mathewhe/aqua_rat huggingface dataset:
Question: In a village of 2,700 people, 900 people are over 70 years old and 1200 people are female. It is known that 60 percent of the females are younger than 70 years old. If no one in the village is 70 years old, what is the probability that a person chosen at random is either a male or younger than 70 years old?
(A) 4/5
(B) 5/7
(C) 13/15
(D) 37/45
(E) 79/90
Rationale: The number of people younger than 70 years old is 2700-900 = 1800
The number of females older than 70 years old is 0.4*1200 = 480
The number of males older than 70 years old is 900-480 = 420
The number of people who are either male or younger than 70 is 1800+420 = 2220.
P(a person is younger than 70 or male) = 2220/2700 = 37/45
The answer is D.
Answer: (D) 37/45
Question: There are 2 sections A and B in a class, consisting of 60 and 70 students respectively. If the average weight of section A is 60kg and that of section B is 80kg, Find the average of the whole class?
(A) 50.78kg
(B) 49.32kg
(C) 70.76kg
(D) 69.15kg
(E) 70.89kg
Rationale: Total weight of 60+70 students = 60*60 + 70*80 = 3600+5600
Average weight of the class is = 9200/130 = 70.76 kg
Answer is C
Answer: (C) 70.76kg
Question: A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 65 Kmph
(B) 70 Kmph
(C) 72 Kmph
(D) 75 Kmph
(E) 78 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 400/20
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph
ANSWER:C
Answer: (C) 72 Kmph
Question: Henry answered 3/5 of the questions he was given for homework in the first hour, 5/17 of the remaining questions in the second hour and the remaining x questions in the third hour where x is an integer. How many questions was Henry given for homework?
(A) x
(B) (85/12)*x
(C) (85/24)*x
(D) (85/36)*x
(E) (85/48)*x
Rationale: Let Q be the number of homework questions.
Q = 3Q/5 + (5/17)(2Q/5) + x
Q = 51Q/85 + 10Q/85 + x
24Q/85 = x
Q = (85/24)*x
The answer is C.
Answer: (C) (85/24)*x
Question: If the population of a certain country increases at the rate of 10 person every 60 seconds, by how many persons does the population increase in 1 hour?
(A) 100
(B) 200
(C) 600
(D) 800
(E) 1000
Rationale: Answer = 10 * 60(1 hour = 60 minutes)= 600
Answer = C
Answer: (C) 600
Question: 252 can be expressed as a product of prime as
(A) 2 x 2 x 3 x 3 x 7
(B) 2 x 2 x 2 x 3 x 7
(C) 3 x 3 x 3 x 3 x 7
(D) 2 x 3 x 3 x 3 x 7
(E) None
Rationale: Solution
Clearly, 252 =2 x 2 x 3 x 3 x 7
Answer A
Answer: (A) 2 x 2 x 3 x 3 x 7
Question: In a T.V. factory, an average of 62 TVs are produced per day for the fist 25 days of the months. A few workers fell ill for the next five days reducing the daily avg for the month to 58 sets/day . The average production per day for day last 5 days is ?
(A) 35
(B) 38
(C) 48
(D) 50
(E) 52
Rationale: Production during these 5 days = Total production in a month - production in first 25 days.
= 30 x 58 - 25 x 62
= 19
âˆ´ Average for last 5 days = 190 / 5
= 38
B
Answer: (B) 38
Question: There are three departments having students 70,58,24 .In an exam they have to be seated in rooms such that each room has equal number of students and each room has students of one type only (No mixing of departments). Find the minimum number of rooms required?
(A) 73
(B) 74
(C) 75
(D) 76
(E) 77
Rationale: WE NEED TO TAKE GCD WHICH IS 2
THUS ALL THE ROOMS WILL HAVE 2 STUDENTS OF THE SAME DEPT
1) 70/2 = 35
2) 58/2 = 29
3) 24/2 = 12
TOTAL NO. OF MIN ROOMS REQD = 35+12+29 = 76
ANSWER:D
Answer: (D) 76
Question: The cost of 16 apples and 8 mangos is $352 and the cost of 4 apples and 4 mangos is $96. Find the cost of each apple?
(A) 40
(B) 20
(C) 30
(D) 35
(E) 28
Rationale: B
20
Let the cost of each apple and mango be 'p' and 'q' respectively.
16p + 8q = 352 --- (1)
4p + 4q = 96
8p + 8q = 192 --- (2)
(1) - (2) => 8p = 160
=> p = 20
Answer: (B) 20
Question: If 0.4 of a number is equal to 0.06 of another number, the ratio of the numbers i
(A) 2 : 3
(B) 3 : 4
(C) 3 : 20
(D) 20 : 3
(E) None
Rationale: Sol.
0.4A = 0.06 B ⇔ A / B = 0.06 / 0.40 = 6/40 = 3/20.
∴ A : B = 3 : 20.
Answer C
Answer: (C) 3 : 20
Question: Population of a city in 20004 was 1000000. If in 2005 there isan increment of 10% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007
(A) 976374
(B) 979923
(C) 980241
(D) 1036750
(E) 1083875
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 10/100)(1 - 35/100)(1 + 45/100)
= 1036750
D
Answer: (D) 1036750
Question: List all the even integers between 1 and 11. Find the lowest positive interger that can be divided by each of those numbers.
(A) 120
(B) 234
(C) 231
(D) 183
(E) 123
Rationale: The even numbers between 1 and 11 are 2,4,6,8,10,
To get the least positive integer that can be divided by each of these numbers 1,2,3,4,5,6,7,8,9,10 you calculate the lowest common denominator of all the numbers. Express each number as a product of their prime factors and multiply the set of prime numbers from each set with the highest exponent value.
LCM=2^3*3*5
The answer is A)
Answer: (A) 120
Question: jerry and Michelle play a card game. In the beginning of the game they have an equal number of cards. Each player, at her turn, gives the other a third of her cards. Michelle plays first, giving jerry a third of her cards. jerry plays next, and Michelle follows. Then the game ends. jerry ended up with 14 more cards than Michelle. How many cards did each player have originally?
(A) 27
(B) 30
(C) 34
(D) 36
(E) 38
Rationale: Game Michelle Jerry michelle
Initially 2727 assume
After game 1 1836
After game 2 3024
After game 3 2034
Now jerry has 14 cards more than Michelle.
So the answer is A
Answer: (A) 27
Question: Using all the letters of the word "ANOTHER", how many words can be formed, which begin with A and end with R?
(A) 80
(B) 90
(C) 110
(D) 120
(E) 100
Rationale: There are seven letters in the given word.
Consider 7 blanks ....
The first blank and last blank must be filled with A and R all the remaining five blanks can be filled with the remaining 5 letters in 5! ways.
The number of words = 5! = 120.
ANSWER:D
Answer: (D) 120
Question: In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. What is the length of the garden?
(A) 22
(B) 24
(C) 26
(D) 28
(E) 30
Rationale: Between the 12 mango trees, there are 11 gaps and each gap has 2 meter length
Also, 1 meter is left from all sides of the boundary of the garden.
Hence, length of the garden = (11 × 2) + 1 + 1 = 24 meter
Answer is B.
Answer: (B) 24
Question: If (1+a)b=b, which of the following must be true?
(A) a=-1 or b=0
(B) a=0 or b=0
(C) a=1 or b=1
(D) a=-1 or b=-1
(E) a=0 or b=1
Rationale: By only having ab=0, we cannot say answer is B as A and E options also satisfy the condition ab=0. ans B
Answer: (B) a=0 or b=0
Question: Each month a retailer sells 100 identical items. On each item he makes a profit of $30 that constitutes 16% of the item's price to the retailer. If the retailer contemplates giving a 5% discount on the items he sells, what is the least number of items he will have to sell each month to justify the policy of the discount?
(A) 157
(B) 213
(C) 221
(D) 223
(E) 226
Rationale: For this question, we'll need the following formula:
Sell Price = Cost + Profit
We're told that the profit on 1 item is $20 and that this represents 16% of the cost:
Sell Price = Cost + $20
Sell Price = $125 + $20
Thus, the Sell Price is $145 for each item. Selling all 100 items gives the retailer...
100($20) = $2,000 of profit
If the retailer offers a 5% discount on the sell price, then the equation changes...
5%(145) = $7.25 discount
$137.75 = $125 + $12.75
Now, the retailer makes a profit of just $12.75 per item sold.
To earn $2,000 in profit, the retailer must sell....
$12.75(X) = $2,000
X = 2,000/12.75
X = 156.8627 =157 items
A
Answer: (A) 157
Question: A bag has 1, 3, 5, 7, 9,11 and 13 cm sticks. Find the probability that they they will form a triangle if 3
sticks are drawn?
(A) 13 / 35
(B) 14 / 35
(C) 1 / 2
(D) 5 / 6
(E) 5 / 5
Rationale: Explanation :
Total Cases: =7C3=35
Favourable Cases: (3,5,7),(3,7,9),(3,9,11),(3,11,13),(5,7,9),(5,7,11),(5,9,11),(5,9,13),(5,11,13),
(7,9,11),(7,9,13),(7,11,13),(9,11,13)=total 13.
[Others are rejected because to form a triangle it is necessary that the sum of 2 small
sides must be greater than the third greatest side.]
Hence (A) is correct answer.
Answer : A
Answer: (A) 13 / 35
Question: Dacid obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
(A) 67
(B) 26
(C) 87
(D) 26
(E) 75
Rationale: Average
= (76 + 65 + 82 + 67 + 85)/5
= 375/5 = 75.
Answer: E
Answer: (E) 75
Question: If the probability that the NY Giants win the Super Bowl is 1/12 and the probability that the NY Mets win the World Series is 1/15, what is the probability that either the NY Giants win the Super Bowl or the NY Mets win the World Series (but not both)?
(A) 1/18
(B) 5/36
(C) 7/48
(D) 11/72
(E) 17/120
Rationale: 11/12*1/15 + 1/12*14/15 = 25/180 = 5/36
The answer is B.
Answer: (B) 5/36
Question: If n is a positive integer and n^3 is a multiple of 550, what is the least possible value of n?
(A) 8
(B) 27
(C) 81
(D) 110
(E) 125
Rationale: cube of a number entails having 3 copies of the original prime factors. Since 550 is a factor of n^3 the least possible value of n is 5(11)2 = 110
the answer is D.
Answer: (D) 110
Question: Two containers of milk contain mixtures of water and milk in ratio 5:4 and 7:9. In what ratio they should be mixed so that mixture is of 6:6 ratio?
(A) 6:5
(B) 7:5
(C) 9:8
(D) 8:9
(E) 8:7
Rationale: 6/6-5/4==>-1/4
7/9-6/6==>-2/9
now, -1/4=-2/9==>1/4=2/9==>9:8
ANSWER:C
Answer: (C) 9:8
Question: A team won 50 percent of its first 60 games in a particular season, and 80 percent of its remaining games. If the team won a total of 70 percent of its games that season, what was the total number of games that the team played?
(A) 75
(B) 90
(C) 120
(D) 150
(E) 180
Rationale: 70% is 20%-points above 50% and 10%-points below 80%.
Thus the ratio of "the first 60 games" to "remaining games" is 1:2.
So the team played a total of 60+120 = 180 games.
The answer is E.
Answer: (E) 180
Question: If a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster, he would have covered 50 more miles than he actually did. How many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that day?
(A)  100
(B)  120
(C)  140
(D)  150
(E)  160
Rationale: Case 1:
let rate = R, Time = T, and Distance =D
so D=RT
Case 2:
(D+50)=(R+5)(T+1)
Case 3:
(D+X)=(R+10)(T+2)
X=100
Ans A
Answer: (A)  100
Question: Angela’s grade was in the 90th percentile out of 80 grades in her class. In another class of 100 students there were 19 grades higher than Angela’s. If nobody had Angela’s grade, then Angela was what percentile of the two classes combined?
(A) 72
(B) 80
(C) 81
(D) 85
(E) 92
Rationale: If someone's grade is in xth percentile of the nn grades, this means that xx of people out of nn has the grades less than this person.
Being in 90th percentile out of 80 grades means Angela outscored 80∗0.9=7280∗0.9=72 classmates.
In another class she would outscored 100−19=8 students (note: Angela herself is not in this class).
So, in combined classes she outscored 72+81=153. As there are total of 80+100=180 students, so Angela is in 153/180=0.85=85, or in 85th percentile.
Answer: D.
Answer: (D) 85
Question: Find the number of square tiles to cover the floor of a room measuring 4.25 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?
(A) 478
(B) 476
(C) 472
(D) 471
(E) 510
Rationale: 3 3/4 * 8 1/2 = 1/4 * 1/4 * x => x
= 510
Answer:E
Answer: (E) 510
Question: Jeremy needs to choose three flowers for his mother from a group of 10 roses, six of which are red and four of which are white. What is the ratio of the number of ways in which he can select only red roses to the number of ways in which he can select only white roses?
(A) 30:1
(B) 10:1
(C) 5:1
(D) 3:2
(E) 1:5
Rationale: you are given 10 roses out of which 6 are red and 4 are white.
Ways of selecting 3 red roses only out of 6 available = 6C3 = 6!/(3!*3!)
Similarly, Ways of selecting 3 white roses only out of 4 available = 4C3 = 4!/(3!*1!)
Thus the ratio = 6C3/4C3 = 5:1
C is the correct answer.
Answer: (C) 5:1
Question: Yane and Thomas are among the 8 people from which a committee of 4 people is to be selected. How many different possible committees of 4 people can be selected from these 8 people if at least one of either Yane or Thomas is to be selected?
(A) 28
(B) 46
(C) 55
(D) 63
(E) 70
Rationale: Ans:C
Solution:
Y+T+6 = total 8 ,
we need to select at least one of the Y and T or both= total 4 out of 8 - 4 out of 6
8C4 - 6C4
=55
Answer: (C) 55
Question: The length of a rectangulat plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 5300, what is the length of the plot in metres?
(A) 40
(B) 50
(C) 200
(D) 120
(E) None
Rationale: Solution
Let breadth = x metres
Then, length = (x + 20)metres.
Perimeter	= (5300 / 26.50) m
= 200m
Answer C
Answer: (C) 200
Question: If two positive numbers are in the ratio 1/8 : 1/5, then by what percent is the second number more than the first?
(A) 67%
(B) 70%
(C) 60%
(D) 62%
(E) 65%
Rationale: Given ratio
= 1/8 : 1/5 = 5 : 8
Let first number be 5x and the second number be 8x.
The second number is more than first number by 3x.
Required percentage
= 3x/5x * 100 = 60%.
Answer:C
Answer: (C) 60%
Question: A shopkeeper sold an article offering a discount of 5% and earned a profit of 20.65%. What would have been the percentage of profit earned if no discount was offered?
(A) 60%
(B) 27%
(C) 30%
(D) 56%
(E) 73%
Rationale: Let C.P. be Rs. 100.
Then, S.P. = Rs. 120.65
Let marked price be Rs. x. Then, 95/100 x = 120.65
x = 12065/95 = Rs. 127
Now, S.P. = Rs. 127, C.P. = Rs. 100
Profit % =27%.
Answer: B
Answer: (B) 27%
Question: At a dinner party 4 people are to be seated around a circular table. Two sitting arrangements are considered different only when the positions of the people are different relative to each other.What is the total number of possible sitting arrangements or the group?
(A) 6
(B) 10
(C) 24
(D) 32
(E) 120
Rationale: Hi there,
You can treat this as an ordering question except thatfor a circular arrangement you need to divide by the number of spaces.So in this case:
4!/4=6
If you spin the circle to right, that doesn't count as a new arrangement. Dividing by the number of spaces takes that into consideration.
Happy Studies,
HG.
A
Answer: (A) 6
Question: Anna worked for h hours each day for d consecutive days. If she earns $3.50 per hour, what is the total amount she earned?
(A) 3.50/d + h
(B) 3.50 + d + h
(C) 3.50 + dh
(D) 3.50h + d
(E) 3.50dh
Rationale: H hours for d days.
Income each day = 3.5*h
Total income = 3.5*h*d
Correct option: E
Answer: (E) 3.50dh
Question: The probability of a team winning a match given Matt is playing the match is 0.65. The probability of the team winning a match given Matt is not playing the match is 0.5. The probability of Matt playing any match is 0.8.
If it is known that the team has won the last match, what is the probability that Matt played the match?
(A) 0.8321
(B) 0.7
(C) 0.8571
(D) 0.7531
(E) 0.8387
Rationale: Out of 100 matches:
Matt is plays in 80 and not plays in 20.
Out of 80 matches Matt plays in, team wins 0.65*80 = 52.
Out of 20 matches Matt does not play in, team wins 0.5*20 = 10.
So, out of 100 matches 52 + 10 = 62 are won.
It is known that the team has won the last match. Out of 62 matches won, Matt is in 52: 52/62 = 0.8387...
Answer: E.
Answer: (E) 0.8387
Question: A dress on sale in a shop is marked at $X. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on thediscounted price. If a staff member buysthe dress what will she have to pay in terms of X?
(A) 0.560X
(B) 0.560X
(C) 0.765X
(D) 0.608X
(E) 0.895X
Rationale: If the price is reduced by 15 %, then the new price will be 0.85D
If this new price is further reduced by 10%, the discounted price will be 0.9 x 0.85X = 0.765X
C
Answer: (C) 0.765X
Question: A password consists of two letters of the alphabet followed by three digits chosen from 0 to 9. Repeats are allowed. How many different possible passwords are there?
(A) 492,804
(B) 650,000
(C) 676,000
(D) 1,757,600
(E) 757,600
Rationale: 26*26*10*10*10=676000
ANSWER:C
Answer: (C) 676,000
Question: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer Q that must divide n is?
(A) 6
(B) 12
(C) 24
(D) 36
(E) 48
Rationale: Q: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer Q that must divide n is:
A 6, B 12, C 24, D 36, E 48
n^2 is divisible by 72, but it must also be greater than 72. If n is an integer, then n^2 must be a perfect square. The factorization of 72 is (8)(9), so if it is multiplied by 2, it will be (2)(8)(9) = (16)(9) = 144, a perfect square. So n^2 must be at least 144 or a multiple of 144, which means that n must be 12 or a multiple of 12.B
Answer: (B) 12
Question: If 0 < x ≤ 6, then which one of the following is the maximum value of (x – 1)^2 + x ?
(A) –2
(B) –1
(C) 0
(D) 31
(E) 2
Rationale: the maximum value of (x – 1)^2 + x for 0 < x ≤ 6 is when x=6 --> (x – 1)^2 + x = 31
Answer: D.
Answer: (D) 31
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 16 sec
(B) 15 sec
(C) 48 sec
(D) 44 sec
(E) 21 sec
Rationale: Relative speed = 45 + 30
= 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 500 + 500
= 1000 m.
Required time = 1000 * 6/125
= 48 sec.
Answer:C
Answer: (C) 48 sec
Question: Machines P and Q are two different machines that make items in a factory. When Machine P works alone, it covers 15 items in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 15 items in n hours. In terms of m and n, how many hours does it take Machine Q, working alone at its constant rate, to cover 15item?
(A) m
(B) n
(C) 15n/225-mn
(D) m+n
(E) m-n
Rationale: working rate p = 15/m ; working rate pq =( 1/p +1/q)* n =15 or mn/15 +n/q =15 0r n/q = 15-mn/15 = 225-mn/15
q = 15n/225-mn
C
Answer: (C) 15n/225-mn
Question: There are 100 freshmen at a particular college, all of whom must take at least one of the three core classes: Art, Biology, and Calculus. Of these freshmen, 9 take only Biology, 10 take only Calculus, 5 take all three classes, and 20 take Art and exactly one of the other two core classes. If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art, how many freshmen take Art?
(A) 25
(B) 32
(C) 36
(D) 48
(E) 67
Rationale: Make a venn diagram to get a clear picture. Look at the diagram:
Each letter represents only one color. b represents the people who take only Art. d represents people who take only Art and Bio etc.
d + f = 20 (People who take Art and one other class)
b = 3e (people who take only Art is 3 times the people who take Bio and Calculus)
9 + 10 + 5 + b + d + e + f = 100 (Total people)
b + b/3 = 56
b = 42
Number of freshmen who take Art = 42 + 20 + 5 = 67
Answer E
Answer: (E) 67
Question: A and B started business in partnership investing Rs. 18,000 and Rs. 16,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
(A) A)7500
(B) B)7389
(C) C)7379
(D) D)7453
(E) E)7653
Rationale: A:B:C = (18000 * 24) : (16000 * 24) : (20000 * 18) = 18:16:15
B's share = 25000 *15/49 = Rs.7653
Answer: E
Answer: (E) E)7653
Question: Four-ninths of a drink mix is dye and the rest is sugar. When the mix is added to water a gallon of drink is made that is 9% sugar. What percentage of the gallon is dye?
(A)  6
(B)  6.5
(C)  7.2
(D)  8
(E)  24
Rationale: The proportion of Dye and sugar will remain constant.
Dye/Sugar = (4/9)/(5/9) = x/9
=> 4/5 = x/9 => x = 4*9/5 = 7.2.
Answer is C.
Answer: (C)  7.2
Question: City A to city B, Michael drove for 1 hour at 80 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?
(A) 57
(B) 57.5
(C) 58.2
(D) 60
(E) 62
Rationale: The total distance is 1×80+3×60=240
And the total time is 4 hours. Hence,
Average Speed=(Total Distance/Total Time)=240/4=60
Answer : D
Answer: (D) 60
Question: If in a race of 80m, A covers the distance in 20 seconds and B in 25 seconds, then A beats B by:
(A) 20m
(B) 16m
(C) 11m
(D) 10m
(E) 15m
Rationale: Explanation:
The difference in the timing of A and B is 5 seconds. Hence, A beats B by 5 seconds.
The distance covered by B in 5 seconds = (80 * 5) / 25 = 16m
Hence, A beats B by 16m.
ANSWER B
Answer: (B) 16m
Question: Kelsey travelled for 10 hours. He covered the first half of the distance at 25 kmph and remaining half of the distance at 40 kmph. Find the distance travelled by Kelsey?
(A) 583 km
(B) 400 km
(C) 670 km
(D) 360 km
(E) 234 km
Rationale: Let the distance travelled be x km.
Total time = (x/2)/25 + (x/2)/40 = 10 => x/50 + x/80
= 10 => (8x + 5x)/400 = 10 => x
= 400 km
Answer: B
Answer: (B) 400 km
Question: In how many ways can 6 boys and 3 girls sit around a table in such a way that no two girls sit together?
(A) 10000
(B) 14000
(C) 14400
(D) 18000
(E) 19000
Rationale: The 6 boys can be seated around a table in 5! Ways. In between them there are 6 places.
The 3 girls can be placed in the 6 places in 6P3 ways.
Therefore, Required number of ways= 5!* 6P3
=120*120
=14400
ANSWER:C
Answer: (C) 14400
Question: John and Ingrid pay 30% and 40% tax annually, respectively. If John makes $56000 and Ingrid makes $74000, what is their combined tax rate?
(A) 32%
(B) 34.4%
(C) 35%
(D) 35.6%
(E) 36.4%
Rationale: (1) When 30 and 40 has equal weight or weight = 1/2, the answer would be 35.
(2) When 40 has larger weight than 30, the answer would be in between 35 and 40. Unfortunately, we have 2 answer choices D and E that fit that condition so we need to narrow down our range.
(3) Get 74000/128000 = 74/128 = 37/65 is a little above 1/2. Thus, our answer is just a little above 35.
Answer: D
Answer: (D) 35.6%
Question: If two integers x,y (x>y) are selected from -3 to 4 (inclusive), how many cases are there?
(A) 20
(B) 22
(C) 24
(D) 26
(E) 28
Rationale: There are 8 integers from -3 to 4 inclusive.
8C2 = 28.
The answer is E.
Answer: (E) 28
Question: How many integers between 100 and 400 are there such that their unit digit is odd?
(A) 100
(B) 120
(C) 200
(D) 50
(E) 150
Rationale: 300 numbers between - 100 and 400
Out of which half would be even, half odd.
Number of odd unit digit number = 150.
correct option is E
Answer: (E) 150
Question: A ball is bought for Rs.400 and sold at a gain of 20% find its selling price
(A) Rs.400/-
(B) Rs.420/-
(C) Rs.480/-
(D) Rs.500/-
(E) Rs.520/-
Rationale: 100 % ------> 400 (100 * 4 = 400)
120 % ------> 480 (120 * 4 = 480)
Selling price = Rs.480/-
C)
Answer: (C) Rs.480/-
Question: Fresh grapes contain 90% water by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 20 kg of fresh grapes?
(A) 2 kg
(B) 2.5 kg
(C) 2.4 kg
(D) None of these
(E) Cannot be determined
Rationale: Explanation :
Fresh grapes contains 10% pulp.
So, 20 kg fresh grapes contains 2kg pulp.
Dry grapes contain 80% pulp.
2kg pulp would contain 2/0.8 = 20/8 = 2.5 kg dry grapes.
Answer : B
Answer: (B) 2.5 kg
Question: If "WATER" is given a code of 67, then what is the difference between "RIVER" and "LAKE"?
(A) 101
(B) 29
(C) 43
(D) 42
(E) 30
Rationale: Case – Codes : A - 1, B - 2, C - 3, D - 4, E - 5, F - 6, G - 7, H - 8, I - 9, J - 10, K - 11, L - 12, M - 13, N - 14, O - 15, P - 16, Q - 17, R - 18, S - 19, T - 20, U - 21, V - 22, W - 23, X - 24, Y - 25, Z - 26
RIVER: 72
LAKE: 29
Answer: C
Answer: (C) 43