divelab/Sys2Bench huggingface dataset:
Question: if 2 pipes take an hour to fill a tank, then how long should 8 pipes take to fill the same tank?
Options:
A)20 min
B)10 min
C)15 min
D)25 min
E)30 min
Rationale: if 2 pipes take an hour to fill a tank, then
8 pipes will take 2*60/8 = 15 mins to dig a ditch of the same type.
ANSWER:C
Answer: C
Question: Find √? /19 = 4 ?
Options:
A)76
B)5776
C)304
D)1296
E)None
Rationale: Answer
Let √N/19 = 4
Then √N = 19 x 4 = 76
∴ N = 76 x 76 = 5776.
Correct Option: B
Answer: B
Question: Mr. Thomas invested an amount of 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be 3508, what was the amount invested in Scheme B?
Options:
A)6200
B)6300
C)6400
D)6500
E)6600
Rationale: Let the sum invested in Scheme A be x and that in Scheme B be (13900 - x).
Then, (x x 14 x 2)/100 + ((13900 - x) x 11 x 2)/100 = 3508
28x - 22x = 350800 - (13900 x 22)
6x = 45000
x = 7500.
So, sum invested in Scheme B = (13900 - 7500) = 6400.
answer : C
Answer: C
Question: How many numbers between 200 and 400 begin or end with 2?
Options:
A)20
B)60
C)100
D)110
E)120
Rationale: How many numbers between 200 and 400 begin or end with 2?
Just think that those numbers are:
i) The ones ending in 2: 202, 212, 222, ... , 392 --> 20 numbers
ii) The ones beginning in 3: 200, 201, 202, 203, ... , 293, ... , 299 --> 100 numbers
BUT 10 out of the first 20 numbers are repeated in the second set.
THEREFORE, the solution is 110 numbers.
Answer: D
Answer: D
Question: A square and an equilateral triangle have the same perimeter. What is the ratio of the area of the circle circumscribing the square to the area of the circle inscribed in the triangle?
Options:
A)9:8
B)15:8
C)27/8
D)8:9
E)8:15
Rationale: let x be side of square
perimeter of square=4x=perimeter of triangle=3*side of triangle
so side of eq. triangle=(4/3)*x
diameter of circle circumscribing the square=sqrt(2)*x
area of circle circumscribing the square= pi*(sqrt(2)*x)^2/4=(pi/2)*x^2 ----(1)
to find radius of the circle inscribed in the triangle
area of triangle=r*s=sqrt(3)/4 * (4x/3)^2
now s=(4/3)*x+(4/3)*x+(4/3)*x/2=2x
so sqrt(3)/4 * (4x/3)^2=r*2x gives
r={2/3*(3^1/2)}*x
area of the circle inscribed in the triangle=pi*[{2/3*(3^1/2)}*x]^2
=pi*(4/27)*x^2 -------(2)
so reqd ratio= eqn(1)/eqn(2)
=[(pi/2)*x^2]/[pi*(4/27)*x^2]=27/8
so reqd ratio=27:8
ANSWER:C
Answer: C
Question: If 600y is a perfect square (the square of an integer) and y is a positive integer, then which of the following must also be an integer?
I y/6
II y/42
III y/30
Options:
A)I only
B)III only
C)I and II only
D)I and III only
E)I, II, and III
Rationale: 600∗y=2^3∗3^1∗5^2∗y
For an integer to be a perfect square means that all its prime factors must have even powers.
Min value of yy required fo that is 2^1∗3^1
Answer A
Answer: A
Question: If m times the mth series of an A.P. is equal to n times its nth series, what is the (m+n)th term of the A.P. ?
Options:
A)1
B)m
C)n
D)0
E)2
Rationale: mth term of an A.P.
Am = a + (m-1)d
nth term of an A.P.
An = a + (n+1)d
[here a= First term of an A.P
d= difference between two consecutive terms
Am= mth term of A.P.]
According to the question;
m*Am = n*An
m(a + (m-1)d)= n(a + (n-1)d)
m(a + md - d)= n(a + nd - d)
am + m^2d-md = an + n^2d - nd
a(m-n)+ (m^2-n^2)d -(m-n)d = 0
a(m-n)+ (m-n)(m+n)d -(m-n)d= 0
(m-n)[a + (m+n)d - d ]= 0
[a + (m+n)d - d ]= 0
[a + (m+n-1)d ]= 0
So Am+n = 0
so answer will be 0
ANSWER:D
Answer: D
Question: A fruit salad mixture consists of apples, peaches, and grapes. There are 2 times as many pounds of apples as grapes and 3 times as many pounds of peaches as grapes. If a mixture that has an average (arithmetic mean) of 24 pounds per fruit, how many more pounds of apples than grapes does the mixture have?
Options:
A)15
B)12
C)8
D)6
E)5
Rationale: A+P+G= 24*2
A=3G
P=2.5G
3G+2G+G= 24*2
G= 24*2/6= 8
A= 8*2=16
Difference = 16-8=8
'C' is the answer
Answer: C
Question: Kim finds a 5-meter tree branch and marks it off in thirds and fifths. She then breaks the branch along all the markings and removes one piece of every distinct length. What fraction of the original branch remains?
Options:
A)8/15
B)1/2
C)7/5
D)3/5
E)7/5
Rationale: 3 pieces of 1/5 length and two piece each of 1/15 and 2/15 lengths. removing one piece each from pieces of each kind of lengths the all that will remain will be
2 pieces of 1/5 i.e 2/5, 1 piece of 1/15, and 1 piece of 2/15
Which gives us 2/5 + 1/15 + 2/15 -----> 3/5
Answer is D
Answer: D
Question: A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
Options:
A)228
B)277
C)350
D)882
E)121
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 39 = 50/3
3(x + 300) = 1950 è x = 350m.
Answer:C
Answer: C
Question: If log a/b + log b/a = log (a + b), then:
Options:
A)a = b
B)a - b = 1
C)a + b = 1
D)15
E)22
Rationale: Explanation:
log a/b + log b/a = log (a + b)
log (a + b)=log(b/a*a/b)= log 1
So, a + b = 1.
answer C
Answer: C
Question: At Tea factory, each employee working the second shift produced 2/3 as many widgets as each employee working the first shift. If the first shift has 3/4 as many employees, what fraction of the total widgets did the second shift produce?
Options:
A)8/17
B)1/2
C)8/9
D)9/8
E)17/8
Rationale: At Tea factory,Let the first shift have 3 employee and each produce 3 widgets, so the total number of widgets produced by the first shift is 3*3=9;
Then the second shift would have 4 employees and each second shift employee would produce 3*2/3=2 widgets, so the total number of widgets produced by the second shift employees would be 4*2=8;
The ratio of the second shift production to the total is 8/(9+8)=8/17.
Answer: A.
Answer: A
Question: The mean of 50 observations was 36. It was found later that an observation 58 was wrongly taken as 43. The corrected new mean is?
Options:
A)36.7
B)36.1
C)36.5
D)36.9
E)36.3
Rationale: Correct sum
= (36 * 50 + 58 - 43)
= 1815.
Correct mean = 1815/50
= 36.3
Answer:E
Answer: E
Question: In a class, the average age of 40 boys is 18 years and the average of 30 girls is 15 years. what is the average age of the whole class?
Options:
A)12 Years
B)12.3 Years
C)12.6 Years
D)16.7 Years
E)15 Years
Rationale: Total age of 70 students
(40X 18+30 X 15) = 1170
Average = 1170/70 = 16.7 Years
D
Answer: D
Question: In a theater, the first row has 14 seats and each row has 2 more seats than previous row. If the last row has 56 seats, what is the total number of seats in the theater?
Options:
A)770
B)780
C)790
D)800
E)810
Rationale: The number of seats in the theater is
14 + (14+2) + ...+ (14+42)=
22(14) + 2(1+2+...+21)=
22(14) + 2(21)(22)/2=
22(14+21) = 22(35) = 770
The answer is A.
Answer: A
Question: If the price of gold increases by 50%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before?
Options:
A)30
B)33 1/3
C)35
D)25
E)20
Rationale: 100---150
150----50
100-----? ==>33 1/3
ANSWER B
Answer: B
Question: A motorcycle importer is planning on increasing the price of a certain model by $1000. At this new price 5 fewer motorcycles will be sold per month, but the total revenues will increase by $26,000 to $594,000. What is the number of motorcycles the manufacturer will sell at this new price?
Options:
A)51
B)61
C)66
D)71
E)76
Rationale: 66 bikes.
Got two equations bikes*price = 568 units
(bikes - 5)*(price + 1 ) = 594 units.
factorise 568 = 71 * 8.
use n = 71 and p = 8 in the second , it works.
Hence 66.
ANSWER:C
Answer: C
Question: Which of the following lines is perpendicular to y = − 2x + 3 and has the same y-intercept as y = 2x − 4?
Options:
A)y = -1/2*x + 3
B)y = 1/2*x - 4
C)y = 1/2*x + 3
D)y = 2x + 3
E)y = 2x − 3
Rationale: Since our line has to perpendicular to y = − 2x + 3
Slope of this line , m = -2
Slope will be required line L = 1/2 ( Product of slope of perpendicular lines = -1)
y-intercept of line L is same as y intercept of line y = 2x − 4
y - intercept of line L = -4
Required line = 1/2* x - 4
Answer B
Answer: B
Question: The average of first ten prime numbers which are odd is?
Options:
A)15.9
B)15.0
C)15.2
D)15.8
E)15.1
Rationale: Sum of first 10 prime no. which are odd = 158
Average = 158/10 = 15.8
Answer: D
Answer: D
Question: For positive integers s and t, which of the following can be written as t^2?
Options:
A)s^2+9
B)s^2+2
C)s^2+3
D)s^2-1
E)s^2-9
Rationale: Plug values: if s=4, then 4^2+9=25
The question asks which of the following CAN be written as t^2. If s=4, then s^2+9 CAN be written as 5^2.
Answer: A
Answer: A
Question: If x is a number such that x^2 + 3x - 10 = 0 and x^2 + x - 20 = 0, then x =
Options:
A)2
B)4
C)-4
D)5
E)-5
Rationale: x^2 + 3x - 10 = (x+5)(x-2) = 0
Then x=-5 or x=2.
x^2 + x - 20 = (x-4)(x+5) = 0
Then x=4 or x=-5.
Thus x=-5.
The answer is E.
Answer: E
Question: Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 3 ½ hours if they are walking in the same direction?
Options:
A)4 3/9 km
B)4 7/8 km
C)4 3/8 km
D)8 3/8 km
E)4 3/2 km
Rationale: Explanation:
RS = 5 ¾ - 4 ½ = 1 ¼
T = 3 ½ h.
D = 5/4 * 7/2 = 35/8
= 4 3/8 km
Answer:C
Answer: C
Question: Navjivan Express from Ahmedabad to Chennai leaves Ahmedabad at 6.30 a.m. and travels at 50 kmph towards Baroda situated 100 km away. At 7.00 a.m. Howrah-Ahmedabad Express leaves Baroda towards Ahmedabad and travels at 40 kmph. At 7.30 a.m. Mr Shah, the traffic controller at Baroda realizes that both the trains are running on the same track. How much time does he have to avert a head-on collision between the two trains?
Options:
A)15 min
B)20 min
C)25 min
D)30 min
E)35 min
Rationale: Explanation :
Let A be ahmedabad and B for baroda.
At 7:30 train from A to B would have covered 50km while train from B to A would have covered 20 km since it travels for only half an hour.
Distance remaining between the trains = 100-(50+20) i.e. 30km and the relative speed =90kmph. Therefore, time =30/90 hours = 20mins.
Answer : B
Answer: B
Question: A chemist mixes one liter of pure water with x liters of a 60% salt solution, and the resulting mixture is a 15% salt solution. What is the value of x?
Options:
A)1/4
B)1/3
C)1/2
D)1
E)3
Rationale: Concentration of salt in pure solution = 0
Concentration of salt in salt solution = 60%
Concentration of salt in the mixed solution = 15%
The pure solution and the salt solution is mixed in the ratio of --> (60 - 15)/(15 - 0) = 3/1
1/x = 3/1
x = 1/3
Answer: B
Answer: B
Question: There are 17 students in a certain class. On the day the test was given, Taqeesha was absent. The other 16 students took the test, and their average was 77. The next day, Taqeesha took the test, and with her grade included, the new average is 78. What is Taqeesha’s grade on the test?
Options:
A)78
B)80
C)87
D)91
E)94
Rationale: Explanations
1) The average of the first 16 students is 77. This means, the sum of these 16 scores is
sum = (average)*(number of scores) = 77*16 = 1232
Once Taqeesha takes her test, the average of all 17 scores is 78. This means, the sum of these 17 scores is:
sum = (average)*(number of scores) =78*17 = 1326
Once we had the sum of the 16 scores, all we had to do was add Taqeesha’s score to that total to get the sum of all 17. Therefore, the difference in these two sums is Taqeesha’s score. 1326 – 1232 = 94.
Answer: E.
Answer: E
Question: A sum was put at simple interest at certain rate for 3 years. Had it been put at 1% higher rate it would have fetched Rs. 78 more. The sum is: A. Rs. 2,400 B. Rs. 2,100 C. Rs. 2,200 D.Rs. 2,480
Options:
A)2000
B)2600
C)2200
D)2300
E)2400
Rationale: 1 percent for 3 years= 78
1 percent for 1 year = 26
=> 100 percent = 2600
ANSWER:B
Answer: B
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?
Options:
A)22877
B)5355
C)2778
D)6787
E)1771
Rationale: 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
Answer: B
Question: On a certain date, Pat invested $8,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 10 years will be $32,000, in how many years total will the total value of the investment plus interest increase to $64,000?
Options:
A)15
B)16
C)18
D)20
E)24
Rationale: 32,000 = 8,000(1 + x)^10
4 = (1+x)^10 = 2^2
(1+x)^10 = ((1+x)^5)^2 = 2^2
Therefore, (1+x)^5 = 2
64,000 = 8,000(1 + x)^n
(1+x)^n = 8
(1+x)^n = 2^3
(1+x)^n = ((1+x)^5)^3 = (1+x)^15
Therefore, n = 15.
The answer is A.
Answer: A
Question: 39x7 - 45x7 - 134x7 - 39x7 + 134x7 + 44x7 =
Options:
A)-x7
B)x7
C)2x7
D)3x7
E)None
Rationale: Solution:
39x7 - 45x7 - 134x7 - 39x7 + 134x7 + 44x7 =
39x7 - 39x7 - 45x7 + 44x7 - 134x7 + 134x7=
0 - x7 + 0= -x7
Answer A
Answer: A
Question: If a function f is defined by f(x)= -1/x for all non zero numbers x. If f(a) = -1/3 and f(ab) = 1/6 then b= ?
Options:
A)2
B)1/2
C)-1/2
D)-2
E)-12
Rationale: f(a) = -1/3 = -1/a, and thus a = 3
f(ab) = 1/6, and thus ab = -6
3b = -6
b = -2
The answer is D.
Answer: D
Question: 270 students appeared for an examination, of which 252 passed. What is the pass percentage?
Options:
A)93(1/3)%
B)93(2/3)%
C)92(2/3)%
D)92%
E)None of these
Rationale: Explanation :
Pass percentage = (252/270) × 100 = 2520/27 = 280/3 = 93(1/3)%
Answer : Option A
Answer: A
Question: Nicky and Cristina are running a 100 meter race. Since Cristina is faster than Nicky, she gives him a 12 second head start. If Cristina runs at a pace of 5 meters per second and Nicky runs at a pace of only 3 meters per second, how many seconds will Nicky have run before Cristina catches up to him?
Options:
A)30
B)35
C)40
D)25
E)60
Rationale: The distance traveled by both of them is the same at the time of overtaking.
3(t+12) = 5t
t=18.
Cristina will catch up Nicky in 18 seconds.
So in 18 seconds Cristina would cover = 18*5 = 90 meter.
Now Time taken my Nicky to cover 90 meter = 90/3 = 30 Seconds.
A
Answer: A
Question: Initially, the men and women in a room were in the ratio of 4 : 5. Then, 2 men entered the room and 3 women left the room. Then, the number of women doubled. Now there are 14 men in the room. How many W women are currently in the room?
Options:
A)12
B)14
C)15
D)24
E)36
Rationale: the number of women doubled means that they have become 24 from 12..
and we have to tell the current strength so 24 is the answer..
let the number be 4x and 5x..
given 4x+2=14.. so x=3..
women number=5*3-3=12, then doubled=24..
ans D
Answer: D
Question: The average weight of a 30 students increases by 2 kg when the weight of their teacher was added. If average weight of the group after including the weight of the teacher is 32 kg, what is the weight of their football coach?
Options:
A)31 kg
B)60 kg
C)61 kg
D)124 kg
E)91 kg
Rationale: let t=teacher's weight
original total weight=(30 students)(30 kg avge)=900kg
(900+t)/(30+2)=32 kg avge
t=124 kg
Answer D
Answer: D
Question: The number of timeshare condos available at Sunset Beach is 3/5 the number of timeshare condos available at Playa del Mar. If the total number of timeshare condos available at the two beaches combined is 320, what is the difference between the number of condos available at Sunset Beach and the number of condos available at Playa del Mar?
Options:
A)80
B)90
C)120
D)150
E)240
Rationale: Let x be the number of timeshare condos available at Playa del Mar.
Then number of timeshare condos available at Sunset Beach = 3/5x
We know, x + 3/5 x = 320
Hence, x = 200. So, number of timeshare condos available at Playa del Mar = 200
the difference between the number of condos available at Sunset Beach and the number of condos available at Playa del Mar = x - 3/5x = 2/5x = 2/5(200) = 80
The correct answer is A.
Answer: A
Question: Truck A is 25 miles ahead of Truck B, which is traveling the same direction along the same route as Truck A. If Truck A is traveling at an average speed of 49 miles per hour and Truck B is traveling at an average speed of 54 miles per hour, how long will it take Truck B to overtake and drive 15 miles ahead of Truck A?
Options:
A)2 hours 20 minutes
B)6 hours
C)8 hours
D)5 hours 45 minutes
E)3 hours
Rationale: Relative speed = 54-49 = 5 miles per hour
Dist required = 25+15 = 40 miles
Time taken to overtake = 40/5 = 8 hours. C is the answer.
Answer: C
Question: A shopkeeper sells two articles at Rs.1000 each, making a profit of 20% on the first article and a loss of 20% on the second article. Find the net profit or loss that he makes?
Options:
A)8
B)7
C)6
D)4
E)3
Rationale: SP of first article = 1000
Profit = 20%
CP = (SP)*[100/(100+P)] = 5000/6 = 2500/3
SP of second article = 1000
Loss = 20%
CP = (SP)*[100/(100-L)] = 5000/4 = 1250
Total SP = 2000
Total CP = 2500/3 + 1250 = 6250/3
CP is more than SP, he makes a loss.
Loss = CP-SP = (6250/3)- 2000 = 250/3
Loss Percent = [(250/3)/(6250/3)]*100 =
0.04 * 100 = 4%
Answer: D
Answer: D
Question: A 260-metre-long train crosses a 120-metre-long wall in 19 seconds. What is the speed of the train?
Options:
A)27 km/hr
B)49 km/hr
C)72 km/hr
D)70 km/hr
E)None of these
Rationale: Speed of train = 260+120/19×18/5=72km/h
Answer C
Answer: C
Question: Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.140. How much was lent at 5%?
Options:
A)1666
B)2688
C)1198
D)1000
E)2321
Rationale: (x*5*1)/100 + [(2500 - x)*6*1]/100 = 140
X = 1000
Answer:D
Answer: D
Question: If x^2=x-2, then x^3=?
Options:
A)3x+2
B)3x-2
C)2x+1
D)-x-2
E)3x+4
Rationale: Given X^2 = X-2
X^3 = X*X^2 = x*(X-2)-- Substituted from above.
= X^2 - 2X = X-2-2X = -X-2.
Hence D.
Answer: D
Question: If 8 people can eat a gallon of ice cream in 10 days, how long would it take 5 people to eat a gallon of ice cream?
Options:
A)12 days
B)14 days
C)16 days
D)18 days
E)20 days
Rationale: 8 * 10 = 5 * x
x = 16
Answer: C
Answer: C
Question: Find the value of 3/11 × [(1 + 1/3) (1 + 1/4) …………. (1 + 1/120)] is
Options:
A)8
B)10
C)11
D)13
E)14
Rationale: 3/11 × [(1 + 1/3) (1 + 1/4) ....... (1 + 1/120)]
3/11 × [4/3 + 5/4 × ........ 121/120]
3/11 × 4/3 × 5/4 × .... 121/120
121/11 = 11.
C
Answer: C
Question: If -2<= x <= 2 and 3 <= y <= 4, which of the following represents the range of all possible values of y-x?
Options:
A) 1 <= y-x <= 6
B) 1 <= y-x <= 5
C) 1 <= y-x <= 6
D) 5 <= y-x <= 10
E) 1 <= y-x <= 10
Rationale: Maximum value of y-x= 4 - (-2)= 6
Minimum value of y-x= 3-2= 1
A mentions the correct range
Answer: A
Question: A chair is bought for Rs.600/- and sold at a loss of 50% find its selling price
Options:
A)s.300/-
B)s.550/-
C)s.560/-
D)s.590/-
E)s.580/-
Rationale: 100 % ------> 600 (100 * 6 = 600)
50 % ------> 540 (50 * 6 = 300)
Selling price = Rs.300/-
A)
Answer: A
Question: 16 children are to be divided into two groups A and B of 10 and 6 children. The average percent marks obtained by the children of group A is 75 and the average percent marks of all the 16 children is 76. What is the average percent marks of children of group B ?
Options:
A)233/3
B)733/3
C)533/3
D)293/3
E)433/3
Rationale: Explanation:
Required average = [(76 * 16) - (75 * 10)] / 6 = (1216 - 750)/6 = 466/3 = 233 /3.
Answer: A
Answer: A
Question: Three table runners have a combined area of 204 square inches. By overlapping the runners to cover 80% of a table of area 175 square inches, the area that is covered by exactly two layers of runner is 24 square inches. What is the area of the table that is covered with three layers of runner?
Options:
A) 18 square inches
B) 20 square inches
C) 24 square inches
D) 28 square inches
E) 30 square inches
Rationale: Total = a + b + c - (sum of EXACTLY 2-group overlaps) - 2*(all three) + Neither
80%*175 = 204 - 24 - 2*(all three) + 0
2*(all three) = 204 - 24 - 140
all three = 20
Answer: B
Answer: B
Question: What is the sum of all the prime numbers greater than 50 but less than 70?
Options:
A)249
B)248
C)246
D)240
E)241
Rationale: Required sum = (53 + 59 + 61 + 67 ) = 240
Note: 1 is not a prime number
Answer D
Answer: D
Question: How many positive three-digit integers are divisible by both 5 and 7?
Options:
A)10
B)15
C)18
D)20
E)26
Rationale: A number to be divisible by both 5 and 7 should be divisible by the least common multiple of 5 and 7 so by 35.
Multiples of 35 between 100 and 999, inclusive is
(last-first)/multiple+1=(980-105)/35+1=25+1=26
Answer: E.
Answer: E
Question: If x = 6^36 and x^x = 6^k, what is k?
Options:
A)6^36
B)6^38
C)6^72
D)6^216
E)6^432
Rationale: Solution:
We know that x=6^36
which implies x^x = (6^36)^(6^36) = 6^(36 * 6^36) [because (x^y)^z = x^(y*z))]
so 6^(6^2 * 6^36) = 6^(6^(2+36)) [because x^a * x^b = x^(a+b)]
therefore x^x = 6^(6^38)
Given that x^x=6^k
so 6^(6^38) = 6^k
Since the base is same the exponent will also be same
therefore k = 6^38
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 is a red card and the second is a king is?
Options:
A)1/26
B)1/27
C)1/24
D)1/21
E)1/22
Rationale: Let E1 be the event of drawing a red card.
Let E2 be the event of drawing a king .
P(E1 ∩ E2) = P(E1) . P(E2)
(As E1 and E2 are independent)
= 1/2 * 1/13 = 1/26
Answer: A
Answer: A
Question: Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 36?Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 4?
Options:
A)5x = y - 6
B)75x^2 = 3y^2 - 12
C)25x^2 = (y + 2)(y - 2)
D)5x = y - 2
E)x^2 = (y^2 - 4)/25
Rationale: 1) Take the original equation and try to manipulate it so that it becomes 4 of the 5 answers
2) Take each answer choice and see if you can manipulate it to make it into the original equation.
With Answer D, we have...
5X = Y - 6
If we square both sides, we end up with....
(5X)^2 = (Y-6)^2
(5X)(5X) = (Y-6)(Y-6)
25X^2 = Y^2 - 12Y + 36
This is NOT a match for the original equation, so it's the answer that is NOT equivalent.A
Answer: A
Question: If m is an integer such that (-2)^2m=2^(6-m) then m=?
Options:
A)1
B)2
C)3
D)5
E)6
Rationale: (-2)^(2m) = 4^m
and
2^(6-m) = 4^((6-m)/2)
Therefore,
m = (6-m)/2
2m = 6 - m
m = 2
Answer B
Answer: B
Question: The least number of complete years in which a sum of money put out at 20% C.I. will be more than doubled is?
Options:
A)7
B)4
C)5
D)3
E)1
Rationale: Explanation:
P(1 + 20/100)n > 2P or (6/5)n > 2
Now, (6/5 * 6/5 * 6/5 * 6/5) > 2. So, n = 4 years.
Answer:B
Answer: B
Question: What Is The Smallest Positive Integer That Leaves A Remainder Of 1 When Divided By 2, Remainder Of 2 When Divided By 3, A Remainder Of 3 When Divided By 4, And A Remainder Of 9 When Divided By 10?
Options:
A)58
B)59
C)60
D)61
E)62
Rationale: remainder of 1 when divided by 2: (2-1=1)
remainder of 2 when divided by 3: (3-2=1)
remainder of 3 when divided by 4: (4-3=1)
remainder of 9 when divided by 10: (2-1=1)
so N+1 should be divisible by 2,3,4,10
(where N is desired number)
L.C.M. of 2,3,4,10 = 60 (= N+1)
N = 59
ANSWER:B
Answer: B
Question: Of the four numbers, whose average is 100, the first is one-fourth of the sum of the last three. The first number is ?
Options:
A)28
B)29
C)80
D)48
E)10
Rationale: Explanation:
Let the first number be x,
Then, sum of the four numbers = x + 4x = 5x.
so, 5x/4 = 100 or x = (100 * 4) / 5 = 80
Answer: C
Answer: C
Question: If the mobile is bought by rs 490 and sold by rs 465.50.find loss%.
Options:
A)3%
B)2%
C)7%
D)5%
E)9%
Rationale: sol. cp=rs490,sp= 465.50.
loss=rs(490-465.50)=rs 24.50.
loss%=[(24.50/490)*100]%=5%
Ans:D
Answer: D
Question: Suppose 6 monkeys take 6 minutes to eat 6 bananas. How many monkeys would it take to eat 18 bananas in 18 minutes?
Options:
A)9
B)10
C)11
D)6
E)13
Rationale: One monkey takes 6 min to eat 1 banana , so in 18 mins 1 monkey will eat 3 bananas , so for 18 bananas in 18 min we need 18/3 =6 monkeys
ANSWER:D
Answer: D