mathewhe/aqua_rat huggingface dataset:
Question: A man purchases 8 pens for Rs.9 and sells 9 pens for Rs.8, how much profit or loss does he make?
(A) 20.97
(B) 20.98
(C) 90.97
(D) 20.95
(E) 20.91
Rationale: 81 ---- 17
100 ----- ? è
20.98%loss
Answer: Option B
ExplanatiB
Answer: (B) 20.98
Question: In the city of San Durango, 90 people own cats, dogs, or rabbits. If 30 people owned cats, 30 owned dogs, 50 owned rabbits, and 14 owned exactly two of the three types of pet, how many people owned all three?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Total = C + D + R - (CD + DR + CR) - 2CDR
90 = 30 + 30 + 50 - (14) - 2x
x = 3
So, answer will be C
Answer: (C) 3
Question: If the speed of X inch per second is equivalent to the speed of Y foot per hour, what is Y in terms of X? (1 foot =12 inch)
(A) 120X
(B) 240X
(C) 360X
(D) 300X
(E) 100x
Rationale: X inch per second -->
--> 3,600X inch per hour(as there are 3,600 seconds in one hour);
--> 3,600X/12 = 300X foot per hour (as there are 12 inches in one foot).
Answer: D.
Answer: (D) 300X
Question: The two lines y=x and x=-7 intersect on the coordinate plane. What is the value of the area of the figure formed by the intersecting lines and the x-axis?
(A) 18.5
(B) 21.5
(C) 24.5
(D) 27.5
(E) 30.5
Rationale: The point of intersection is (-7,-7).
The triangle has a base of length 7 and a height of 7.
area = (1/2)*base*height = (1/2)*7*7 = 24.5
The answer is C.
Answer: (C) 24.5
Question: Which of the following is between 53/70 and 5/6?
(A) 1/3
(B) 3/8
(C) 1/2
(D) 5/8
(E) 7/9
Rationale: I see this as a POE (Process of Elimination) and Ballparking (Estimation) question. Not sure if this is the most efficient, but it worked:
1) I estimate 53/70 to be ~3/4+ (approximately slightly greater than 3/4)
2) I estimate 5/6 to be ~4/5+ (approximately slightly greater than 4/5)
3) So now I'm looking for an answer choice that is .75 < x < .80
It should be pretty easy to identify which answer choices are less than .75 (or 3/4) if you have had practice with fractions.
A) clearly wrong - it's less than 3/4
B) also clearly wrong - it's less than 3/4
C) also clearly wrong - it's less than 3/4
D) also clearly wrong - it's less than 3/4
I would just stop here and select E. But to verify:
E) 7/9 ~ .77 which is greater than .75 and less than .80
Answer: (E) 7/9
Question: What is the least number should be added to 1056, so the sum of the number is completely divisible by 28?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 8
Rationale: (1056 / 28) gives remainder 20
20 + 8 = 28, So we need to add 8
E
Answer: (E) 8
Question: What will come in place of the question mark (?) in the following question?
112.36 + 225.05 + ? = 815.30
(A) 474.46
(B) 477.89
(C) 524.41
(D) 564.40
(E) None of these
Rationale: Explanation:
815.30 - ( 112.36 + 225.05) = ?
= 477.89
ANSWER: B
Answer: (B) 477.89
Question: An amount of Rs. 65000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 3/4 %, then the amount invested in each share was?
(A) s. 52500; Rs. 47500
(B) s. 40625; Rs. 24375
(C) s. 72500; Rs. 27500
(D) s. 82500; Rs. 17500
(E) s. 72500; Rs. 17500
Rationale: Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (65000 - x). Then,
(x * 9 * 1)/100 + [(65000 - x) * 11 * 1]/100 = (65000 * 39/4 * 1/100)
(9x + 715000 - 11x)/100 = 39000/4 = 12675/2
x = 40625
Sum invested at 9% = Rs. 40625
Sum invested at 11% = Rs. (65000 - 40625) = Rs. 24375.
ANSWER:B
Answer: (B) s. 40625; Rs. 24375
Question: Ajith and Rana walk around a circular course 115 km in circumference, starting together from the same point. If they walk at speed of 4 and 5 kmph respectively, in the same direction, when will they meet ?
(A) after 20 hours
(B) after 115 hours
(C) after 115 minutes
(D) after 20 minutes
(E) after 30 minutes
Rationale: Rana is the faster person. He gains 1 km in 1 hour. So Rana will gain one complete round over
Ajith in 115 hours. i.e. they will meet after 115 hours.
ANSWER:B
Answer: (B) after 115 hours
Question: How much time will take for an amount of Rs. 360 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
(A) 5 years
(B) 6 years
(C) 7 years
(D) 12 years
(E) 15 years
Rationale: Time = (100 * 81) / (360 * 4.5) = 5 years
ANSWER:A
Answer: (A) 5 years
Question: The average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher
(A) 34 Years
(B) 37 Years
(C) 49 Years
(D) 51 Years
(E) 57 Years
Rationale: Total age of students is 32X16 = 512 Years
Total age inclusive of teacher = 33X (16+1) = 561
So, Teacher's age is 561-512 = 49 Yrs
There is a shortcut for these type of problems
Teacher's age is 16+(33X1) = 49 Years
C
Answer: (C) 49 Years
Question: In a family 7 children dont eat spinach, 6 dont eat carrot, 5 dont eat beans, 4 dont eat spinach & carrots, 3 dont eat carrot & beans, 2 dont eat beans & spinach. One doesnt eat all 3. Find the no. of children.
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: do not spinach only=2
do not carrot only=0
do not beans only=1
do not spinach & carrots only=3
do not beans & carrots only=2
do not spinach & beans only=1
do not all three=1
total 10 children(2+0+1+3+2+1+1)
ANSWER:B
Answer: (B) 10
Question: To deliver an order on time, a company has to make 25 parts a day. After making 25 parts per day for 3 days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced. Find how many parts the company made and how many days this took.
(A) 530
(B) 675
(C) 330
(D) 987
(E) 854
Rationale: Let x e the number of days the company worked. Then 25x is the number of parts they planned to make. At the new production rate they made:
3⋅25+(x−3)⋅30=75+30(x−3)
Therefore: 25x=75+30(x−3)−100
25x=75+30x−90−100
190−75=30x−25
115=5x
x=23
So the company worked 23 days and they made 23⋅25+100=675 pieces.
Answer: (B) 675
Question: A boy has six trousers and 13 shirts. In how many different ways can he select a trouser and a shirt?
(A) 238 ways
(B) 87 ways
(C) 66 ways
(D) 78 ways
(E) 121 ways
Rationale: Explanation:
The boy can select one trouser in six ways.
The boy can select one shirt in 13 ways.
The number of ways in which he can select one trouser and one shirt is 6 * 13 = 78 ways.
Answer: D
Answer: (D) 78 ways
Question: A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 45
(B) 60
(C) 75
(D) 90
(E) None
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Hence, total number of notes = 3x = 90.
Answer D
Answer: (D) 90
Question: From a group of boys and girls, 15 girls leave. There are then left 2 boys for each girl. After this, 45 boys leave. There are then 5 girls for each boy. Find the number of girls in the beginning?
(A) 40
(B) 10
(C) 50
(D) 30
(E) 20
Rationale: Let at present there be x boys.
Then, no of girls at present=5x
Before the boys had left: no of boys=x+45
And no of girls=5x
X+45=2*5x
9x=45
x=5
no of girls in the beginning=25+15=40
Answer is A
Answer: (A) 40
Question: The average temperature for Monday, Tuesday, Wednesday and Thursday was 48 degrees and for Tuesday, Wednesday, Thursday and Friday was 46 degrees. If the temperature on Monday was 42 degrees. Find the temperature on Friday?
(A) 65 degrees
(B) 73 degrees
(C) 37 degrees
(D) 34 degrees
(E) 74 degrees
Rationale: M + Tu + W + Th = 4 * 48 = 192
Tu + W + Th + F = 4 * 46 = 184
M = 42
Tu + W + Th = 192 -42 = 150
F = 184 – 150 = 34
Answer:D
Answer: (D) 34 degrees
Question: The perimeter of a triangle is 32 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
(A) 46 cm2
(B) 42 cm2
(C) 29 cm2
(D) 25 cm2
(E) 40 cm2
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 32/2
= 40 cm2
Answer: E
Answer: (E) 40 cm2
Question: If two positive numbers are in the ratio 1/10 : 1/7, then by what percent is the second number more than the first?
(A) 67%.
(B) 42.8%.
(C) 60%.
(D) 68%.
(E) 80%.
Rationale: Given ratio = 1/10 : 1/7 = 7 : 10
Let first number be 7x and the second number be 10x.
The second number is more than first number by 3x.
Required percentage = 3x/7x * 100 = 42.8%.
Answer: B
Answer: (B) 42.8%.
Question: How many integers between 100 and 180, inclusive, cannot be evenly divided by 3 nor 5?
(A) 39
(B) 41
(C) 43
(D) 45
(E) 47
Rationale: The total numbers between 100 and 180, inclusive, is 81.
3*34=102 and 3*60=180 so the number of multiples of 3 is 27.
5*20=100 and 5*36=180 so the number of multiples of 5 is 17.
However, the multiples of 15 have been counted twice.
15*7=105 and 15*12=180 so the number of multiples of 15 is 6.
Thus the total number is 81-27-17+6=43.
The answer is C.
Answer: (C) 43
Question: Two digits number is divided by the product of their digit and the result is 3.now 18 is added to the number the digit will be inter changed. what is the number.
(A) 16
(B) 18
(C) 20
(D) 22
(E) 24
Rationale: Let tenth digit of the number is X and Unit digit of that number is Y, Then the number will be (10X +Y).
Now According to question,
(10X +Y)/XY = 3
(10X +Y) = 3XY --------------------------- (1)
And,
10X +Y +18 = 10Y +X
Y -X = 2 ------------------------------------ (2)
Y = 2 +X ------------------------------ (3)
On solving all the equations, we get number is 24.
answer : E
Answer: (E) 24
Question: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is
(A) 5/9
(B) 5/12
(C) 1/36
(D) 7/12
(E) 4/9
Rationale: Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9) = 5/12
ANSWER:B
Answer: (B) 5/12
Question: Two persons start running simultaneously around a circular track of length 300 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
(A) 11
(B) 10
(C) 28
(D) 27
(E) 12
Rationale: Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 300 / (15 + 25)5/18 = 300* 18 / 40 * 5 = 27 seconds.
Answer: D
Answer: (D) 27
Question: Two employees X and Y are paid a total of Rs. 800 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
(A) s.200.63
(B) s.250.63
(C) s.290.63
(D) s.300.63
(E) s.363.63
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 800
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 800
⇒ y[12/10 + 1] = 800
⇒ 22y/10 = 800
⇒ 22y = 8000
⇒ y = 8000/22 =Rs.363.63
E)
Answer: (E) s.363.63
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?
(A) 399
(B) 267
(C) 350
(D) 788
(E) 277
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) 350
Question: How many ltrs of water must beadded to 16ltrs of milk and water containing 10% water to make it 20% water in it?
(A) 1 liter
(B) 2 liter
(C) 3 liter
(D) 5 liter
(E) 7 liter
Rationale: By rule of alligation,
% Concentration
of water in pure water (100) % Concentration
of water in the given mixture (10)
Mean % concentration
(20)
20 - 10 = 10 100 - 20 = 80
=> Quantity of water : Quantity of the mixture = 10 : 80 = 1 : 8
Here quantity of the mixture = 16 litres
=> Quantity of water : 16 = 1 : 8
=> Quantity of water =16×18=2 liter
B
Answer: (B) 2 liter
Question: If log12 27 = a, then log6 16 is:
(A) (3-a)/4(3+a)
(B) (3+a)/4(3-a)
(C) 4(3+a)/(3-a)
(D) 4(3-a)/(3+a)
(E) 5(3-a)/(3+a)
Rationale: log12 27 = a => log 27/ log 12 = a
=> log 33 / log (3 * 22) =a
=> 3 log 3 / log 3 + 2 log 2 = a => (log 3 + 2 log 2)/ 3 log 3 = 1/a
=> (log 3/ 3 log 3) + (2 log 2/ 3 log 3) = 1/3
=> (2 log 2)/ (3 log 3) = 1/a – 1/3 = (3-a)/ 3a
=> log 2/ log 3= (3-a)/3a => log 3 = (2a/3-a)log2
log16 16 = log 16/ log 6 = log 24/ log (2*3) = 4 log 2/ (log 2 + log 3)
= 4(3-a)/ (3+a)
ANSWER:D
Answer: (D) 4(3-a)/(3+a)
Question: The average age of a class of 12 students is 19 years. The average increased by 2 when the teacher's age also included. What is the age of the teacher?
(A) 40 years
(B) 34 years
(C) 42 years
(D) 43 years
(E) 44 years
Rationale: If age of the teacher was 12, average would not have changed.
Since average increased by 2,
Age of the teacher=12+22×1=34
ANSWER:B
Answer: (B) 34 years
Question: A car is traveling 75 kilometers per hour. How many meters does the car travel in one minute?
(A) 1250m/min
(B) 1360m/min
(C) 2560m/min
(D) 1670m/min
(E) 1890m/min
Rationale: Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify
75 kilometers per hour = 75 km/hr
= (75 × 1000 meters) / (60 minutes) = 1,250 meters / minute
correct answer is A)1250m/min
Answer: (A) 1250m/min
Question: For how many prime pairs (p, q) does there exist an integer n such that
(p2 + 1)*(q2 + 1) = n2 + 1 ?
(A) 2
(B) 4
(C) 6
(D) 8
(E) infinitely many
Rationale: First, we show that one of p and q is 2. If both p and q are odd, then n2 + 1 = (p2 + 1)(q2 + 1)
is even so that n is also odd. Hence, there is an integer t such that n = 2t + 1 so that n2 + 1 =
4t2+4t+2. But this means n2+1 is not divisible by 4 whereas (p2+1)(q2+1) clearly is. Thus, we
must have one of p or q is 2. We now have n2 + 1 = 5(x2 + 1) where either x = p or x = q. Note
that x 3. We deduce that 5x2 = n2 − 4 = (n − 2)(n + 2). Since x is prime and n + 2 > n − 2,
we obtain that n−2 2 {1, 5, x} and n+2 = 5x2/(n−2). Since also (n+2)−(n−2) = 4, we get
that one of 5x2 − 1, x2 − 5 and 4x equals 4. As x is prime, we obtain x = 3. Thus, (p, q) = (2, 3)
or (3, 2). Each pair gives a solution to the equation n2+1 = (p2+1)(q2+1), implying the answer.
correct answer A
Answer: (A) 2
Question: Each shelf of a bookcase contained 11 books. If the librarian took out 30 books and rearranged the remaining books so that all shelves but the last one contained 7 books and that last shelf contained 5 books, how many shelves does the bookcase have?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Let x be the number of shelves.
11x - 30 = 7(x-1) + 5
4x = 28
x = 7
The answer is C.
Answer: (C) 7
Question: If k and y are integers, then ky(k + y) is
(A) Always positive
(B) Always negative
(C) Positive when k is positive
(D) Negative when k is negative
(E) It cannot be determined by the information given
Rationale: Given k and y are integers, then ky(k + y)
Let's take even as 2 / -2 and odd as 3 / -3..we get the following.. and IMO option D is correct answer..
I presume its Option E if am not missing anything.
k=-3 and y=1
ky(k + y) is positive = 6
Answer: (E) It cannot be determined by the information given
Question: There are 6 boxes numbered 1, 2,...6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is
(A)  5
(B)  21
(C)  33
(D)  60
(E)  40
Rationale: Given the constraints of this question, we have to consider 6 possible outcomes...
1 green ball: 6 options
GRRRRR
RGRRRR
RRGRRR
RRRGRR
RRRRGR
RRRRRG
2 green balls: 5 options
GGRRRR
RGGRRR
RRGGRR
RRRGGR
RRRRGG
3 green balls: 4 options
GGGRRR
RGGGRR
RRGGGR
RRRGGG
4 green balls: 3 options
GGGGRR
RGGGGR
RRGGGG
5 green balls: 2 options
GGGGGR
RGGGGG
6 green balls: 1 option
GGGGGG
6+5+4+3+2+1 = 21 options.
B
Answer: (B)  21
Question: If (18^a) * 9^(3a – 1)= (2^3)(3^b) and a and b are positive integers, what is the value of a?
(A) 22
(B) 11
(C) 9
(D) 6
(E) 3
Rationale: 18^a) * 9^(3a – 1)= (2^3)(3^b)
= 2^a . 9^a . 9^(3a – 1) = (2^3)(3^b)
Just compare powers of 2 from both sides (no need to calculate powers of 3, 9 as value of b is not asked)
Answer = 3
ANSWER:E
Answer: (E) 3
Question: A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A?
(A) 120
(B) 180
(C) 200
(D) 280
(E) 300
Rationale: 80* 7: x* 3 = 1:1 1/2
560: 3x = 2: 3
x = 280
ANSWER:D
Answer: (D) 280
Question: If 40% of a number is equal to 2/3 of another number, what is the ratio of first number to the second number?
(A) 5/3
(B) 3/5
(C) 3/7
(D) 5/7
(E) 7/9
Rationale: Let 40% of A = 2/3 B
Then, 40*A/100 = 2 *B /3
A/B = 5/3
Ans- A
Answer: (A) 5/3
Question: If n is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
.
(A) √n + 1
(B) n + 1
(C) n^2 + 1
(D) n + 2√n + 1
(E) n^2 + 2n + 1
Rationale: Let a= +ve integer such that
n= a^2
(a+1)= next +ve integer
(a+1)^2 = a^2 + 1 + 2a
and a=n^(1/2)
Therefore ,
(a+1)^2=n+1+2*n^(1/2)
Answer D
Answer: (D) n + 2√n + 1
Question: A bag contains 5 red, 6 blue and 4 green balls. If 2 ballsare picked at random, what is the probability that both are red?
(A) 2/15
(B) 2/21
(C) 5/26
(D) 3/29
(E) 4/27
Rationale: P(Both are red),
=5C215C2=5C215C2
=10/105=2/21
B
Answer: (B) 2/21
Question: For a certain set of numbers, if x is in the set, then x - 2 is also in the set. If the number 1 is in the set , which of the following must also be in the set ?
a) -4
b) -1
c) -5
(A) a only,
(B) b only,
(C) c only,
(D) a and b only
(E) b and c only
Rationale: Notice that the question asks which of the following MUST be in the set, not COULD be in the set.
Since 1 is in the set, then so must be 1-2=-1. Similarly, since -1 is in the set, then so must be -1-3=-4. Could 4 and -1 be in the set? Certainly, but we don't know that for sure.
Answer: D.
Regarding your question: we don't know which is the source integer in the set, if it's 1, then 4 won't be in the set but if the source integer is say 7, then 4 will be in the set. So, 4 may or may not be in the set.
Answer: (D) a and b only
Question: Excluding stoppages, the speed of a bus is 64 kmph and including stoppages, it is 50 kmph. For how many minutes does the bus stop per hour?
(A) 15.5
(B) 12.3
(C) 10.5
(D) 10.12
(E) 13.12
Rationale: Due to stoppages, it covers 14 km less.
Time taken to cover 14 km = ((14/64)Ã—60) = 13.12 min.
Option(E) is correct
Answer: (E) 13.12
Question: A rectangular field 30 m long and 20 m broad. How much deep it should be dug so that from the earth taken out, a platform can be formed which is 8 m long, 5.5 m broad and 1.5 m high where as the earth taken out is increase by 10/5?
(A) 37 cm
(B) 10 cm
(C) 17 cm
(D) 88 cm
(E) 87 cm
Rationale: 30 * 20 * x = (8 * 5.5 * 1.5)/2
\Answer:B
Answer: (B) 10 cm
Question: If the price of a certain computer increased 30 percent from d dollars to 351 dollars, then 2d =
(A) 540
(B) 570
(C) 619
(D) 649
(E) 700
Rationale: Before Price increase Price = d
After 30% Price increase Price = d+(30/100)*D = 1.3d = 351 (Given)
i.e. d = 351/1.3 = $270
i.e. 2d = 2*270 = 540
Answer: option A
Answer: (A) 540
Question: A certain drink of type A is prepared by mixing 4 parts milk with 3 parts fruit juice. Another drink of type B is prepared by mixing 4 parts of fruit juice and 3 parts of milk. How many liters of fruit juice must be added to 21 liters of drink A to convert it to drink B?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: In 21 liters of drink A, there are 12 liters of milk and 9 liters of juice.
With 12 liters of milk, we need a total of 16 liters of juice to make drink B.
We need to add 7 liters of juice.
The answer is E.
Answer: (E) 7
Question: A is half good a work man as B and together they finish a job in 10 days. In how many days working alone B finish the job?
(A) 98 days
(B) 21 days
(C) 17 days
(D) 18 days
(E) 15 days
Rationale: WC = 1:2
2x + x = 1/10 => x = 1/30
2x = 1/30 => 15 days
Answer:E
Answer: (E) 15 days
Question: If a town of 35,000 people is growing at a rate of approx. 1% per year, the population of the town in 5 years will be closest to?
(A) a.36000
(B) b.37000
(C) c.38000
(D) d.39000
(E) e.40000
Rationale: 1% is quite small and hence the answer is A)
Answer: (A) a.36000
Question: We have a rectangular metallic piece of paper that covers exactly the area of a cube. The length of the piece of paper is 120 inches and the width is 108 inches. What is the volume of the cube in cubic feet is 1 feet is 12 inches?
(A) a 125
(B) b 120
(C) c 70
(D) d 40
(E) e 10
Rationale: l = 120 /12 = 10 ft
w = 108 / 12 = 9 ft
Area of paper = 90
Area of cube = 10 * side^2
side of cube = 5
V of cube = 125
Answer: (A) a 125
Question: A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 10% less than the price each head sold for the day before.what was the gross profit Q on this shipment?
(A) a) $100
(B) b) $115
(C) c) $125
(D) d) $130
(E) e) $135
Rationale: I recommend one should use fractions to solve this one rather than converting it into decimals
Sol:
1500 heads -> $600
1 head -> $600/1500
1 head -> $(2/5)
25% more of (2/5) -> 125/100 * 2/5 = $(1/2)
He sold 2/3*1500 = 1000 heads for $(1/2) per head
Total revenue by selling 1000 heads = 1000 * 1/2 = $500
Heads left: 500
Cost per head: 90% of the previous price: 90/100 * 1/2 = $(9/20)
Total revenue by selling 500 heads = 9/20 * 500 = 225
Total revenue after selling 1500 cabbage heads - 225+500 = $725
Money spent on the purchase: $600
Profit Q= 725-600 = $125
Ans:C
Answer: (C) c) $125
Question: Two unbiased coins are tossed. What is the probability of getting two heads?
(A) 1/2
(B) 1/4
(C) 2/3
(D) 1/5
(E) 2/7
Rationale: S = {HH, HT, TH, TT}
E = event of getting 2 heads
E = {TT}
P(E) = 1/4
Answer is B
Answer: (B) 1/4
Question: If r is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of r ?
(A)  10
(B)  12
(C)  14
(D)  16
(E)  18
Rationale: Answer is C.
numbers in format of 3^k in the series from 1 to 30 inclusive r are: 3*1, 3*2, 3*3, 3*4, 3*5, 3*3*2, 3*7, 3*8, 3*3*3, 3*10. Total number of 3 = 13. So k=14.
Answer: (C)  14
Question: What is the total cost of 2 sandwiches at $2.45 each and 4 sodas at $0.87 each?
(A) $8.38
(B) $6.85
(C) $8.46
(D) $10.08
(E) $11.85
Rationale: Answer = A
2 * 2.45 + 4 * 0.87
= 2 (2.50 - 0.05) + 4 (1.00 - 0.13)
= 5 + 4 - 0.1 - 0.52
= 9 - 0.62
= 8.38
Answer: (A) $8.38
Question: A,B,C can complete a piece of work in 3,9and 15 days respectively. Working together, they will complete the same work in how many days?
(A) 45/23
(B) 55/23
(C) 61/57
(D) 12/13
(E) 22/23
Rationale: (A+B+C)'s 1day work = (1/3)+(1/9)+(1/115) = 23/45
A,B,C together will complete the work in 45/23 days
Answer is A
Answer: (A) 45/23
Question: A person got Rs.48 more when he invested a certain sum at compound interest instead of simple interest for two years at 8% p.a. Find the sum?
(A) Rs.7500
(B) Rs.7503
(C) Rs.7227
(D) Rs.7528
(E) Rs.1281
Rationale: Explanation:
P = (d * 1002) / R2
=> (48 * 100 * 100) / 8 * 8 = Rs.7500
Answer: A
Answer: (A) Rs.7500
Question: What is the remainder when the number T=14^2 * 15^8 is divided by 5?
(A) 0
(B) 1
(C) 2
(D) 4
(E) 5
Rationale: 14^2 has units digit 6
15^8 has units digit 5
Thus T=14^2*15^8 has units digit 0 and will be divisible by 5. The remainder will be zero
Answer: (A)
Answer: (A) 0
Question: How many 2 digit number contain number 3 ?
(A) 18
(B) 28
(C) 38
(D) 68
(E) 58
Rationale: total 2 digit no. = 9*10* = 90
not containing 3 = 8*9 = 72
total 2 digit number contain 3 = 90 - 72 = 18
ANSWER:A
Answer: (A) 18
Question: Half a number plus 6 is 11.What is the number?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Let x be the number. Always replace "is" with an equal sign
(1/2)x + 6 = 11
(1/2)x = 11 - 6
(1/2)x = 5
x = 10
correct answer is C
Answer: (C) 10