divelab/Sys2Bench huggingface dataset:
Question: If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area?
Options:
A)120 cm2
B)176 cm2
C)267 cm2
D)268 cm2
E)976 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: The speed of a boat in upstream is 80 kmph and the speed of the boat downstream is 120 kmph. Find the speed of the boat in still water and the speed of the stream?
Options:
A)21 kmph.
B)22 kmph.
C)20 kmph.
D)25 kmph.
E)28 kmph.
Rationale: Speed of the boat in still water = (80+120)/2 = 100 kmph. Speed of the stream
= (120-80)/2
= 20 kmph.
Answer:C
Answer: C
Question: What was the day of the week on 15th May, 2006?
Options:
A)Thursday
B)Friday
C)Saturday
D)Monday
E)Sunday
Rationale: 28 May, 2006 = (2005 years + Period from 1.1.2006 to 28.5.2006)
Odd days in 1600 years = 0
Odd days in 400 years = 0
5 years = (4 ordinary years + 1 leap year) = (4 x 1 + 1 x 2) 6 odd days
Jan. Feb. March April May
(31 + 28 + 31 + 30 + 15 ) = 135 days
135 days = (19 weeks + 2 day) 1 odd day.
Total number of odd days = (0 + 0 + 6 + 2) = 8 0 odd day.
Given day is Monday.
Answer: Option D
Answer: D
Question: Of 61 players on a cricket team, 37 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?
Options:
A)53
B)55
C)59
D)71
E)92
Rationale: Total = 61
Thrower = 37
Rest = 61 - 37 = 24
Left Handed = 24/3 = 8
Right handed = 16
If all Thrower are right handed then total right handed is 37 + 16 = 53
so A. 53 is the right answer
Answer: A
Question: A company plans to gradually replace its fleet of 20 cars with newer models. At the end of every year starting with 2000 it retires 5 of its old cars and buys 6 new models.How many years did it take before the number of older cars left in the company's fleet was less than 50 percent of the fleet?
Options:
A)6
B)3
C)2
D)4
E)5
Rationale: Total fleet--20
End of year 2000 -- (retires 5 and buys 6) total fleet--21(15 old 6 new).
End of year 2001 -- (retires 5 and buys 6) total fleet--22(10 old 12 new).
Answer is C--after 2 years the company has a total of 22 cars (10 old 12 new), the old cars are already less than 50% of its fleet.
Answer: C
Question: A 40 gallon solution of salt and water is 10% salt. How many gallons of water must be added to the solution in order to decrease the salt to 8% of the volume?
Options:
A)810
B)12
C)13
D)14
E)16
Rationale: Amount of salt = 4.0
Assume x gallons of water are added.
4.0 / 40 + x = 8/100
400 = 8x + 320
8x = 80
x = 10
Correct Option: A
Answer: A
Question: The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 24, how many more dollars, in terms of x, will it cost per person?
Options:
A) x/6
B) x/17
C) x/40
D) 3x/40
E) 3x/80
Rationale: Just plugging in values
X= 240
Cost per person if we consider 10 = 24
Cost per person if we consider 24 = 10
Difference between costs is 14 dollars.
Plugging in the value of x into the answer choices, let's see which one yields a result of 14. And that is B.
Answer: B
Question: Find the value of m 32519 x 9999 = m?
Options:
A)724533811
B)353654655
C)545463251
D)725117481
E)325157481
Rationale: 32519 x 9999 = 32519 x (10000 - 1)
= 32519 x 10000 - 32519 x 1
= 325190000 - 32519
= 325157481
E
Answer: E
Question: A, Band C enter into partnership. A invests 3 times as much as B and B invests two-third of what C invests. At the end of the year, the profit earned is Rs. 7700. What is the share of B ?
Options:
A)1100
B)800
C)1400
D)1200
E)None of them
Rationale: Let C's capital = Rs. x. Then, B's capital = Rs. (2/3)x
A’s capital = Rs. (3 x (2/3).x) = Rs. 2x.
Ratio of their capitals = 2x : (2/3)x :x = 6 : 2 : 3.
Hence, B's share = Rs. ( 7700 x (2/11))= Rs. 1400.
Answer is C
Answer: C
Question: An ant walks an average of 600 meters in 12 minutes. A beetle walks 15% less distance at the same time on the average. Assuming the beetle walks at her regular rate, what is its speed in km/h?
Options:
A)2.215.
B)2.55
C)2.775.
D)3.2.
E)3.5.
Rationale: the ant walks an average of 600 meters in 12 minutes
600 meters in 1/5 hours
the beetle walks 15% less distance = 600-90=510 meters in 12 minutes
0.510 km in 12/60 = 1/5 hours
speed = 0.510*5 = 2.55 km/h
Correct answer B=2.55
Answer: B
Question: An empty fuel tank with a capacity of 218 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 30 gallons of ethanol, how many gallons of fuel A were added?
Options:
A)122
B)150
C)100
D)80
E)50
Rationale: Say there are A gallons of fuel A in the tank, then there would be 218-A gallons of fuel B.
The amount of ethanol in A gallons of fuel A is 0.12A;
The amount of ethanol in 218-A gallons of fuel B is 0.16(218-A);
Since the total amount of ethanol is 30 gallons then 0.12A+0.16(218-A)=30 --> A=122.
Answer: A.
Answer: A
Question: eight mobsters have arrived at the theater for the premiere of the film “Goodbuddies.” One of the mobsters, Frankie, is an informer, and he's afraid that another member of his crew, Joey, is on to him. Frankie, wanting to keep Joey in his sights, insists upon standing behind Joey in line at the concession stand, though not necessarily right behind him. How many ways can the eight arrange themselves in line such that Frankie’s requirement is satisfied?
Options:
A)22222
B)20160
C)8644
D)46060
E)40320
Rationale: 8 mobsters can stand in 8! ways = 40320
in half of the cases one person will be ahead and in the other person in the other half.
thus 20160 cases.
B
Answer: B
Question: If all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100(both inclusive) varies by
Options:
A)330
B)340
C)350
D)360
E)370
Rationale: 1 11 21 .......91
2 12 22........92
3 13 23........93
. . . .. . .. . .
. . .. .. . .. .
. . .. . . .. . ...
there are total 20 occurrence of 6. once place at 6 th row in every column and tens place in 6 th column
and diff of 6 and 9 is 3 so
3*1*10+3*10*10 = 330
ANSWER:A
Answer: A
Question: If n is an integer greater than 8, which of the following must be divisible by 8 ?
Options:
A)n(n + 5)(n – 6)
B)n(n + 2)(n – 1)
C)n(n + 1)(n – 4)
D)n(n + 3)(n – 5)
E)n(n + 5)(n – 6)
Rationale: If n= 9 , then (n-1) is divisible by 8 .
B
Answer: B
Question: Tough and Tricky questions: Statistics.
Set X consists of prime numbers {3, 11, 7, A, 17, 19}. If integer Y represents the product of all elements in set X and if 11Y is an even number, what is the range of set X?
Options:
A) 14
B) 16
C) 17
D) 20
E) 26
Rationale: Since 11Y = Even therefore Y has to beEVENsince 11 is a odd integer (Even * Odd = Even)
Similarly, Y is the product of all integers in set X But all integers in Set X are odd except the unknown A and since X contains only prime numbers, A has to equal to 2... ( 2 is the only even prime number and the product of all prime numbers in set X has to be Even, Even * Odd = Even)
Since you know value of A you can calculate the range = Largest integer in the set minus Smallest integer in the set = 19-2 =17
Answer is C
Answer: C
Question: A paper is in a square form whose one side is 20 cm. Two semi circles are drawn on its opposites as diameters. If these semi circles are cut down what is the area of the remaining paper?
Options:
A)(400 - 100π) cm2
B)(400 - 2π) cm2
C)(400 – 200π) cm2
D)200π cm2
E)None of these
Rationale: Explanation:
400- π*10*10=400-100 π
Answer IS A
Answer: A
Question: A restaurant meal cost $34.50 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then total amount paid must have been between:
Options:
A)$40 and $42
B)$39 and $41
C)$38 and 40
D)$37 and $39
E)$36 and $37
Rationale: let tip=t
meal cost=34.50
range of tip = from 10% of 34.5 to 15% of 34.5 = 3.55 to 5.325
hence range of amount paid= 34.5+T= 38.05 to 39.825
ANSWER:C
Answer: C
Question: The ratio of two numbers is 3:4 and their sum is 28. The greater of the two numbers is?
Options:
A)12
B)16
C)18
D)19
E)20
Rationale: 3:4
Total parts = 7
= 7 parts --> 28 (7 × 4 = 28)
= 1 part ---->4 (1 × 4 = 4)
= The greater of the two number is = 4
= 4 parts ----> 16 (4 × 4 = 16)
B
Answer: B
Question: The sum of three consecutive even numbers is 42. Find the middle number of the three?
Options:
A)14
B)16
C)18
D)24
E)34
Rationale: Three consecutive even numbers (2P - 2), 2P, (2P + 2).
(2P - 2) + 2P + (2P + 2) = 42
6P = 42 => P = 7.
The middle number is: 2P = 14.
ANSWER:A
Answer: A
Question: Mohit sold an article for Rs. 18000. Had he offered a discount of 25% on the selling price, he would have earned a profit of 8%. What is the cost price of the article?
Options:
A)12500
B)27767
C)16688
D)26678
E)19987
Rationale: Let the CP be Rs. x.
Had he offered 25% discount, profit = 8%
Profit = 8/100 x and hence his SP = x + 8/100 x = Rs. 1.08x = 18000 - 25/100(18000) = Rs. 13500
=> 1.08x = 13500
=> x = 12500
\Answer: A
Answer: A
Question: An empty pool being filled with water at a constant rate takes 3hours to fill to 3/5 of its capacity.how much more time will it take to finish filling the pool?
Options:
A)5hr 30min
B)5hr 20min
C)4hr 48min
D)3 hr 12min
E)2hr 40 min
Rationale: As pool is filled to 3/5 of its capacity then 2/5 of its capacity is left to fill.
To fill 3/5 of the pool took 8 hours --> to fill 2/5 of the pool will take 8/(3/5)*2/5=16/3 hours = 5 hours 20 minutes (because if t is the time needed to fill the pool then t*3/5=8 --> t=8*5/3 hours --> to fill 2/5 of the pool 8*5/3*2/5=16/3 hours will be needed).
Or plug values: take the capacity of the pool to be 5 liters --> 3/5 of the pool or 3 liters is filled in 8 hours, which gives the rate of 3/8 liters per hour --> remaining 2 liters will require: time = job/rate = 2/(3/8) = 16/3 hours = 2 hours 40 minutes.
Answer: E.
Answer: E
Question: The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, how many subsequent flights need to depart from Phoenix on-time, for the airport's on-time departure rate to be higher than 80%?
Options:
A)6
B)7
C)9
D)10
E)11
Rationale: We need on-time departure rate to be higher than 8/10, so it should be at least 9/11, which means that 9 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then 9-3=6 subsequent flights need to depart on-time.
Answer: A
Answer: A
Question: Average of 8 numbers is zero. At most how many numbers may be greater than zero
Options:
A)0
B)7
C)5
D)6
E)10
Rationale: Answer: Option B
Answer: B
Question: Sachin is younger than Rahul by 6 years. If the ratio of their ages is 7:9, find the age of Sachin
Options:
A)24.58
B)14
C)15
D)24.9
E)24.1
Rationale: If Rahul age is x, then Sachin age is x-6,
so (x-6)/x = 7/9
=> 9x-42 = 7x
=> 2x = 42
=> x = 21
So Sachin age is 21 - 6 = 15
Answer: C
Answer: C
Question: Which of the following could be the sum of the reciprocals of two prime numbers?
Options:
A)7/13
B)11/12
C)11/30
D)23/50
E)14/33
Rationale: 10/12 it is
14/33=(1/3) + (1/11)
Answer - E
Answer: E
Question: If KING is coded as 17 and MASS is coded as 29 Then DOG is coded as
Options:
A)21
B)20
C)19
D)29
E)None
Rationale: KING = 11+9+14+7=41 i.e (4*4)+(1*1)=17
MASS = 13+1+19+19=52 i.e (5*5)+(2*2)=29
DOG = 4+14+7=25 i.e(2*2)+(5*5)=29
ANSWER:D
Answer: D
Question: If 3x+y=40, 2x-y=20, for integers of x and y, y^2=?
Options:
A)2
B)4
C)0
D)16
E)3
Rationale: 3x+y = 40
2x-y = 20
5x = 60
x = 12
y = 4
y^2 = 16
Answer is D
Answer: D
Question: Two dice are thrown together .What is the probability that the sum of the number on the two faces is divided by 4 or 6
Options:
A)7/9
B)7/5
C)7/18
D)4/7
E)2/7
Rationale: Clearly n(S)=6*6=36
Let E be the event that the sum of the numbers on the two faces is divided by 4 or 6.Then
E={(1,3),(1,5),(2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4),(5,1),(5,3),(6,2),
(6,6)}
n(E)=14.
Hence p(e)=n(e)/n(s)=14/36=7/18
Option C
Answer: C
Question: The average of nine numbers is 15. The average of first four numbers is 11 and the average of last four numbers is 14. What is the middle number?
Options:
A)19
B)20
C)35
D)31
E)27
Rationale: The total of nine numbers = 9X15 = 135
The total of first 4 and last 4 numbers is = 4 X 11+4 X 14 = 100
So, the middle number is (135 - 100 ) = 35
C
Answer: C
Question: Machine A takes 50 hours to complete a certain job and starts that job at 6AM. After four hour of working alone, machine A is joined by machine B and together they complete the job at 1PM. How long would it have taken machine B to complete the job if it had worked alone for the entire job?
Options:
A)9
B)88.88
C)4.88
D)2.88
E)3.88
Rationale: Let us assume total job = 100 units
A finishes 100 units in 50 hrs(given)
Hence A (working rate)= 2 units /hr
Now Given that A works for 4 hr( so 8 units done) then A and B finish total work in 7 hours. Hence A and B finish 92 units in 3 hours. Of these 3x2=6 units were done by A. Hence B did 86 units in 3 hours.
Hence B(working rate)= 86/3 units /hr
Hence B takes 100x3/86 = 3.88 hours to complete the job.
Answer E.
Answer: E
Question: Mother is aged three times more than her daughter Rose. After 8 years, she would be two and a half times of Rose's age. After further 8 years, how many times would he be of Rose's age?
Options:
A)A)15
B)B)2
C)C)20
D)D)21
E)E)26
Rationale: Let Ronit's present age be x years. Then, father's present age =(x + 3x) years = 4x years.
(4x + 8) =	5	(x + 8)
2
8x + 16 = 5x + 40
3x = 24
x = 8.
Hence, required ratio =	(4x + 16)/(x + 16)	=	48/24= 2.
B
Answer: B
Question: If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean?
I. 13.7
II. 12.3
III. 9.3
Options:
A)I only
B)I and II only
C)II only
D)III only
E)I and III only
Rationale: Mean = 12
SD = 1.3
2 SD above mean = 12+2*1.3 = 14.6
2 SD below mean = 12-2*1.3 = 9.4
12.3 and 13.7 lies in the range of 2SD from mean
Answer: Option D
Answer: D
Question: How many ways can 8 friends be arranged around a circular dinner table?
Options:
A)1280
B)2460
C)5040
D)40320
E)85670
Rationale: The number of ways to order 8 people is 8!
However, around a circular table, each pattern would be repeated 8 times.
So the number of ways to seat 8 friends around a circular table is 7! = 5040
The answer is C.
Answer: C
Question: An uneducated retailer marks all his goods at 55% 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)12.50 %
B)13.50 %
C)14 %
D)14.50 %
E)None
Rationale: Sol.
Let C.P. = Rs. 100. Then, marked price = Rs. 155.
S.P. = 75% of Rs. 155 = Rs. 116.25.
∴ Gain% = 16.25%.
Answer E
Answer: E
Question: A and B start a business with Rs.6000 and Rs.18000 respectively. Hoe should they share their profits at the end of one year?
Options:
A)3:5
B)3:4
C)3:1
D)1:3
E)3:9
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
6000 : 18000 => 1:3
Answer:D
Answer: D
Question: If f(x) = 12 - x^2/2 and f(2k) = 4k, what is one possible value for k?
Options:
A)2
B)3
C)4
D)6
E)8
Rationale: First of all, see thisGMAT blog postand check the related lesson linked below for some background on function notation.
We can plug anything in for x and get a result. You can find f(1), for example, by plugging in 1 where x is, and you would get 12 - 1/2 = 11.5. Or we could find f(2), which would be 12 - 4/2 = 10.
So the notation f(2k) means that we are going to plug a 2k in for x everywhere in the formula for f(x). That would be:
f(2k) = 12 - (2k)^2/2 = 12 - 2k^2.
Remember that we have to square both the 2 and the k, to get 4k2. Now, this expression, the output, we will set equal to 2k.
12 - 2k^2 = 2k --> k = -5 or k = 4.
All the answers are positive, so we choose k = 4.
Answer = C
Answer: C
Question: Two pipes A and B can fill a cistern in 12 and 15 minutes respectively. Both are opened together but after 2 minutes A is turned off. After how much more time will the cistern be filled?
Options:
A)8 1/7
B)8 1/1
C)8 1/4
D)10 1/2
E)8 3/7
Rationale: 2/12 + (2 + x)/15 = 1
x = 10 1/2
Answer: D
Answer: D
Question: If MADRAS can be written as NBESBT, how can BOMBAY be written in that code ?
Options:
A)DHHIIIY
B)CPNCBZ
C)SYUOKJ
D)SUOOHH
E)WUHSW
Rationale: Explanation:
Each letter in the word is moved one step forward to obtain the corresponding letter of the code.
Answer: B
Answer: B
Question: There are two sets A and B. The range of set A is 7, and the range of set B is 13. If the two sets are combined and get a new set Y, which cannot be the range of the set Y?
Options:
A)8
B)B.11
C)C.14
D)D.17
E)E.21
Rationale: Let Set A has 1,8 as elements
B has 1,14 as elements.. So Range for Combined set Y becomes 14-1=13
For range to be 14,
A = 1,8
B= 2,15 (Range=14)
For range to be 17
A=1,8
B= 5,18
For range to be 21:
A=1,8
B= 9 ,22
So we are left with A and B.
Now consider A has elements A= -1,-8 and Thus Range =-1-(-8) =7
So for Range of combined set to be 11, B needs to have largest elementxso that x- (-8)=11 or x=3...But if x=3, the largest element in Combined Set then smallest element in the combined set will be 3-y=13 or y=-10....And the range of combined set 3-(-10)=13...
Consider Option A
A=-1,-8
B= y,x where y and x are smallest and largest element in Set B
Elements of Combined Set: -8,-1,y and x
Now x-(-8)=8 or x=0, then x-y=13 or y=-13...
Range of Combined Set: 0-(-13)= 13...
I don't see how range can be 8 or 11...Can you please post the source and explanation for the OA in spoiler...=B
Answer: B
Question: Find the face value of 6 in 654321
Options:
A)6
B)60000
C)600
D)6000000
E)6000
Rationale: Face value is the value of digit itself
face value of 6 = 6
Answer : A
Answer: A
Question: If an object travels at eight feet per second, how many feet does it travel in one hour?
Options:
A)34880
B)3778
C)12788
D)18000
E)28800
Rationale: Explanation:
If an object travels at 5 feet per second it covers 5x60 feet in one minute, and 5x60x60 feet in one hour.
Answer = 28800
Answer: E) 28800
Answer: E
Question: Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill?
Options:
A)7
B)9
C)5
D)4
E)8
Rationale: 1/10 + 1/15 = 1/6 * 4 = 2/3
1 - 2/3 = 1/3
1/10 + 1/15 - 1/x = 1/3
x = 8
ANSWER E
Answer: E
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 64 hours respectively. The ratio of their speeds is?
Options:
A)4:5
B)8:3
C)8:4
D)4:8
E)4:1
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √64 : √9
= 8:3
Answer: B
Answer: B
Question: Find the area of a parallelogram with base 15 cm and height 40 cm?
Options:
A)200 cm2
B)100 cm2
C)42 cm2
D)600 cm2
E)230 cm2
Rationale: Area of a parallelogram
= base * height
= 15 * 40
= 600 cm2
Answer: D
Answer: D
Question: The area of a triangle is with base 8m and height 4m?
Options:
A)88 m2
B)10 m2
C)16 m2
D)77 m2
E)31 m2
Rationale: 1/2 * 8 * 4 = 16 m2
Answer: C
Answer: C
Question: What approximate value should come in place of the question mark (?) in the following equation ?
4⁄7 of 1596 + 3015 = ? – 2150
Options:
A)7200
B)48000
C)5300
D)58000
E)6070
Rationale: ? ≈ 4 × 230 + 3000 + 2150
= 920 + 3000 + 2150 = 6070
Answer E
Answer: E
Question: If a portion of a half water/half alcohol mix is replaced with 25% alcohol solution, resulting in a 30% alcohol solution, what percentage of the original alcohol was replaced?
Options:
A)3%
B)20%
C)66%
D)75%
E)80%
Rationale: let x be water, y - alcohol. so we have -
0.5x+0.5y -0.25y=0.3x+0.3y
x=1/4y
x/y=1/4
so in a new solution y 's portion is 4/5 or 80%
ANSWER:E
Answer: E
Question: A school’s annual budget for the purchase of student computers increased by 50% this year over last year. If the price of student computers increased by 20% this year, then the number of computers it can purchase this year is what percent greater than the number of computers it purchased last year?
Options:
A)33.33%
B)40%
C)25%
D)28%
E)60%
Rationale: Lats year: budget = $100, price = $1 --> the number of computers purchased = 100/1 = 100;
This year: budget = $150, price = $1.2 --> the number of computers purchased = 150/1.2 = 125.
Increase in the number of computers purchased = 25%.
Answer: C.
Answer: C
Question: A sells an article to B at a profit of 10% B sells the article back to A at a loss of 10%. In this transaction:
Options:
A)A neither losses nor gains
B)A makes a profit of 11%
C)A makes a profit of 20%
D)B loses 20%
E)None of these
Rationale: Solution: First Method
Let CP was 100 for A originally.
A sells article to B at 10% profit,
CP for B = 100 + 10% of 100 = 110.
Now, B sells it A again with loss 10%.
Now, CP for A this time = 110 - 10% of 110 = 99.
A makes Profit = 110 - 99 = 11.
%profit for A = (11*100)/100 = 10%.
Second Method
It could be easily shown by net percentage change graphic.
100(A)==10%(Profit)==>110(B)==10%(Loss)==>99(A)
In this transaction A makes a profit of (110-99 = 11%) 11% .
[10% on selling to B and 1% profit on buying back from B].
Answer: Option B
Answer: B
Question: If the sides of a triangle are 65 cm, 60 cm and 25 cm, what is its area?
Options:
A)350 cm^2
B)850 cm^2
C)550 cm^2
D)750 cm^2
E)650 cm^2
Rationale: The triangle with sides 65 cm, 60 cm and 25 cm is right angled, where the hypotenuse is 65 cm.
Area of the triangle
= 1/2 * 60 * 25
= 750 cm^2
Answer: D
Answer: D
Question: If TIER is written as 8163 and BRAIN is written as 23415, how is RENT coded ?
Options:
A)3653
B)3658
C)2977
D)2790
E)2711
Rationale: Explanation:
Given :
Letter : T I E R B A N
Code : 8 1 6 3 2 4 5
Thus, the code for RENT is 3658.
ANSWER:B
Answer: B
Question: From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first card is a queen and the second card is a jack is?
Options:
A)1/169
B)1/52
C)1/26
D)1/120
E)1/4
Rationale: Probability of a queen = 4/52 = 1/13
Probability of a jack = 4/52 = 1/13
Probability of both = P1*P2 = 1/(13*13) = 1/169
Answer is A.
Answer: A
Question: List I: 15, 12, 17, 20 List II: x,15, 12, 17, 20
Options:
A)15
B)16
C)20
D)22
E)24
Rationale: List I has even number of terms, thus its median is the average of two middle terms (when arranged in ascending/descending order), so median=(15+17)/2=16
List II has odd number of terms, thus its median is the middle term (when arranged in ascending/descending order). As no other number in the list equal to 16, then x=16.
Answer: B
Answer: B
Question: How many prime numbers F exist such that 90 < F < 106 and F is a factor of 99999919?
Options:
A)1. Zero
B)2. One
C)3. Two
D)4. Three
E)5. More than three
Rationale: I found that considering the constraint..F is a prime num in between 90 to 106 not inclusive , only 3 numbers (91,97 and 101) are present but those numbers are not the factors of the number mentioned....Therefore, i doubt the answer.C
Answer: C
Question: If x and y are positive integers, and x^3*y^4 = 648, which of the following is the value of xy?
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: 648 = 2^3*3^4
xy = 2*3 = 6
The answer is C.
Answer: C
Question: Abhijit started a business investing 70000. Anuja joined him after 4 months with an amount of 105000 and Sunil joined them with 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Abhijit, Anuja and Sunil respectively, three years after Abhijit started the business?
Options:
A)9: 13: 26
B)9 :12 :13
C)8 :14: 24
D)12:14:16
E)8 :15: 12
Rationale: Ratio of their investments
= 70 × 36 : 105 × 32: 140 × 26 = 9 : 12 : 13
Answer B
Answer: B