mathewhe/aqua_rat huggingface dataset:
Question: Two men Amar and Bhavan have the ratio of their monthly incomes as 6:5. The ratio of their monthly expenditures is 3:2. If Bhavan saves one-fourth of his income, find the ratio of their monthly savings?
(A) 3:19
(B) 3:10
(C) 3:16
(D) 3:11
(E) 3:12
Rationale: Let the monthly incomes of Amar and Bhavan be 6x and 5x respectively.
Let the monthly expenditures of Amar and Bhavan be 3y and 2y respectively.
Savings of Bhavan every month = 1/4 (5x)
=(his income) - (his expenditure) = 5x - 2y
=> 5x = 20x - 8y => y = 15x/8
Ratio of savings of Amar and Bhavan
= 6x - 3y : 1/4 (5x) = 6x - 3(15x/8) : 5x/4
= 3x/8 : 5x/4 => 3:10
Answer: B
Answer: (B) 3:10
Question: Look at this series: 2, 1, (1/2), (1/4), ... What number should come next?
(A) (1/3)
(B) (1/8)
(C) (2/8)
(D) (1/16)
(E) None
Rationale: Explanation: This is a simple division series; each number is one-half of the previous number. In other terms to say, the number is divided by 2 successively to get the next result.
4/2 = 2
2/2 = 1
1/2 = 1/2
(1/2)/2 = 1/4
(1/4)/2 = 1/8 and so on.
Answer: Option B
Answer: (B) (1/8)
Question: If x/(11p) is an odd prime number, where x is a positive integer and p is a prime number, what is the least value of x?
(A) 22
(B) 33
(C) 44
(D) 66
(E) 99
Rationale: x/(11p) = odd prime number
x = odd prime number * 11p
Least value of x = Lowest odd prime number * 11 * Lowest value of p
= 3 * 11* 2 = 66
Answer D
Answer: (D) 66
Question: Given that 100.48 = x, 100.70 = y and xz = y2, then the value of z is close to:
(A) 2.2
(B) 8.2
(C) 2.9
(D) 2.1
(E) 2.6
Rationale: xz = y2 10(0.48z) = 10(2 x 0.70) = 101.40
0.48z = 1.40
z =	140	=	35	= 2.9 (approx.)
48	12
Answer: C
Answer: (C) 2.9
Question: The sum of two numbers is 65. Their difference is 5. The bigger number is
(A) 20
(B) 25
(C) 30
(D) 35
(E) 45
Rationale: X + Y = 65
X - Y = 5
Adding 2X = 70 ==> X = 35 and Y = 65 - 35 = 30
Bigger number is X = 35
Answer D.
Answer: (D) 35
Question: 40 is subtracted from 60% of a number, the result is 50. Find the number?
(A) 150
(B) 189
(C) 177
(D) 167
(E) 190
Rationale: (60/100) * X – 40 = 50
6X = 900
X = 150
Answer: A
Answer: (A) 150
Question: 21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement.
(A) 3/41
(B) 2/41
(C) 9/42
(D) 3/37
(E) 4/49
Rationale: The probability that first toy shows the even number,
=1021=1021
Since, the toy is not replaced there are now 9 even numbered toys and total 20 toys left.
Hence, probability that second toy shows the even number,
=920=920
Required probability,
=(1021)×(920)=(1021)×(920)
=9/42
C
Answer: (C) 9/42
Question: A 600 m long train crosses a tree in 60sec, how much time will It take to pass a platform 450 m long?
(A) 288
(B) 190
(C) 188
(D) 188
(E) 105
Rationale: L = S*T
S= 600/60
S= 10 m/Sec.
Total length (D)= 1050 m
T = D/S
T = 1050/10
T = 105 Sec
Answer:E
Answer: (E) 105
Question: √4 percent of 4√4 =
(A) 0.16
(B) 0.17
(C) 0.18
(D) 0.2
(E) 0.19
Rationale: √4 = 2
So, √4 percent of 4√4 = 2 percent of (4)(2)
= (2/100)(8)
= 16/100
= 0.16
Answer:
A
Answer: (A) 0.16
Question: Tim came second in Math. When his mother asked him how much he had scored, he answered that he got the sum of the first 11 even numbers. His mother immediately worked out the answer. How much had he scored in Math?
(A) 80
(B) 190
(C) 132
(D) 170
(E) 60
Rationale: C
132
Sum = (n x n) + n
Hence,11 x 11 = 121 + 11 = 132
Answer: (C) 132
Question: The length of a rectangle is 2 times its width. If the width of the rectangle is 5 inches, what is the rectangle's area, in square inches?
(A) 50 square inches
(B) 75 square inches
(C) 68 square inches
(D) 89 square inches
(E) 92 square inches
Rationale: If the width is 5 in and the length is 2 times the width, then the length is
2 * 5 = 10 in
The area is given by
5 * 10 = 50 square inches
correct answer A
Answer: (A) 50 square inches
Question: Nicky and Cristina are running a 500 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?
(A) 50
(B) 45
(C) 40
(D) 35
(E) 30
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.
E
Answer: (E) 30
Question: The average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person ?
(A) 70 kg
(B) 75 kg
(C) 80 kg
(D) 85 kg
(E) 95 kg
Rationale: Explanation:
Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg. Answer: D
Answer: (D) 85 kg
Question: If (a – b) is 11 more than (c + d) and (a + b) is 3 less than (c – d), then (a – c) is:
(A) 6
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: (a – b) – (c + d) = 11 and (c – d) – (a + b) = 3
=> (a – c) – (b + d) = 11 and (c – a) – (b + d) = 3
=> (b + d) = (a – c) – 11 and (b + d) = (c – a) – 3
=> (a – c) – 11 = (c – a) – 3 => 2(a – c) = 8 => (a – c) = 4
ANSWER:D
Answer: (D) 4
Question: If a1 = 1 and an+1= 2an + 5, n = 1, 2 .. , then a40 is equal to ?
(A) a. 5*2^99-6
(B) b. 5*2^99+6
(C) c. 6*2^99+5
(D) d. 6*2^39- 5
(E) e. 6*2^99-6
Rationale: Here is my solution:
an+1=2an+5............(1)
lets ADD 5 to both sides....
so (an+1) + 5= 2 (an+5)....................taking 2 as common factor
now a1=1. so for n=1, an+5=6.......
putting n=1. we get both sides as,
a2 + 5= 2 * 6 ..............as ( an+5=6 .......(for n=1)..)
a2= 2 *6 - 5
a2= 2 * 2 *3 - 5
a2= 2^2 *3 - 5................. so with same progression
a40= 2^40 * 3 - 5
a40=2 * 2^39 * 3 - 5
a40= 6 * 2^39 - 5
D
Answer: (D) d. 6*2^39- 5
Question: The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is:
(A) 36.5
(B) 21.4
(C) 19.5
(D) 18.2
(E) 17.9
Rationale: Explanation:
Correct sum = (36 * 50 + 48 - 23) = 1825.
Correct mean = 1825/50 = 36.5
Option A
Answer: (A) 36.5
Question: he number of times a bucket of capacity 4 liters to be used to fill up a tank is less than number of ties another bucket of capacity 3 liters used for the same purpose by 4. What is the capacity of the tank?
(A) 360 liters
(B) 256
(C) 48
(D) 525
(E) 425
Rationale: 4x=3(x+4),where x may be number of times 4l bucket is used.
4x=3(x+4)-->1.
x=12,
substitute x to lhs or rhs of 1,which
gets you the capacity,and it is 48.
ANSWER:C
Answer: (C) 48
Question: The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square?
(A) 5:15
(B) 5:19
(C) 5:13
(D) 5:11
(E) 5:16
Rationale: Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.
a2 = 4096 = 212
a = (212)1/2 = 26 = 64
L = 2a and b = a - 24
b : l = a - 24 : 2a = 40 : 128 = 5:16
Answer: E
Answer: (E) 5:16
Question: n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4 ?
(A) 1
(B) 3
(C) 5
(D) 2
(E) 0
Rationale: Let n = 4q + 3. Then 2n = 8q + 6 = 4(2q + 1 ) + 2.
Thus, when 2n is divided by 4, the remainder is 2.
ANSWER D
Answer: (D) 2
Question: A bicyclist's wheel has a circumference of 8 meters. if the bicyclist covers 160 meters in 5 hours at a constant speed, how many rotations does the wheel make per hour at that speed?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: The bicyclist covers y meters in t hrs. So he covers y/t meters in one hour.
To cover y/t meters, the bicycle's wheel went round and round that is, multiple times, the wheel completed one circumference on the road. How many times did it complete one full rotation. Since the circumference is x, the number of times it completes the circumference is y/xt. =160/8*5 =4
Answer (C)
Answer: (C) 4
Question: What is the tens digit of 36^30?
(A) 1
(B) 7
(C) 5
(D) 3
(E) 9
Rationale: 36^10 = 6^20
(6^2)=6*6 = 36
(6^3)= 36*6 = .16
(6^4)= .16*6 = ..96
(6^5) = ..96*6 = ..76
(6^6) = ..76*6 = ...56
(6^7) = ....56*6 = ....36
If you see there is a pattern here in tens digits 3,1,9,7,5,3,1 and so on...
Continue the pattern up to 6^30 ( dont actually calculate full values) and answer is B: 7
Answer: (B) 7
Question: . If A is 35% greater than B then how much percentage is B smaller than A?
(A) 16 2/3%
(B) 18 2/3%
(C) 16%
(D) 17%
(E) None of these
Rationale: Explanation:
A = 120
B = 100
A-B/A * 100 = 20/120 * 100 = 2000/120 % = 200/12 % = 16 2/3%
Smaller than A
Answer: Option A
Answer: (A) 16 2/3%
Question: Which of the following could be the sides of an obtuse angled triangle?
I. 51, 29, 100
II. 10,110, 60
III. 40 ,20 70
(A) I and III only
(B) II only
(C) III only
(D) I and II only
(E) I, II and III
Rationale: obtuse angled triangle means one angle more than 90 deg and total 180 deg.. I and II only
HENCE, (D)
Answer: (D) I and II only
Question: k, l, m together started a business. k invested Rs.6000 for 5 months l invested Rs.3600 for 6 months and m Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of l ?
(A) Rs. 1640
(B) Rs. 2500
(C) Rs. 2160
(D) Rs. 3000
(E) None of these
Rationale: Explanation:
=> 60x5 : 36x6 : 75x3
=> 100 : 72 : 75
=> 72/247 x 7410 = Rs. 2160
ANSWER IS C
Answer: (C) Rs. 2160
Question: 5 baseball players each stand at different corners of a baseball diamond. The sides of the diamond are all of equal length. Two arrangements of baseball players are considered different only when the relative positions of the players differ. How many different ways can the baseball players arrange themselves around the diamond?
(A) 4
(B) 6
(C) 16
(D) 24
(E) 256
Rationale: it is like a circular arrangement.
total ways for n people to arrange in a circle is = factorial (n-1)
in this case n= 5
hence ans = 4 factorial = 24
hence D
Answer: (D) 24
Question: The average salary of the employees in a office is Rs.120/month.The avg salary of officers is Rs.430 and of non officers is Rs 110. If the no.of officers is 15,then find the No of nonofficers in the office.
(A) 400
(B) 465
(C) 430
(D) 450
(E) 510
Rationale: Let no. of non- officers be x
15 * 430 + x * 110 = (x + 15) 120
x = 465
B
Answer: (B) 465
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. 1,80,000 as total savings, how much has he saved in Public Provident Fund ?
(A) 80000
(B) 60000
(C) 50000
(D) 72000
(E) 90000
Rationale: Let savings in N.S.C and P.P.F. be Rs. x and Rs. (180000 - x) respectively. Then,
=1/3 x = 1/2 (180000 - x)
=x/3 + x/2 = 90000
=5x/6 = 90000
=x = 90000 x 6 /5	= 108000
Savings in Public Provident Fund = Rs. (180000 - 108000) = Rs. 72000
Answer is D.
Answer: (D) 72000
Question: A rectangular field is to be fenced on three sides leaving a side of 40 feet uncovered.If the area of the field is 680 sq.ft, how many feet of fencing will be required?
(A) 44ft
(B) 88ft
(C) 74ft
(D) 11ft
(E) 66ft
Rationale: Given that length and area, so we can find the breadth.
Length x Breadth = Area
40 x Breadth = 680
Breadth = 17 feet
Area to be fenced = 2B + L = 2 (17) + 40 = 74 feet
Answer: C) 74ft
Answer: (C) 74ft
Question: In Township K each property is taxed at 10 percent of its assessed value. If the assessed value of a property in Township K is increased from $20,000 to $28,000, by how much will the property tax increase?
(A)  $800
(B)  $1000
(C)  $600
(D)  $400
(E)  $500
Rationale: Increase in house value = $28,000 - $20,000 =$8000
So, tax increase = 10% of$8000=$800
Answer: A
Answer: (A)  $800
Question: a natural numbr has exactly 10 divisors including 1 and itself.how many distint prime factors this natural numbr will have?
(A) 1 or2
(B) 1 or3
(C) 1 or 2or 3
(D) 2 or 3
(E) 2 or 5
Rationale: Here it is given that the number has exactly 10 divisor including 1 and itself.
So the number may be (any one prime factors)power 9 .....I.e (2)pow 9, (3)pow 9....etc.total 10 factor=(9+1)=10.
Also the number may be as (any one prime factors)pow 1*(any one prime factors)pow 4........I.e...(2)pow 1*(3)pow 4...etc= total 10 factor((1+1)*(4+1))=10.
Hence either 1 or 2 is correct
ANSWER:A
Answer: (A) 1 or2
Question: If c is a positive integer, which of the following could NOT be the square of c?
(A)  5,008,644
(B)  5,004,169
(C)  4,999,696
(D)  4,995,225
(E)  4,990,752
Rationale: A number ending with 2 can never be a perfect square.
Units digit of a perfect square must be:
1,4,9,6,5
Answer E)
Answer: (E)  4,990,752
Question: In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. If 20% of the votes polled were invalid and a total of 6720 votes were polled, then how many valid votes did B get?
(A) 1888
(B) 2999
(C) 2834
(D) 2777
(E) 2184
Rationale: Let the total number of votes polled in the election be 100k.
Number of valid votes = 100k - 20% (100k) = 80k
Let the number of votes polled in favour of A and B be a and b respectively.
a - b = 15% (100k) => a = b + 15k
=> a + b = b + 15k + b
Now, 2b + 15k = 80k and hence b = 32.5k
It is given that 100k = 6720
32.5k = 32.5k/100k * 6720 = 2184
The number of valid votes polled in favour of B is 2184.
Answer: E
Answer: (E) 2184
Question: Of 70 players on a football team, 40 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?
(A) 60
(B) 59
(C) 63
(D) 71
(E) 92
Rationale: Total = 70
Thrower = 40
Rest = 70 - 40 = 30
Left Handed = 30/3 = 10
Right handed = 20
If all Thrower are right handed then total right handed is 40 + 20 = 60
so A. 60 is the right answer
Answer: (A) 60
Question: It takes Joey the postman 1 hours to run a 1 mile long route every day. He delivers packages and then returns to the post office along the same path. If the average speed of the round trip is 5 mile/hour, what is the speed with which Joey returns?
(A) 1.67
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: let his speed for one half of the journey be 3 miles an hour
let the other half be x miles an hour
now,
avg speed =5 mile an hour
2*1*x/1+x=5
2x=5x+5=>3x=5=5/3=1.67
A
Answer: (A) 1.67
Question: what is the angle between the hands of a clock when time is 10:30?
(A) 65deg
(B) 75deg
(C) 45deg
(D) 15deg
(E) 135deg
Rationale: Angle between two hands =
30h - 11/2 m = 30*10 - 30*11/2 = 300 - 165 = 135deg
ANSWER:E
Answer: (E) 135deg
Question: A man travels from A to B at a speed of 30 kmph and returns with a speed of 60 kmph. What is the average speed of the man?
(A) 87
(B) 29
(C) 40
(D) 77
(E) 101
Rationale: Explanation:
The average speed ‘v’, when a man travels two same distance with different speeds ‘v1’ and ‘v2’ is:
v = (2*v1*v2) / (v1 + v2)
In the above problem, v1 = 30 and v2 = 60
Therefore, v = (2*30*60)/(30 + 60) = 3600/90
v = 40
ANSWER:C
Answer: (C) 40
Question: Find the remainder of the division (3^14)/4.
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Find the pattern of the remainders after each power:
(3^1)/4 remainder 3
(3^2)/4 remainder 1 -->this is where the cycle ends
(3^3)/4 remainder 3 -->this is where the cycle begins again
(3^4)/4 remainder 1
Continuing the pattern to (3^14)/4 gives us a remainder of 1
Final Answer:
A) 1
Answer: (A) 1
Question: The price ratio of oranges to lemons is 2:3. The price ratio of grapefruits to lemons is 3:5. What is the ratio, by price, of grapefruit to oranges?
(A) 18:20
(B) 10:9
(C) 2:5
(D) 5:2
(E) 3:2
Rationale: Let price of Lemons be 30 ( since that is common )
So, Price of Oranges = 20 & Price of Lemons is = 30
Further price of Grapefruit will be 6*3 = 18
Thus price, of grapefruit to oranges = 18 : 20
ANSWER:A
Answer: (A) 18:20
Question: A hiker walked for 3 days. She walked 18 miles on the first day, walking 2 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day she walked the same number of hours as on the first day, but at the same speed as on the second day. How many miles in total did she walk?
(A) 24
(B) 44
(C) 58
(D) 69
(E) 62
Rationale: She walked 18 miles on the first day, walking 2 miles per hour i.e. total time of walk on Day-1 = 18/2 = 9 Hours
Second day time of walk = 9-1 = 8 hours and Speed = 2+1=3 miles per hour i.e. Distance walked on second day = 8*3 = 24 miles
Third day time of walk = 9 hours and Speed = 3 miles per hour i.e. Distance walked on second day = 9*3 = 27 miles
Total Distance travelled on three days = 18+24+27 = 69
Answer: Option D
Answer: (D) 69
Question: 39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
(A) 22
(B) 13
(C) 88
(D) 77
(E) 91
Rationale: Explanation:
Let the required number of days be x.
Less persons, More days (Indirect Proportion)
More working hours per day, Less days (Indirect Proportion)
\inline {\color{Blue} \left.\begin{matrix} persons &30:39 \\ working\; hours/day & 6:5 \end{matrix}\right\}::12:x}
\inline {\color{Blue} \therefore } 30 x 6 x x = 39 x 5 x 12
=> x= \inline {\color{Blue}\frac{39\times 5\times 12}{30\times 6}}
=> x= 13
Answer: B) 13
Answer: (B) 13
Question: A foreign language club at Washington Middle School consists of n students, 1/2 of whom are boys. All of the students in the club study exactly one foreign language. 1/3 of the girls in the club study Spanish and 4/5 of the remaining girls study French. If the rest of the girls in the club study German, how many girls in the club, in terms of n, study German?
(A) 2n / 5
(B) n / 3
(C) n / 5
(D) 2n / 15
(E) n / 15
Rationale: 1/2 of the students are boys, thus 1/2 of the students are girls.
1/3 of the girls in the club study Spanish and 4/5 of the remaining girls study French.
Thus 1/5 of 2/3 = 2/15 of the girls study German.
Since girls comprise 1/2 of the students, then 1/2*2/15 = 1/15 are girls who study German.
The answer is E.
Answer: (E) n / 15
Question: Jacob purchased a TV set for $ 12500 after getting a discount of 20% on the labelled price. He spent $ 125 on transport and $ 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered?
(A) 14900
(B) 12900
(C) 15400
(D) 17600
(E) 14700
Rationale: D
17600
Price at which the TV set is bought = $ 12,500
Discount offered = 20%
Marked Price = 12500 * 100/80 = $ 15625
The total amount spent on transport and installation = 125 + 250 = $ 375\Total price of TV set = 15625 + 375 = $ 16000
The price at which the TV should be sold to get a profit of 10% if no discount was offered = 16000 * 110/100 = $ 17600
Answer: (D) 17600
Question: rahul played weel in this season.his current batting averagge is 51.if he score 78 runs in today match.his batting average will become 54.how many matches had he played in this season.
(A) 8
(B) 10
(C) 9
(D) 6
(E) 5
Rationale: 51x+78=54(x+1)
=>3x=24
=>x=8
ANSWER:A
Answer: (A) 8
Question: What approximate value should come in place of the question mark (?) in the following equation?
35% of 1478 + 29% of 3214 = ?
(A) 1600
(B) 1250
(C) 1300
(D) 1450
(E) 1500
Rationale: ? = 35% of 1478 + 29% of 3214
≈ 35% of (1500 – 22) + (30% – 1%) of 3200
≈ 35 × 15 – 8 + 30 × 32 – 32
= 525 + 960 – 40 = 525 + 920
= 1445 ≈ 1450
Answer D
Answer: (D) 1450
Question: The average (arithmetic mean) of 4 positive integers is 30. If the average of 2 of these integers is 15, what is the greatest possible value that one of the other 2 integers can have?
(A) 55
(B) 89
(C) 100
(D) 109
(E) 115
Rationale: a + b + c + d = 120
a + b = 30
c + d = 90
Greatest possible = 89 (Just less than 1)
Answer = B
Answer: (B) 89
Question: The population of a town is 10000. It decreases annually at the rate of 20% p.a. What will be its population after 2 years?
(A) 6400
(B) 4500
(C) 5120
(D) 5230
(E) 5366
Rationale: 10000 × 80/100 × 80/100 = 6400
Answer : A
Answer: (A) 6400
Question: If 1/2 of the air in a tank is removed with each stroke of a vacuum pump, what fraction of the original amount of air has been removed after 1 strokes ?
(A) 1/2
(B) 7/8
(C) 1/4
(D) 1/8
(E) 1/16
Rationale: Left After 1st stroke = 1/2
So removed = 1- 1/2 = 1/2
Answer: (A) 1/2
Question: The maximum number of student amoung them 2010 pens and 1050 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
(A) 90
(B) 60
(C) 30
(D) 1911
(E) None of these
Rationale: Solution
Required number of student = H.C.F of 2010 and 1050 = 30. Answer C
Answer: (C) 30
Question: The average of temperatures at noontime from Monday to Friday is 25; the lowest one is 15, what is the possible maximum range of the temperatures?
(A) 20
(B) 25
(C) 50
(D) 45
(E) 75
Rationale: Average=25, Sum of temperatures=25*5=125
As the min temperature is 15, max would be 125-4*15=65 --> The range=65(max)-15(min)=50
Answer: C
Answer: (C) 50
Question: A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is?
(A) 25/42
(B) 25/46
(C) 25/41
(D) 25/49
(E) 25/23
Rationale: Total fruits = 9
Since there must be at least two apples,
(⁵C₂ * ⁴C₁)/⁹C₃ + ⁵C₃/⁹C₃ = 25/42.
Answer:A
Answer: (A) 25/42
Question: How many positive integers less than 80 are multiples of 4 but NOT multiples of 6?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
Rationale: The LCM of 4 and 6 is 12.
If x <80 and x is divisible by 4 not by 6 --> x is NOT divisible by 12.
From 1--> 80, we have 6 numbers which is divisible by 12: 12, 24, 36, 48, 60, 72.
From 1-->80, we have (72-4)/4 +1 =18 numbers divisible by 4.
Therefore, our answer is 18-6 = 12 numbers.
E
Answer: (E) 12
Question: What is the total number of integers between 111 and 222 that are divisible by 9?
(A) 12
(B) 10
(C) 11
(D) 14
(E) 13
Rationale: 117, 126, 135, ..., 207,216
This is an equally spaced list; you can use the formula:
n = (largest - smallest) / ('space') + 1 = (216 - 117) / (9) + 1 = 99/9+ 1 = 11 + 1 = 12
Answer is A
Answer: (A) 12
Question: The price of lunch for 15 people was $211.00, including a 15 percent gratuity for service. What was the average price per person, EXCLUDING the gratuity?
(A)  $11.73
(B)  $12.78
(C)  $13.80
(D)  $14.00
(E)  $15.87
Rationale: Take the initial price before the gratuity is 100
The gratuity is calculated on the final price, so as we assumed the final bill before adding gratuity is 100 so gratuity is 15% of 100 is 15 so the total price of meals is 115 so the given amount i.e 211 is for 115 then we have to calculate for 100
for 115 211
for 100 x
so by cross multiplication we get 115x=100*211 => x=100*211/110 by simplifying we get x as 191.81 which is the price of lunch before gratuity so the gratuity is 19.19 so
as the question ask the average price person excluding gratuity is 191.81/15=12.78 so our answer is B)
Answer: (B)  $12.78
Question: A salesman’s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1400 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 600 more than that by the previous schema, his sales were worth?
(A) 12028
(B) 12000
(C) 20000
(D) 12197
(E) 12012
Rationale: [1400 + (X-4000) * (2.5/100)] - X * (5/100)
= 600
X = 20000
Answer: C
Answer: (C) 20000
Question: 45 men working 8 hours per day dig 30 m deep. How many extra men should be put to dig to a depth of 50 m working 6 hours per day?
(A) 77
(B) 66
(C) 50
(D) 55
(E) 44
Rationale: (45 * 8)/30 = (x * 6)/50 => x =100
100 – 45 = 55
Answer: D
Answer: (D) 55