minutes; the beluga whale, a close relative, comes up for air on average once every six minutes. The number of times a bottle-nosed dolphin would come up for air in a 24 hour period is approximately what percent greater than the number of times a beluga whale would come up for air in that same period?
Options:
A)50%
B)100%
C)150%
D)200%
E)250%
Rationale: Dolphin once in 4 min;
Beluga once in 6 min;
So, dolphin comes up 1.5 times frequently than beluga, which is 100% (6-4)/2*100.
Answer: B.
Answer: B
Question: What is the sum of all the composite numbers up to 8?
Options:
A)16
B)6
C)10
D)12
E)6
Rationale: Explanation:
4 + 6+8 = 16
Answer: A
Answer: A
Question: The mean of (54,822)^2 and (54,824)^2 =
Options:
A)(54,821)^2
B)(54,821.5)^2
C)(54,820.5)^2
D)(54,823)^2 + 1
E)(54,821)^2 – 1
Rationale: 54822^2 = (54823-1)^2 = 54823^2 + 1^2 - 2*54823*1
54824^2 = (54823+1)^2 = 54823^2 +1^2 + 2*54821*1
Taking the average of above 2 , we get (54823)^2 +1
hence the answer is D
Answer: D
Question: A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 40 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours?
Options:
A)18/79
B)1/200
C)1/25
D)1/50
E)1/900
Rationale: So there are 900 cars that they have to search.. Each takes 40mins, total of 36000 mins.. Have to find in 180 mins.. Prob180/36000 = 1/200 (ANSWER B)
Answer: B
Question: Tina has 12 shirts and 9 pants. How many clothing combinations does Barbara have, if she doesn’t wear 5 specific shirts with 3 specific pants?
Options:
A)93
B)66
C)36
D)85
E)108
Rationale: Total no of combinations available is= 12 shirts X 9 pants = 108
Eliminate the 5 shirts X 3 pants combo = 15 which gives.......>> 108-15=93
ANSWER:A
Answer: A
Question: The contents of a certain box consist of 14 apples and 12 oranges. How many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples?
Options:
A)3
B)6
C)14
D)17
E)20
Rationale: The objective here is that 70% of the fruit in the box should be apples.
Now, there are 14 apples at start and there is no talk of removing any apples, so number of apples should remain 14 and they should constitute 70% of total fruit, so total fruit = 14/0.7 = 20
So we should have 20-14 = 6 oranges.
Right now, there are 12 oranges, so to get to 6 oranges, we should remove 12 - 6 = 6 oranges.
Answer B
Answer: B
Question: (0.0088)(4.5) / (0.05)(0.1)(0.008)=
Options:
A)950
B)940
C)980
D)960
E)990
Rationale: (0.0088)(4.5) / (0.05)(0.1)(0.008)=0.0088 * 450/5 * (0.1)(0.008)
= 0.088*90/1 * 0.008 = 88*90/8 = 11*90
=990
Answer : E
Answer: E
Question: X and Y put in 3,000 and 4,000 respectively into a business. X reinvests into the business his share of the first year?s profit of 2,100 whereas Y does not reinvest. In what ratio should they share the second year?s profit?
Options:
A)39 : 40
B)3 : 4
C)3 : 7
D)40 : 79
E)None of these
Rationale: For first year, ratio of profit = 3 : 4
X?s profit of first year = 3?7 � 2100 = 900
Now, for second year,Now, for second year,
ratio of profit = 3000 � 12 + 900 � 12 : 4000 � 12
= 46800 : 48000 = 39 :40
Answer A
Answer: A
Question: One computer can upload 100 megabytes worth of data in 3 seconds. Two computers, including this one, working together, can upload 1300 megabytes worth of data in 30 seconds. How long would it take for the second computer, working on its own, to upload 100 megabytes of data?
Options:
A) 6
B) 10
C) 9
D) 11
E) 13
Rationale: Since the first computer can upload 100 megabytes worth of data in 3 seconds then in 3*10=30 seconds it can upload 10*100=1000 megabytes worth of data, hence the second computer in 30 seconds uploads 1300-1000=300 megabytes worth of data. The second computer can upload 100 megabytes of data in 10 seconds.
Answer: B.
Answer: B
Question: Liz drove from point A to point B at 40 Km/h. On her way back she drove at 50 Km/h and therefore her way back lasted one hour less. What is the distance (in Km) between A and B?
Options:
A)150
B)200
C)450
D)500
E)600
Rationale: Distance is same
S1t1=s2t2
40t= 50 (t-1)
t=5
distance= speed *time
40*5= 200
ANSWER:B
Answer: B
Question: Pipe A can fill a tank in 12 minutes and pipe B cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe B be closed, so that the tank is filled in 30 minutes?
Options:
A)18
B)27
C)98
D)27
E)36
Rationale: Let the pipe B be closed after x minutes.
30/12 - x/24 = 1 => x/24 = 30/12 - 1 = 3/2
=> x = 3/2 * 24
= 36.
Answer:E
Answer: E
Question: Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are
Options:
A)42,30
B)42,31
C)42,32
D)42,33
E)42,55
Rationale: Explanation:
Let their marks be (x+9) and x.
Then, x+9 = 56/100(x + 9 +x)
=> 25(x+9)
=> 14 (2x + 9)
=> 3x = 99
=> x = 33.
So, their marks are 42 and 33
Answer: Option D
Answer: D
Question: In a throw of coin what is the probability of getting tails.
Options:
A)1
B)2
C)1/2
D)0
E)None of these
Rationale: Explanation:
Total cases = [H,T] - 2
Favourable cases = [T] -1
So probability of geƫng tails = 1/2
Answer: C
Answer: C
Question: A person's present age is one-fifth of the age of his mother. After 8years, he will be one - half of the age of his mother. How old is the mother at present ?
Options:
A)A)25
B)B)44
C)C)32
D)D)45
E)E)40
Rationale: Let the mother's present age be x years
Then the person's present age = 2x/5
(3x/5)+8 = 1/2(x+8)
2(3x+40) = 5 (x+8)
x = 40
Answer is E
Answer: E
Question: If a fair coin is tossed six times, what is the probability of getting exactly four heads in a row?
Options:
A)5/64
B)3/32
C)3/16
D)3/8
E)1/8
Rationale: Let X represent either H or T (it doesn't matter which).
P(HHHHTX) = 1/32
P(THHHHT) = 1/64
P(XTHHHH) = 1/32
The sum of these three probabilities is 5/64
The answer is A.
Answer: A
Question: The average of 35 students in a class is 16 years. The average age of 21 students is 14. What is the average age of remaining 14 students?
Options:
A)79 years
B)18 years
C)19 years
D)19 years
E)13 years
Rationale: Sum of the ages of 14 students
= (16 * 35) - (14 * 21) = 560 - 294 = 266
Required average = (266/14) = 19 years.
Answer:D
Answer: D
Question: An uneducated retailer marks all his goods at 60% above the cost price and thinking that he will still make 25% profit, offers a discount of 25% on the marked price. What is his actual profit on the sales?
Options:
A)20 %
B)13.50 %
C)14 %
D)14.50 %
E)None
Rationale: Sol.
Let C.P. = Rs. 100. Then, marked price = Rs. 160.
S.P. = 75% of Rs. 160 = Rs. 120.
∴ Gain% = 20%.
Answer A
Answer: A
Question: If x < z < -1, which of the following is true?
Options:
A)x/z > xz
B)z/x > x+z
C)z/x > xz
D)z/x < x+z
E)z/x > x/z
Rationale: Consider :
x= -3
z= -2
then put for every option. U'll get ans B.
Answer: B
Question: The profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448. What should be the sale price for making 40% profit?
Options:
A)$480
B)$450
C)$896
D)$870
E)$660
Rationale: Let C.P. = $ x.
Then, 832 - x = x - 448
2x = 1280 => x = 640
Required S.P. = 140% of $ 640 = $ 896.
C
Answer: C
Question: The average age of 60 students in a class is 10years. If teacher's age is also included then average increases 1year then find the teacher's age?
Options:
A)71
B)65
C)61
D)45
E)36
Rationale: Total age of 50 students = 60*10 = 600
Total age of 51 persons = 61*11 = 671
Age of teacher = 671-600 = 71years
Answer is A
Answer: A
Question: In a three digit number, the hundred digit is 2 more than the tens digit and the units digit is 2 less than the tens digit. If the sum of the digits is 15, find the number?
Options:
A)867
B)864
C)753
D)946
E)549
Rationale: C
753
Let the three digit numbers be 100a + 10b + c
a = b + 2
c = b - 2
a + b + c = 3b = 15=> b = 5
So a = 7 and b = 3
Hence the three digit number is: 753
Answer: C
Question: How many pieces of 0.36 meteres can be cut from a rod 26.5 meteres long
Options:
A)30
B)40
C)50
D)60
E)73
Rationale: Explanation:
We need so simple divide 26.5/0.36,
=(2650/36) = 73
Option D
Answer: D
Question: man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
Options:
A)12
B)22
C)30
D)88
E)13
Rationale: US = 25
DS = 35
M = (35 + 25)/2
= 30
Answer:C
Answer: C
Question: A man bought 6 pencils for Rs 5 and sold them at 5 pencils for Rs. 6. Calculate his gain percentage
Options:
A)78
B)26
C)44%
D)43
E)82
Rationale: Explanation:
No explanation is available for this question!
ANSWER:C
Answer: C
Question: When 30 is subtracted from a number, it reduces to seven-twelve of the number. What is the sum of the digit of the number
Options:
A)40
B)44
C)46
D)48
E)72
Rationale: Explanation:
Let the number be x. Then,
x -30 = 7x/12 => x - 7x/12 = 30
5x/12 = 30 => x = 72
Answer: Option E
Answer: E
Question: A line of 24 children walk single file down the 54-meter hallway of their school at a speed of 20 meter/min. If each child takes up 1/4 meter of space in line, how long does it take for all of them to traverse the full length of the hallway?
Options:
A)1 min
B)2 min
C)3 min
D)4 min
E)5 min
Rationale: C
3 min
d = 24 * 1/4 m + 54 m = 60 m
T = 60 meters / 20 meters/min = 3 min
Answer: C
Question: Each of 16 individuals is to be given an identifying code consisting of one or more distinct digits in ascending order. What is the minimum number of distinct digits needed to give each individual a unique code?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: TWO WAYS-
1) we can do by looking at choices too
3-digits
since 3 is the lowest lets see how many can be nad ewith 3..
1) single digit - 3
2) 2 digits - different digits - 3*2/2 = 3.... 12,13,23
3) 3-digits - 123 - only 1
total = 3+3+1 =7...
4-digits
1) single digit - 4
2) 2 digits - different digits - 4*3/2 = 6.... 12,13,14,23,24,34
3) 3-digits - 4*3*2/3! = 4
4) 4-digits - 4*3*2/4! = 1
Total = 4+6+4+1 = 15
so 5 should be the answer
ANSWER:C
Answer: C
Question: If it was two hours later, it would be half an hour as long until midnight as it will be if it were an hour later. What is the time now?
Options:
A)9.10 pm
B)7.00 pm
C)9.00 pm
D)8.00 pm
E)9.30 pm
Rationale: Let the present time be x, the time after one hour is (x+1) and the time after two hours is (x+2), the time at mid night is 12
The time from one hour later to midnight is 12-(x+1)
The time from two hours later to midnight is 12-(x+2)
Given, the time from one hour later is twice of the time from two hours later,
12-(x+1) is twice of 12-(x+2)
12-x-1 = 24-2x-4
x=9
The present time is 9.00 pm
The time after one hour is 10.00 pm( two hours to 12) and the time after two hours is 11.00 pm( one hour to midnight)
The answer is 9.00 pm
ANSWER:C
Answer: C
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?
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: 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.
Answer: 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.
Options:
A)Only conclusion I follows
B)Only conclusion II follows
C)Either I or II follows
D)Neither I nor II follows
E)Both I and II follow
Rationale: 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
Answer: B
Question: A began business with Rs.45000 and was joined afterwards by B with Rs.27000. When did B join if the profits at the end of the year were divided in the ratio of 2:1?
Options:
A)1
B)6
C)7
D)8
E)2
Rationale: 45*12 : 27*x = 2: 1
x = 10
12 -10 = 2
Answer: E
Answer: E
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?
Options:
A)72
B)75
C)80
D)81
E)90
Rationale: 44 + 28 + 10 = 82%
100 – 82 = 18%
450 * 18/100 = 81
ANSWER:D
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?
Options:
A)690 km/hr
B)720 km/hr
C)730 km/hr
D)750 km/hr
E)760 km/hr
Rationale: 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
Answer: A
Question: For any non-zero a and b that satisfy |ab| = ab and |a| = -a
|b - 4| + |ab + b| = ?
Options:
A)a) ab - 4
B)b) 2b - ab - 4
C)c) ab + 4
D)d) ab - 2b + 4
E)e) 4 - ab
Rationale: |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
Answer: 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?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: 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
Answer: C
Question: The greatest number of four digits which is divisible by 12, 20, 36 and 60 is:
Options:
A)9000
B)9900
C)9500
D)9800
E)9700
Rationale: 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
Answer: 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?
Options:
A)32 hours
B)40 hours
C)35 hours
D)30 hours
E)36 hours
Rationale: 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
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
Options:
A)I only
B)I and II only
C)I and III only
D)III only
E)I, II, and III
Rationale: 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
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.
Options:
A)10
B)22
C)15
D)30
E)8
Rationale: 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
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?
Options:
A)300
B)120
C)150
D)160
E)270
Rationale: 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...
Answer: 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.
Options:
A)27
B)5
C)4
D)9
E)8
Rationale: 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
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?
Options:
A)12
B)13
C)14
D)15
E)16
Rationale: w:x:y = 100:30:20
20:6:4
20 --- 10
30 --- ? => 15
Answer:D
Answer: D
Question: If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area?
Options:
A)120 cm2
B)197 cm2
C)876 cm2
D)267 cm2
E)268 cm2
Rationale: 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
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?
Options:
A)6.25
B)5.5
C)25
D)15
E)6
Rationale: 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
Answer: C
Question: If the number 872,152,24x is divisible by 11, what must be the value of x?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: 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
Answer: C
Question: What is the measure of the radius of the circle inscribed in a triangle whose sides measure 8, 15 and 21 units?
Options:
A)8.5 units
B)2.6 units
C)3 units
D)5 units
E)12 units
Rationale: 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
Answer: B