divelab/Sys2Bench huggingface dataset:
Question: Two trains of equal length 120 metres move in the same direction. The faster train completely overtakes the slower one in 15 seconds. If the slower train were to move at half its speed, the over taking would take in 10 seconds. At what speeds are the 2 trains moving (faster and slower respectively in m/s)
Options:
A)24, 22
B)32, 16
C)30, 18
D)28, 14
E)26, 14
Rationale: The total distance covered for over taking = length of the two trains = 120 +120 = 240
Speed of faster train be x m/s and slower train be y m/s
In the first case Relative speed = x-y
Relative Speed = Distance / Time taken = x-y = 240/15 = 16 m/s………(1)
In the second case, the slower train moves at half its speed
Relative Speed = x-0.5y = 240/10 = 24 m/s …………………..(2)
Solving equation 1 & 2 we get x = 32 and y = 16 .
:. The speed of the faster and slower trains are 32 m/s and 16 m/s respectively
ANSWER:B
Answer: B
Question: There are 3000 students in a school and among them 20 % of them attends chess class. 40% of the students who are in the chess class are also enrolled for swimming. No other students are interested in swimming so how many will attend the swimming class if all enrolled attends?
Options:
A)240
B)10
C)100
D)50
E)20
Rationale: 20% of 3000 gives 600. so 600 attends chess and 40% of 600 gives 240
so 240 enrolled for swimming
Answer: A
Answer: A
Question: What is the total number of prime numbers less than 45?
Options:
A)17
B)18
C)19
D)20
E)14
Rationale: Solution
Prime numbers less than 45 are	=14.
2,3,5,7,11,13,17,19,23,29,31,37,41,43
Their number is 14.
Answer E
Answer: E
Question: The first three terms of an infinite sequence are 2, 7, and 22. After the first term, each consecutive term can be obtained by multiplying the previous term by 3 and then adding 1. What is the sum of the tens digit and the units digit of the 31st term in the sequence?
Options:
A)48
B)49
C)4
D)8
E)4
Rationale: Following the rule of Infinite sequence we obtain the terms of the sequence as mentioned below
02,07,22,67, 202, 607, 1822, 5467...
Observe the last two digits of the sequence which have the cyclicity of4and the last two digits repeat in the order {02, 07, 22, 67}
Also 31st Term =4*7 +3
i.e. 31st Terms will have same Last two digits as 3rd term of the sequence = 22
i.e. Sum of lat two digits of 35th Term = 2+2 = 4
C
Answer: C
Question: A certain roller coaster ride has more than 29 people waiting in line to board. If riders are let on only in groups of 5 there will be 2 riders that do not get on. If the riders are let on only in groups of 6 all riders will be able to get on the roller coaster. If less than 112 people are in the line, which of the following is the largest possible value of number of people in the line?
Options:
A)112
B)108
C)106
D)102
E)96
Rationale: No which leaves 2 as remainder when divided by 5 = ( 7, 12, 17, .....)
No which leaves 0 remainder when divided by 6 = (6, 12, 18...)
Common no in two sets = 12
So the numbers which satisfy this condition will be of the form 30x + 12.
Now we know that the no is greater than 29 and has to be less than 112...so option which satisfies is 102
ANSWER:D
Answer: D
Question: In how many ways Chief Minister and Minister be elected from a team of 12 members?
Options:
A)128
B)130
C)132
D)135
E)165
Rationale: To do this, if captain is elected first, then we have 12 ways of doing this.
For election of vice-captain, we have only 11 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 12*11 = 132 ways.
C
Answer: C
Question: what is the remainder of 18!/23?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Let rem[18!/23]=r
Wilson's Theorem says rem[(p-2)!/p]=1
rem[21!/23]=1
rem[21*20*19*18!/23]=1
rem[(-2)(-3)(-4)*r/23]=1
rem[-24r/23]=1
24r=-23K+1 ... k=-1
r=23+1/24
r=1
ANSWER:A
Answer: A
Question: The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?
Options:
A)43
B)52
C)12
D)65
E)13
Rationale: Explanation:
x, 2x
(x-2):(2x-2) = 1:3
3x-6 = 2x-2
x = 4
x+2x = 3x
=> 3*4 = 12
Answer: Option C
Answer: C
Question: In a factory that produces computer circuit boards, 4.5 percent of all boards produced are found to be defective and are repaired before being sold, but 10 percent of all defective boards are sold without being repaired. What percentage of boards produced in the factory are defective?
Options:
A)4.5%
B)5.0%
C)6.0%
D)10.0%
E)14.5%
Rationale: Total Boards = X
Total Defective Boards = Y
Out of this Y "Defective" boards 10% "Escaped" (GIVEN) and 90% "Get caught and fixed"
We know that "Get Caught and fixed" = 4.5% of X. This implies
90% of Y = 4.5% of X.
(90/100) * Y = (4.5/100) * X ===> Y = 0.05 * X ===> 5% of X.
ANSWER:B
Answer: B
Question: John spent a total of $135 on baseball tickets. The price of a ticket is either $12 for the field seats or $5 for the balcony. What is the minimum amount X of dollars he could have spent for the $12 tickets?
Options:
A)$48
B)$60
C)$84
D)$96
E)$120
Rationale: 60 ..... 12 *5 X= 60. (min). Thus answer .B
Answer: B
Question: 110 is increased by 50%. Find the final number.
Options:
A)100
B)110
C)150
D)155
E)165
Rationale: Final number = Initial number + 50%(original number) = 110 + 50%(110) = 110 + 55 = 165.
Answer E
Answer: E
Question: There are 361 doctors and nurses in a hospital. If the ratio of the doctors to the nurses is 8 : 11, then how many nurses are there in the hospital?
Options:
A)152
B)209
C)57
D)171
E)181
Rationale: Given,
The ratio of the doctors to the nurses is 8 : 11
Number of nurses = 11/19 x 361 = 209
ANSWER:A
Answer: A
Question: What will be the fraction of 25%
Options:
A)1/4
B)1/5
C)1/10
D)1/11
E)None of above
Rationale: Explanation:
It will 25*1/100 = 1/4
Option A
Answer: A
Question: A cistern 4 m long and 8 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
Options:
A)49 m2
B)50 m2
C)52 m2
D)62 m2
E)55 m2
Rationale: Area of the wet surface	= [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (8 x 1.25 + 4 x 1.25) + 8 x 4] m2
= 62 m2.
answer :D
Answer: D
Question: A student chose a number, multiplied it by 3, then subtracted 220 from the result and got 110. What was the number he chose?
Options:
A)90
B)100
C)110
D)120
E)130
Rationale: Let x be the number he chose, then
3⋅x−220=110
3x=330
x=110
correct answer C
Answer: C
Question: The smallest number which when subtracted from the sum of squares of 11 and 13 gives a perfect square is
Options:
A)1
B)4
C)5
D)9
E)8
Rationale: 11^2 + 13^2 = 121 + 169 = 290
290 - 1 = 289 = 17^2
1 must be subtracted to give a perfect square.
Answer A.
Answer: A
Question: There are 50 employees in the office of ABC Company. Of these, 22 have taken an accounting course, 14 have taken a course in finance and 15 have taken a marketing course. Nine of the employees have taken exactly two of the courses and 2 employee has taken all three of the courses. How many of the 50 employees have taken none of the courses?
Options:
A)9
B)5
C)8
D)12
E)10
Rationale: 50 Employees. Counting every different attendand to the courses we have:
Accounting: 22
Finance: 14
Marketing: 15
Which would add up to 51 different attendands, which is not possible.
Now 9 have taken exactly 2 courses, which means that there are 9 less different attendands. Say that 9 of the Finance attentands also attended Accounting.
51-9= 42
2 Person has taken all three courses. As above, we subtract him from the number of different attendands. Since this time the person took all three courses, we have to substract him two times.
42-4= 38.
Answer : D
Answer: D
Question: What is the area of square field whose side of length 17 m?
Options:
A)225
B)777
C)266
D)289
E)261
Rationale: 17 * 17 = 289 sq m
Answer: D
Answer: D
Question: The average temperature on Monday, Tuesday and Wednesday was 250. The average temperature on Tuesday, Wednesday and Thursday was 240. If the temperature on Thursday was 270, what was the temperature on Monday?
Options:
A)240
B)210
C)270
D)300
E)400
Rationale: Explanation :
Total temperature on Monday, Tuesday and Wednesday was 250 * 3 = 750
Total temperature on Tuesday, Wednesday and Thursday was 240 * 3 = 720
Hence, difference between the temperature on Monday and Thursday = 30
If Thursday temperature = 270, then Monday's temperature = 270 + 30 = 300
Answer : D
Answer: D
Question: John makes $60 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase?
Options:
A)16%
B)16.66%
C)17.8%
D)18%
E)19.5%
Rationale: Increase = (10/60)*100 = (1/6)*100 = 16.66%.
B
Answer: B
Question: How many two-digit numbers that do not contain the digits 1 or 4 are there?
Options:
A)112
B)56
C)64
D)49
E)84
Rationale: We can have 7 digits ( 2,3,5,6,7,8,9) for the first place ( tenth's place).
and similarly 8 digits for the unit digit. ( 0,2,3,5,6,7,8,9)
So in total 7*8= 56
Hence B
Answer: B
Question: A motorist travel to a place 220 km away at an average speed of 72 km/hr and returns at 55 km/hr.His average speed for the whole jouney in km/hr is
Options:
A)65
B)47
C)62.36
D)70.4
E)None of these
Rationale: Explanation :
Average Speed = (2xy/x +y )km/hr =(2x72 x55/ 72+55) = 7920/127 = 62.36 km/hr.
Answer : C
Answer: C
Question: A fruit seller had some apples. He sells 50% apples and still he has 5000. Originally he had how many apples?
Options:
A)10000
B)15200
C)11005
D)12540
E)12450
Rationale: Suppose originally he had x apples
then (100-50)% of x = 5000
50x/100 = 5000
x= 10000
Answer is A
Answer: A
Question: What is the area A of the square with the following coordinates: (x, y), (20, 20), (20, 5), (x, 5)?
Options:
A)60.
B)85.
C)125.
D)225.
E)It cannot be determined from the information given
Rationale: Length of one side= 15 (20-5)
Since, its a square, the area will be A= 15^2= 225
D is the answer
Answer: D
Question: Find the odd man out
2880, 480, 90, 24, 8, 4, 4
Options:
A)480
B)90
C)24
D)8
E)4
Rationale: from the right side
4*1=4,
4*2=8
8*3=24
24*4=96 but here given 90 so it's not.
96*5=480
480*6=2880
ANSWER:B
Answer: B
Question: A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is:
Options:
A)6 hours
B)10 hours
C)15 hours
D)30 hours
E)none
Rationale: Suppose, first pipe alone takes x hours to fill the tank .
Then, second and third pipes will take (x -5) and (x - 9) hours respectively to fill the tank.
1/x + 1/(x-5) = 1/(x-9)
(2x - 5)(x - 9) = x(x - 5)
x2 - 18x + 45 = 0
(x - 15)(x - 3) = 0
x = 15. [neglecting x = 3]
Answe = C
Answer: C
Question: A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?
Options:
A)40 minutes
B)1 hour
C)1 hour 15 min
D)1 hour 30 min
E)1 hour 10 min
Rationale: speed (upstream) =2/1 = 2 kmhr
speed (downstream)=1/(10/60)= 6 kmhr
speed in still water = 1/2 (2+6) = 4 kmhr
time taken in stationary = 5/4 = 1 hrs 15 min
ANSWER:C
Answer: C
Question: The center of a circle is (5, -2). (5, 5) is outside the circle, and (1, -2) is inside the circle. If the radius, r, is an
integer, how many possible values are there for r?
Options:
A) 9
B) 5
C) 8
D) 3
E) 2
Rationale: r must be greater than 4 and smaller than 7, hence r=5 or 6.
Answer B
Answer: B
Question: Of the diplomats attending a summit conference, 22 speak French, 32 do not speak Russian, and 20% of the diplomats speak neither French nor Russian. If 10% of the diplomats speak both languages, then how many diplomats attended the conference?
Options:
A)72
B)96
C)100
D)120
E)150
Rationale: {Total} = {French} + {Russian} - {Both} + {Neither}
{Total} = 22 + ({Total} - 32) - (0.1*{Total}) + 0.2*{Total}
Solving gives {Total} = 100.
Answer: C.
Answer: C
Question: A train 350 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
A)22 sec
B)16 sec
C)17 sec
D)88 sec
E)20 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 350 * 2/35 = 20 sec
Answer:E
Answer: E
Question: The average salary of all the workers in a workshop is Rs. 8000. The average salary of 6 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is?
Options:
A)A)23
B)B)21
C)C)18
D)D)56
E)E)12
Rationale: Let the total number of workers be x. Then,
8000x
= (12000 * 6) + 6000(x - 6)
=> 2000x = 36000
= x =18.
Answer:C
Answer: C
Question: A letter lock consists of three rings each marked with four different letters. The number of distinct unsuccessful attempts to open the lock is at the most?
Options:
A)63
B)64
C)65
D)67
E)90
Rationale: Since each ring consists of four different letters, the total number of attempts possible with the three rings is
= 4* 4 * 4 = 64. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts
= 64 - 1 = 63.
Answer: A
Answer: A
Question: In a box there is a number of toys, out of which 1/6 are dolls, 1/12 are balls, and the remaining 18 are plastic cubes. How many dolls are in the box?
Options:
A)2
B)6
C)4
D)16
E)3
Rationale: Let x be the number of toys.
x(1/6+1/12)=3x/12=x/4.
x-x/4=3x/4 is the number of cubes
Thus, 3x/4=18. From here, x=24.
The number of dolls is 1/6*24 = 4.
Answer C 4.
Answer: C
Question: If x is equal to the sum of the integers from 10 to 30, inclusive, and y is the number of even integers from 10 to 30, inclusive, what is the value of x + y?
Options:
A)401
B)411
C)421
D)431
E)441
Rationale: x = 10 + 11 +...+ 30 = 21(20) = 420
y = 11
x+y = 431
The answer is D.
Answer: D
Question: The winning relay team in a high school sports competition clocked 48 minutes for a distance of 13.2 km. Its runners A, B, C and D maintained speeds of 19 kmph, 20 kmph, 21 kmph, and 22 kmph respectively. What is the ratio of the time taken by B to than taken by D?
Options:
A)11:10
B)5:17
C)9:8
D)8:9
E)None of these
Rationale: Explanation :
Since it is a relay race, all the runners ran the same distance.
Hence for a same distance, (ratio of times) = 1/(ratio of speeds).
Hence ratio of times taken by B t& D = 22 : 20 = 11 : 10.
Answer : A
Answer: A
Question: If a particular player is never chosen, in how many ways can 11 cricket players be chosen out of 13 players?
Options:
A)12
B)56
C)64
D)72
E)90
Rationale: A particular players is never chosen, it means that 11 players are selected out of 12 players.
=> Required number of ways = 12C11
= 12
A
Answer: A
Question: If {x} is the product of all even integers from 1 to x inclusive, what is the greatest prime factor of {14} + {12}?
Options:
A)23
B)20
C)15
D)5
E)2
Rationale: Soln:
{14} + {12} = 14*{12} +{12} = 15*{12}
ANSWER:C
Answer: C
Question: Rs. 3900 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/2:1/3:1/4?
Options:
A)187
B)187
C)300
D)600
E)900
Rationale: 1/2:1/3:1/4
= 6:4:3
3/13*3900
= 900
Answer: E
Answer: E
Question: Using all the letters of the word "THURSDAY", how many different words can be formed?
Options:
A)7
B)6
C)8!
D)5
E)4
Rationale: Total number of letters = 8
Using these letters the number of 8 letters words formed is 8P8
= 8!.
Answer: C
Answer: C
Question: A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is:
Options:
A)4 am
B)4 pm
C)5 am
D)6 am
E)6 pm
Rationale: time 7 am to 4.15 pm = 37/4
37/720 hrs 1/20==>37/4
clock(1/20*720/37*37/4)= 9 hrs after 7 am
==> 4 pm
ANSWER B
Answer: B
Question: Rs.590 is divided amongst A, B, C so that 5 times A's share, six times B's share and eight times C's share are all equal. Find C's share?
Options:
A)Rs.157
B)Rs.150
C)Rs.289
D)Rs.128
E)Rs.129
Rationale: A+B+C = 590
5A = 6B = 8C = x
A:B:C = 1/5:1/6:1/8
= 24:20:15
15/59 * 590 = Rs.150
Answer:B
Answer: B
Question: This topic is locked. If you want to discuss this question please re-post it in the respective forum.
If y ≠ 3 and 3w/y is a prime integer greater than 2, which of the following must be true?
I. w = y
II. y = 1
III. w and y are prime integers.
Options:
A) None
B) I only
C) II only
D) III only
E) I and III
Rationale: 3w/y and if w=y then ans is 3 and 3 is prime number, which is greater than 2. so ans must be B. Please post OA.
Answer: A
Question: Tea worth Rs. 126 per kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be?
Options:
A)122.50 per kg
B)266.50 per kg
C)175.50 per kg
D)172.50 per kg
E)176.50 per kg
Rationale: Since first second varieties are mixed in equal proportions, so their average price = Rs.(126+135/2) = Rs.130.50
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.
Cost of 1 kg tea of 1st kind Cost of 1 kg tea of 2nd kind
x-153/22.50 = 1 => x - 153 = 22.50 => x=175.50.
Hence, price of the third variety = Rs.175.50 per kg.
Answer: C
Answer: C
Question: The banker's gain on a bill due due 1 year hence at 12% per annum is Rs.9. The true discount is
Options:
A)Rs.75
B)Rs.36
C)Rs.54
D)Rs.50
E)none
Rationale: Solution
T.D	= [B.G x 100 / R x T]
= Rs.(9 x 100 / 12 x 1)
= Rs.75.
Answer A
Answer: A
Question: When p is divided by 9, the remainder is 6. All of the following are possible values of p, except for which of the following?
Options:
A)15
B)33
C)51
D)59
E)69
Rationale: Four of these numbers can be expressed in the form of 9x+6, where x can be 0,1,2,3,4....
However, 59 = 9(6) + 5
The answer is D.
Answer: D
Question: Which of the following is the greatest possible common divisor of two different positive integers, both smaller than 124?
Options:
A)123.
B)122.
C)63.
D)62
E)61
Rationale: Given to find the greatest possible common divisor for two different positive number.
Let X be GCD and A and B are two different number.
We need to see the XA and XB has to be less than 124.
Now from options,
if we consider 62 * 2 = 124, which is equal to 124, we need to consider some number lesser than 124.
Consider 61 * 2 = 122 and 61 * 1 = 61 ( Both these numbers are lesser than 124 as requested ).
So GCD will be 61.
Answer: E is correct option
Answer: E
Question: The average (arithmetic mean) of 4 different integers is 76. If the largest integer is 90, what is the least possible value of the smallest integer?
Options:
A)1
B)19
C)29
D)30
E)37
Rationale: Total of Integers=76*4=3004
Lowest of the least possible integer is when the middle 2 intergers are at the maximum or equal to the highest possible integer.
But all integers are distinct. So if the largest integer is 90, then the middle 2 will be 88 and 89
Lowest of least possible integer = 304-(90+89+88)=304-267=37
Answer: E
Answer: E
Question: Bhanu spends 30% of his income on petrol on scooter 14% of the remaining on house rent and the balance on food. If he spends Rs.300 on petrol then what is the expenditure on house rent?
Options:
A)98
B)140
C)62
D)797
E)123
Rationale: Given 30% (Income ) = 300 ⇒⇒ Income = 1000
After having spent Rs.300 on petrol, he left with Rs.700.
His spending on house rent = 14% (700) = Rs.98
Answer:A
Answer: A
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 250 resolutions?
Options:
A)277 m
B)704 m
C)352 m
D)288 m
E)378 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 250 resolutions.
= 250 * 2 * 22/7 * 22.4 = 35200 cm
= 352 m
Answer: C
Answer: C
Question: A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17thinnings?
Options:
A)22
B)77
C)26
D)37
E)88
Rationale: 16x + 85 = 17(x + 3)
x = 34 + 3 = 37
Answer: D
Answer: D
Question: One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ?
Options:
A)30000
B)60000
C)50000
D)90000
E)70000
Rationale: Let savings in N.S.C and P.P.F. be Rs. x and Rs. (150000 - x) respectively. Then,
(1/3)	x =(1/2)(150000 - x)
(x/3)	+(x/2)= 75000
5x/6	= 75000
x =	75000 x 6/5= 90000
Savings in Public Provident Fund = Rs. (150000 - 90000)
= Rs. 60000
Answer is B.
Answer: B
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 15 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
Options:
A)432
B)444
C)2881
D)287
E)221
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 15 + 21 = 36
T = 12
D = 36 * 12 = 432
Answer:A
Answer: A
Question: Gold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio should these be mixed to get an alloy 15 times as heavy as water ?
Options:
A)3 : 2
B)3 : 8
C)5 : 7
D)3 : 7
E)3 : 6
Rationale: Let us say, water weighs 1kg/1 liter. Then Gold weighs 19 kgs and copper weighs 9 kgs.
Assume x kgs of gold and y kgs of copper required to get the required alloy.
We use weighted average formula = Ax=n1.A1+n2.A2n1+n2Ax=n1.A1+n2.A2n1+n2
Therefore, 15=x.19+y.9x+y15=x.19+y.9x+y
15x + 15y = 19x + 9y
4x = 6y ⇒ x/y = 3 : 2
So Gold and Copper should be mixed in the ratio 3 : 2.
Answer:A
Answer: A
Question: If w,x,y,z are consecutive positive integers ; then which of the following is always odd?
[1] w*x+(y+2)^2*z
[2] w^x + z^y
[3] 13x^2
Options:
A)1
B)2
C)3
D)1 and 2
E)2 and 3
Rationale: Plug in some numbers
w = 1
x = 2
y = 3
z = 4
Check the options -
[1] w*x+(y+2)^2*z = 1*2 + (3+2)^2 * 4 => 2 + 25*4 = 102{ Not an odd Number }
[2] w^x + z^y = 1^2 + 4^3 => 1 + 64 = 65{ Odd number }
[3] 13x^2 = 13*4 =52 even
[2]
B
Answer: B
Question: 1^x + 1^-x = 2 What is the value of x?
Options:
A)-1
B)-1/2
C)0
D)1/2
E)1
Rationale: let 1^x = t
t+1/t =2
t^2 -2t +1 =0
(t-1)^2=0
t-1=0
t=1
1^x=1
x=1
Ans: E
Answer: E
Question: In a class,7 students like to play Basketball and 8 like to play Cricket. 5 students like to play on both Basketball and Cricket. How many students like to play Basketball or Cricket or both?
Options:
A)10
B)15
C)16
D)18
E)22
Rationale: Draw a Venn Diagram yourself !
B + C - BC = Number of students that play either Basketball or Cricket
7 +8 - 5 = 10
A)
Answer: A
Question: If the wheel is 9 cm then the number of revolutions to cover a distance of 1056 cm is?
Options:
A)18
B)26
C)14
D)18.7
E)91
Rationale: 2 * 22/7 * 9 * x = 1056 => x
= 18.7
Answer: D
Answer: D
Question: When positive integer n is divided by 3, the remainder is 2. When n is divided by 6, the remainder is 5. How many values less than 100 can n take?
Options:
A) 0
B) 2
C) 3
D) 4
E) 5
Rationale: a quick approac to this Q is..
the equation we can form is.. 3x+2=7y+5..
3x-3=7y... 3(x-1)=7y...
so (x-1) has to be a multiple of 7 as y then will take values of multiple of 3..
here we can see x can be 1,8,15,22,29 so 5 values till 100 is reached
as (29-1)*3=84 and next multiple of 7 will be 84+21>100..
ans 4.. D
Answer: D
Question: A theater charges $12 for seats in the orchestra and $8 for seats in the balcony. On a certain night, a total of 340 tickets were sold for a total cost of $3,320. How many more tickets were sold that night for seats in the balcony than for seats in the orchestra?
Options:
A) 40
B) 110
C) 120
D) 130
E) 220
Rationale: Orchestra Seats - a
Balcony Seats - b
a+b = 340
and 12a + 8b = 3320
Solving equations simultaneously (Multiply Equation 1 with 8 and subtract from second equation)
4a = 3320 - 8*340 = 3320 - 2720 = 600
i.e. a = 150
and b = 340-150 = 190
More seats in balcony than orchestra = b-a = 190 - 150 = 40
Answer: option A
Answer: A
Question: The wages earned by Robin is 40% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much percent is the wages earned by Charles more than that earned by Robin?
Options:
A)14%
B)23%
C)30%
D)50%
E)100%
Rationale: Let wage of Erica = 10
Wage of Robin = 1.4*10 = 14
Wage of Charles = 1.6 *10 = 16
Percentage by which wage earned by Charles is more than that earned by Robin = (16-14)/14 * 100%
= 2/14 * 100%
=14%
Answer A
Answer: A