mathewhe/aqua_rat huggingface dataset:
Question: A guy was asked to specify his age in years. He said, “Take my age 8 years hence, multiply it by eight and subtract eight times of my age 8 years ago and get the half of the result and you will know my age.” What was the age of that guy?
(A) 18
(B) 55
(C) 63
(D) 64
(E) 70
Rationale: Current age of the guy = A years.
Then, 8 (A + 8) – 8 (A – 8) = A
(8A + 64) – (8A – 64) = A
A = 128/2 =64
D
Answer: (D) 64
Question: What is the sum of the numbers between 1 and 14, inclusive?
(A) 105
(B) 110
(C) 125
(D) 150
(E) 160
Rationale: Sol. add up the numbers between 1 and 14.
Answer is A, 105
Answer: (A) 105
Question: The HCF of two numbers is 12 and their difference is also 12. The numbers are
(A) 66, 78
(B) 94, 106
(C) 70, 82
(D) 84, 96
(E) None
Rationale: Explanation:
The difference of required numbers must be 12 and every number must be divisible by 12. Therefore, they are 84, 96.
Correct Option: D
Answer: (D) 84, 96
Question: A set consists of 12 numbers, all are even or multiple of 5. If 7 numbers are even and 14 numbers are multiple of 5, how many numbers is multiple of 10?
(A)  0
(B)  1
(C)  2
(D)  3
(E)  9
Rationale: {Total} = {Even} + {Multiple of 5} - {Both} + {Nether}.
Since{Neither}=0(allare even or multiple of 5) then:
12 = 7 + 14 - {Both} + 0;
{Both}=9(so 1 number is both even AND multiple of 5, so it must be a multiple of 10).
Answer: E.
Answer: (E)  9
Question: The salary of a worker is first increased by 10% and afterwards reduced by 10%. What is the net change in the worker's salary?
(A) 1% increase
(B) 1% decrease
(C) 2% increase
(D) 2% decrease
(E) no change
Rationale: Let x be the original salary.
The final salary is 0.9(1.1x) = 0.99x
The answer is B.
Answer: (B) 1% decrease
Question: In how many ways can 5 boys and 3 girls sit around a table in such a way that no two girls sit together?
(A) 1000
(B) 1400
(C) 1440
(D) 1800
(E) 1900
Rationale: The 5 boys can be seated around a table in 4! Ways. In between them there are 5 places.
The 3 girls can be placed in the 5 places in 5P3 ways.
Therefore, Required number of ways= 4!* 5P3
=24*60
=1440
ANSWER:C
Answer: (C) 1440
Question: Out of 8 people working on a project, 3 are graduates. If 3 people are selected at random, what is the probability that there is at least one graduate among them?
(A) 16/21
(B) 19/24
(C) 23/28
(D) 29/34
(E) 36/41
Rationale: P(no graduates) = 5C3 / 8C3 = 10/56 = 5/28
P(at least one graduate) = 1- 5/28 = 23/28
The answer is C.
Answer: (C) 23/28
Question: The manager of a produce market purchased a quantity of tomatoes for $0.80 per pound. Due to improper handling, 10 percent of the tomatoes, by weight, were ruined and discarded. At what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 9 percent of the cost of the tomatoes.
(A) $0.94
(B) $0.97
(C) $0.98
(D) $1.00
(E) $1.20
Rationale: Assume the manager bought 100 tomatoes.
Cost Price = 80
Given: 10% are damaged --> Available tomatoes to sell = 90
90 * x - 80 = 0.09 * 80
90x - 80 = 7.2
90x = 87.2
x = 87.2/90 = 0.968
x is slightly under 0.9688 = 0.97
Answer: B
Answer: (B) $0.97
Question: P and Q started a business investing Rs, 85,000 and Rs. 15,000 respectively. In what ratio the profit named after 2 years bo divided between P and Q respectively ?
(A) 17:9
(B) 17:3
(C) 17:2
(D) 17:1
(E) 17:0
Rationale: P : Q = 85000 : 15000 = 86 : 15 = 17 : 3
Answer: B
Answer: (B) 17:3
Question: A certain telephone company offers two plans, A and B. Under plan A, the company charges a total of $0.60 for the first 6 minutes of each call and $0.06 per minute thereafter. Under plan B, the company charges $0.08 per minute of each call. What is the duration of a call, in minutes, for which the company charges the same amount under plan A and under plan B?
(A) 12
(B) 9
(C) 15
(D) 21
(E) 30
Rationale: Let the duration, in minutes, for which the company charges the same under plan A and plan B be t minutes.
Then under plan A the cost would be $0.6+0.06(t-6) and under plan B the cost would be $0.08t. We want these amount to be equal: 0.6+0.06(t-6)=0.08t --> 60+6(t-6)=8t --> t=12.
Answer: A.
Answer: (A) 12
Question: One pump drains one-half of a pond in 6 hours, and then a second pump starts draining the pond. The two pumps working together finish emptying the pond in one-half hour. How long would it take the second pump to drain the pond if it had to do the job alone?
(A) 1 hour
(B) 1.1 hour
(C) 3 hours
(D) 5 hours
(E) 6 hours
Rationale: First pump drains 1/2 of the tank in 6 hours
so 12 hours it will take to drain the full tank.
Let, 2nd pump drains the full tank in a hours
so both together can drain (1/12+1/a) part in 1 hour
son in 1/2 hour they drain 1/2*(1/12+1/a) part of the tank
given that in 1/2 hour they drain 1/2 of the tank
hence we can say
1/2*(1/12+1/a) = 1/2
solving u get a = 12/11=1.1
Hence answer is B
Answer: (B) 1.1 hour
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)
(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) 32, 16
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?
(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) 240
Question: What is the total number of prime numbers less than 45?
(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) 14
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?
(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) 4
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?
(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) 102
Question: In how many ways Chief Minister and Minister be elected from a team of 12 members?
(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) 132
Question: what is the remainder of 18!/23?
(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) 1
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?
(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) 12
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?
(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) 5.0%
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?
(A) $48
(B) $60
(C) $84
(D) $96
(E) $120
Rationale: 60 ..... 12 *5 X= 60. (min). Thus answer .B
Answer: (B) $60
Question: 110 is increased by 50%. Find the final number.
(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) 165
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?
(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) 152
Question: What will be the fraction of 25%
(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) 1/4
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:
(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) 62 m2
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?
(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) 110
Question: The smallest number which when subtracted from the sum of squares of 11 and 13 gives a perfect square is
(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) 1
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?
(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) 12
Question: What is the area of square field whose side of length 17 m?
(A) 225
(B) 777
(C) 266
(D) 289
(E) 261
Rationale: 17 * 17 = 289 sq m
Answer: D
Answer: (D) 289
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?
(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) 300
Question: John makes $60 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase?
(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) 16.66%
Question: How many two-digit numbers that do not contain the digits 1 or 4 are there?
(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) 56
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
(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) 62.36
Question: A fruit seller had some apples. He sells 50% apples and still he has 5000. Originally he had how many apples?
(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) 10000
Question: What is the area A of the square with the following coordinates: (x, y), (20, 20), (20, 5), (x, 5)?
(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) 225.
Question: Find the odd man out
2880, 480, 90, 24, 8, 4, 4
(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) 90
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:
(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) 15 hours
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?
(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) 1 hour 15 min
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?
(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)  5
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?
(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) 100
Question: A train 350 m long, running with a speed of 63 km/hr will pass a tree in?
(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) 20 sec
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?
(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) C)18
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?
(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) 63
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?
(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) 4
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?
(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) 431
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?
(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) 11:10
Question: If a particular player is never chosen, in how many ways can 11 cricket players be chosen out of 13 players?
(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) 12
Question: If {x} is the product of all even integers from 1 to x inclusive, what is the greatest prime factor of {14} + {12}?
(A) 23
(B) 20
(C) 15
(D) 5
(E) 2
Rationale: Soln:
{14} + {12} = 14*{12} +{12} = 15*{12}
ANSWER:C
Answer: (C) 15
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?
(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) 900
Question: Using all the letters of the word "THURSDAY", how many different words can be formed?
(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) 8!
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:
(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) 4 pm
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?
(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) Rs.150
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.
(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)  None
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?
(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) 175.50 per kg
Question: The banker's gain on a bill due due 1 year hence at 12% per annum is Rs.9. The true discount is
(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) Rs.75
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?
(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) 59
Question: Which of the following is the greatest possible common divisor of two different positive integers, both smaller than 124?
(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) 61
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?
(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) 37