mathewhe/aqua_rat huggingface dataset:
Question: A fair price shopkeeper takes 10% profit on his goods. He lost 20% goods during theft. His loss percent is:
(A) 72%
(B) 42%
(C) 32%
(D) 12%
(E) 22%
Rationale: Explanation:
Suppose he has 100 items. Let C.P. of each item be Re. 1.
Total cost = Rs. 100. Number of items left after theft = 80.
S.P. of each item = Rs. 1.10
Total sale = 1.10 * 80 = Rs. 88
Hence, loss % = 12/100 * 100 = 12%
Answer:D
Answer: (D) 12%
Question: Tom had 63 apples. He divides all apples evenly among 9 friends. How many apples did Tom give to each of his friends?
(A) 1
(B) 2
(C) 18
(D) 7
(E) 8
Rationale: Total number of apples = 63
There are 9 friends of seats on the bus.
To find how many apples Tom gave to each of his friends, divide the total number of apples by the number of friends.
We get, divide 63 by 9
63 ÷ 9 = 7
Therefore, Tom gives 7 apples to each of his friends.
ANSWER IS D
Answer: (D) 7
Question: A cricket bat is sold for $850, making a profit of $230. The profit percentage would be
(A) 24%
(B) 25%
(C) 30%
(D) 37%
(E) 40%
Rationale: 230/(850 - 230) = 230/620 = 23/62 =37%
Answer: D.
Answer: (D) 37%
Question: You play the following game with a friend. You share a pile of chips, and you take turns
removing between one and four chips from the pile. (In particular, at least one chip must be
removed on each turn.) The game ends when the last chip is removed from the pile; the one
who removes it is the loser.
It is your turn, and there are 2014 chips in the pile. How many chips should you remove to
guarantee that you win, assuming you then make the best moves until the game is over?
(A) 1
(B) 2
(C) 3
(D) 4
(E) there is no way to guarantee a win, even with the best play
Rationale: The key to winning this game is that if you leave your opponent with 5k +1 chips,
for any integer k 0, then you win. When your opponent removes r chips, you remove 5-r,
and so there are now 5(k- 1) + 1 chips left, and you keep using this strategy until there is
only one chip left, at which point your opponent takes it and loses.
So, you should take 3 chips to leave 2011 = 5 402 + 1.
correct answer C
Answer: (C) 3
Question: 36 men can complete a piece of work in 18 days. In how many days will 108 men complete the same work ?
(A) 24
(B) 77
(C) 6
(D) 29
(E) 21
Rationale: Explanation:
Less Men, means more Days {Indirect Proportion}
Let the number of days be x
then,
108 : 36 :: 18 : x
x = 6
Answer: C) 6 days
Answer: (C) 6
Question: A bag contains one rupee, 50 paisa and 10 paisa coins in the ratio of 3:2:1. How many 50 paisa coins are there, if the total number of money in the bag is Rs 820?
(A) 400 coins
(B) 40 coins
(C) 100 coins
(D) 4100 coins
(E) 4200 coins
Rationale: Let the number of 100p, 50p and 10p coins be 3x ,2x and x .
The ratio of the values of coins = 100 p: 50p :10 p = 10:5:1
Total amount = (10 x 3x ) + (5 x 2x) +( 1 x x) = 30x+10x+x=41x
The ratio of their values in rupees= 30x:10x:x
Given total amount is Rs 820 => 41x = 820 => x=Rs 20
Total value of 50p coins (in rupees) = 10 x 20 =Rs 200
Total 50 paisa coins are = 200 x 2 = 400 coins
Answer:A
Answer: (A) 400 coins
Question: It was a beautiful sunny morning. The air was fresh and a mild wind was blowing against my wind screen. I was driving from Bangalore to Brindavan Gardens. It took me 1 hour and 30 minutes to complete the journey.
After lunch I returned to Bangalore. I drove for 90 rhinutes. How do you explain it ?
(A) 75 min
(B) 60 min
(C) 90 min
(D) 80 min
(E) 88 min
Rationale: C
90 min
Jansi went out for shopping. She had in her handbag approximately Rs. 15/- in one rupee notes and 20 p. coins. When she returned she had as many one rupee notes as she originally had and as many 20 p. coins as she originally had one rupee notes. She actually came back with about one-third of what she had started out with.
How much did she spend and exactly how much did she have with her when she started out ?
There is nothing to explain here. The driving time there and back is absolutely the same because 90 minutes and 1 hour and 30 minutes are one and the same thing.
This problem is meant for inattentive readers who may think that there is some difference between 90 minutes and 1 hour 30 minutes.
Answer: (C) 90 min
Question: How many positive 5-digit integers have the odd sum R of their digits?
(A) 9*10^2
(B) 9*10^3
(C) 10^4
(D) 45*10^3
(E) 9*10^4
Rationale: We are looking at numbers between 10000 and 99999 both inclusive.
There are 90000 numbers.
Now for
10000 : sum of digits is odd;
10001 :sum of digits is even;
10002 : sum of digits is odd ; so on and so forth. So every alternate number is such that the sum of digit is odd.
(Exception for the above statement :
When it is 10009 the sum is even and for 10010 again the sum is even; But if you look at 10019 :sum is odd; 10020 : sum is odd
and this pattern continues so basically the number of odd sum of digits and even sum of digits are equal)
This means exactly half of the numbers will have odd sum of their digits. i.e 45000
Answer :D
Answer: (D) 45*10^3
Question: The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?
(A) Rs. 1200
(B) Rs. 2400
(C) Rs. 4800
(D) Cannot be determined
(E) None of these
Rationale: Let the price of a saree and a shirt be Rs. x and Rs. y respectively.
Then, 2x + 4y = 1600 .... (i)
and x + 6y = 1600 .... (ii)
Divide equation (i) by 2, we get the below equation.
=> x + 2y = 800. --- (iii)
Now subtract (iii) from (ii)
x + 6y = 1600 (-)
x + 2y = 800
----------------
4y = 800
----------------
Therefore, y = 200.
Now apply value of y in (iii)
=> x + 2 x 200 = 800
=> x + 400 = 800
Therefore x = 400
Solving (i) and (ii) we get x = 400, y = 200.
Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.
Answer: Option B
Answer: (B) Rs. 2400
Question: What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second?
(A) 1100
(B) 1200
(C) 1349
(D) 1400
(E) 1450
Rationale: First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9.
First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12.
Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18.
Hence the number is 1349
C
Answer: (C) 1349
Question: Two cars are driving toward each other. The first car is traveling at a speed of 75 km/h, which is 25% slower than the second car's speed. If the distance between the cars is 1050 km, how many hours will it take until the two cars meet?
(A) 4
(B) 4.5
(C) 5
(D) 5.5
(E) 6
Rationale: The speed of the first car is 75 km/h.
The speed of the second car is 75 / 0.75 = 100 km/h.
The two cars complete a total of 175 km each hour.
The time it takes the cars to meet is 1050 / 175 = 6 hours.
The answer is E.
Answer: (E) 6
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
(A) 3887
(B) 2689
(C) 2678
(D) 4530
(E) 3780
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls
= 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3)
= 906 sq.ft.
Total cost = 906 * 5 = Rs. 4530
Answer: D
Answer: (D) 4530
Question: Machine A produces 100 parts twice as fast as Machine B does. Machine B produces 100 parts in 40 minutes. If each machine produces parts at a constant rate, how many parts does Machine A produce in 10 minutes?
(A) 20
(B) 50
(C) 60
(D) 40
(E) 30
Rationale: Machine B produces 100 part in 40 minutes. Machine A produces 100 parts twice as fast as B, so Machine A produces 100 parts in 40/2=20 minutes.
Now, Machine A produces 100 parts in 20 minutes which is 100/20 = 5 parts/minute.
5 parts X a total of 10 minutes = 50
B
Answer: (B) 50
Question: After 6 games, team B had an average of 65 points per game. If it got only 47 points in game 7, how many more points does it need to score to get its total above 500?
(A) 85
(B) 74
(C) 67
(D) 63
(E) 28
Rationale: (6*65) + 47 +x >500
390+47+x > 500
437+x >500
=> x>63
Option D
Answer: (D) 63
Question: There are 23 distinct numbers in set M, there are 28 distinct numbers in set N, and there are 12 distinct numbers that are in both sets M and N. Set H is the set containing the elements that are in at least one of sets M and N. How many elements are in set H?
(A) 39
(B) 40
(C) 51
(D) 58
(E) 63
Rationale: {Total} = {M} + {N} - {Both}
{Total} = 23 + 28 - 12 = 39.
Answer: A.
Answer: (A) 39
Question: A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had
(A) 588 apples
(B) 600 apples
(C) 672 apples
(D) 700 apples
(E) None
Rationale: Solution
Suppose originally he had x apples.
Then,(100-40)% of x = 420.
‹=› 60/100×x = 420
x ‹=› (420 ×100 / 60
‹=› 700.
Answer D
Answer: (D) 700 apples
Question: A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?
(A) 12.9
(B) 12.6
(C) 12.4
(D) 12.5
(E) 12.1
Rationale: Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.
Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7
Solving the equation, the speed of man in still water is 12.5 kmph.
Answer:D
Answer: (D) 12.5
Question: What is the probability that when a hand of 6 cards is drawn from a well shuffled deck of 52 cards, It contains 2 Queen?
(A) 1/23445
(B) 113/22434
(C) 29187/1017926
(D) 1017926/29187
(E) None of these
Rationale: nCr = n!/(n-r)!r!
Total number of possible hands = 52C6
52C6 = (52!)/((52-6)! × 6!)
52C6 = 61075560.
Number of hands with 2 Queen and 4 non-Queen cards = 4C2 × 48C4
4C2 = (4!)/(2! × 2!) = 6.
48C4 = (48!)/(44! × 4!) = 3 × 47 × 46 × 45 = 291870
(other 2 cards must be chosen from the rest 48 cards)
P (2 Queen) = (4C2 × 48C4)/52C6 = 29187/1017926
C
Answer: (C) 29187/1017926
Question: In the following sequence of alphabets, if the second half is reversed, which letter would be the fifth to the right of the letter which is twelveth from the left ?
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
(A) J
(B) W
(C) T
(D) G
(E) K
Rationale: Explanation:
Case 1 : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
After reversal of the second half of the sequence of alphabet, we get,
Case 2 : A B C D E F G H I J K L M Z Y X W V U T S R Q P O N
The twelveth letter from the left end of the above sequence of alphabet Case 2 is L. The letter which is 5th to the right of L is W.
ANSWER: B
Answer: (B) W
Question: If the price of a certain computer increased 30 percent from d dollars to 364 dollars, then 2d =
(A) 540
(B) 570
(C) 619
(D) 649
(E) 560
Rationale: Before Price increase Price = d
After 30% Price increase Price = d+(30/100)*D = 1.3d = 364 (Given)
i.e. d = 364/1.3 = $280
i.e. 2d = 2*280 = 560
Answer: option E
Answer: (E) 560
Question: Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.36000 after completion of one year. What will be Jose's share of profit?
(A) 20000
(B) 10000
(C) 25000
(D) 34000
(E) 30000
Rationale: SoL = ~s- So Anju’s share = [5/9] x 36000 = 20000
A
Answer: (A) 20000
Question: There were two candidates in an election. Winner candidate received 60% of votes and won the election by 288 votes. Find the number of votes casted to the winning candidate?
(A) 776
(B) 864
(C) 299
(D) 257
(E) 125
Rationale: W = 60% L = 40%
60% - 40% = 20%
20% -------- 288
60% -------- ? => 864
Answer:B
Answer: (B) 864
Question: The sum of two numbers is 50 and their product is 375. What will be the sum of their reciprocals?
(A) 1/40
(B) 8/75
(C) 2/15
(D) 75/8
(E) 75/6
Rationale: (1/a)+(1/b)=(a+b)/ab=50/375=2/15
ANSWER:C
Answer: (C) 2/15
Question: A couple has two children, one of whom is a girl. If the probability of having a girl or a boy is 50%, what is the probability that the couple has two daughters?
(A) 1/8
(B) 1/4
(C) 1/3
(D) 1/2
(E) 2/3
Rationale: First child ---- Second child:
B ---------------------------- B;
B ---------------------------- G;
G ---------------------------- B;
G ---------------------------- G.
We know that one if the kids is a girl. So, we have one of the three cases in red. Each case there is equally likely (each has the probability of 1/2*1/2=1/4). So, the probability of GG is 1/3.
Answer: C.
Answer: (C) 1/3
Question: Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.18 per cubic meter?
(A) 2998
(B) 2799
(C) 1782
(D) 1485
(E) 2780
Rationale: 22/7 * 14 * 3/2 * 3/2
= 99 m2
99 * 18
= 1782
Answer:C
Answer: (C) 1782
Question: A train running at 25 km/hr takes 18 seconds to pass a platform. Next, it takes 12 seconds to pass a man standing still. Find the length of the train and that of the platform.
(A) 83.3m41.7m
(B) 100m50m
(C) 50.8m45.7m
(D) 100/3 m200/3
(E) none of these
Rationale: A train running at 25 km/hr takes 18 seconds to pass a platform. Next, it takes 12 seconds to pass a man walking at 5 km/hr in the same direction. Find the length of the train and that of the platform.
Distance = Speed*time
It's probably best to convert to meters so we can find the length of the platform.
Distance = 25000 meters/h * 18 seconds*(1/60*60)
Distance =(25000*18 / [3600] ) = 125m
I'm not sure how we take the length of the train into account (if we do at all) to solve this problem. For example, If we were measuring by the time the very front of the train passed one end of the platform to the time the very front of the train passed the other end, the result would be different than if we counted when the very front of the train passed one end of the platform to the time the back side of the train passed the end.
As for the problem involving the man, the man is standing still while the train is moving forward at a speed of 25km/h. Therefore, the train is moving past the man at a total speed of 25km/h.
distance = speed * time
distance = 25km/h * 12 seconds
distance (length of train) = 83.3 m
We know the length of the train is roughly 83.3m and the distance covered passing the platform was 125m. However, The platform isn't 125m long - it is 125m minus the length of the train long (or so I think) which is 125-83.3 or roughly 41.7m. Both of these answers are in A so I think that is the right answer. I am still having a bit of trouble conceptualizing why we have to subtract out the length of the train, however.
ANSWER: A) 83.3m41.7m
Answer: (A) 83.3m41.7m
Question: A no. when divided by 35leaves a remainder 20, what is the remainder if the same no.be divided by 15?
(A) 2
(B) 4
(C) 7
(D) 8
(E) 9
Rationale: Explanation:
35 + 25 = 60/15 = 4 (Remainder)
B
Answer: (B) 4
Question: x ÷ 4 × 5 + 10 – 12 = 48, then x =
(A) 60
(B) 40
(C) 100
(D) 28
(E) 50
Rationale: Follow reverse process
48 + 12 = 60 – 10 = 50 ÷ 5 = 10
×
× 4 = 40
Option B
Answer: (B) 40
Question: How many of the integers between 25 and 45 are even ?
(A) 21
(B) 20
(C) 11
(D) 10
(E) 9
Rationale: Number start between 25 to 45 is 20 numbers
half of them is even..which is 10
ANSWER:D
Answer: (D) 10
Question: How many numbers from 10 to 1000000 are exactly divisible by 9?
(A) 900
(B) 8000
(C) 1100
(D) 111110
(E) 14
Rationale: 10/9 = 1 and 1000000/9 = 111111 ==> 111111 - 1 = 111110.
Answer : D
Answer: (D) 111110
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) 45 Years
(B) 46 Years
(C) 49 Years
(D) 52 Years
(E) 54 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: The number obtained by interchanging the two digits of a two digit number is lesser than the original number by 54. If the sum of the two digits of the number is 12, then what is the original number?
(A) 28
(B) 39
(C) 82
(D) Can’t say
(E) None of these
Rationale: Let with two digits x and y, original number= 10x+y
Number obtained by reversing the digits= 10y+x
Given the later number is less by 54 than the original, so 10x+y -(10y+x)=54 or x-y=6 ---(i)
Also Sum of the two digits is 12, so x+y= 12 ----(ii)
From (i) & (ii), x=9, y=3
So original number=10x+y= 10*9 +3= 93
ANSWER:E
Answer: (E) None of these
Question: n a 1000m race, if A gives B a start of 40m, A wing by 19sec. But if A gives B start of 30sec, B wins by 40m.
Find the time taken by B to run 5000m race?
(A) 300
(B) 400
(C) 500
(D) 600
(E) 750
Rationale: then 960/B -1000/A = 19 => 24/B - 25/A = 19/40
and 1000/B - 960/A = 30 => 25/B - 24/A = 30/40
solving equation A speed =8 and B=20/3
for 1000m b will take 5000/20/3= 750 sec
#
E
Answer: (E) 750
Question: A certain high school has 500 students. Of these students, 30 are taking music, 20 are taking art, and 10 are taking both music and art. How many students are taking neither music nor art?
(A) 430
(B) 440
(C) 450
(D) 460
(E) 470
Rationale: We're given a series of facts to work with:
1) A certain high school has 500 students.
2) Of these students:
X are taking music,
Y are taking art, and
Z are taking BOTH music and art.
We're asked how many students are taking NEITHER music nor art?
Let's TEST
X = 30
Y = 20
Z = 10
So, we have 30 students taking music, 20 taking art and 10 taking BOTH music and art.
20 student taking JUST music
10 student taking JUST art
10 student taking BOTH music and art
Total = 40 students
We're asked for the total number of students who are taking NEITHER Course. That is 500 - 40 = 460.
D
Answer: (D) 460
Question: A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. Find out the number of days for which the remaining food will last
(A) 44
(B) 42
(C) 40
(D) 38
(E) 36
Rationale: Explanation :
Given that fort had provision of food for 150 men for 45 days
Hence, after 10 days, the remaining food is sufficient for 150 men for 35 days
Remaining men after 10 days = 150 - 25 = 125
Assume that after 10 days,the remaining food is sufficient for 125 men for x days
More men, Less days (Indirect Proportion)
⇒Men150:125}::x:35
⇒ 150 × 35 = 125x
⇒ 6 × 35 = 5x
⇒ x =6 × 7 = 42
⇒The remaining food is sufficient for 125 men for 42 days. Answer : Option B
Answer: (B) 42
Question: If 100,000 microns = 1 decimeter, and 1,000,000 angstroms = 1 decimeter, how many angstroms equal 1 micron?
(A) 1.0e-05
(B) 0.0001
(C) 0.001
(D) 10
(E) 100,000
Rationale: Given that 100,000 microns = 1 decimeter
1,000,000 angstroms = 1 decimeter
So 100,000 microns =1,000,000 angstroms
1 micron = 1,000,000/100,000 = 10
Answer : D
Answer: (D) 10
Question: After giving a discount of rs.100the shopkeeper still gets a profit of 30%,if the cost price is rs.1000.find the markup %?
(A) .50
(B) .45
(C) .40
(D) .48
(E) .52
Rationale: cost price=1000
s.p=1000*130/100=1300
disc=100
so...mark price=1300+100=1400......
mark up%=1400-1000/1000=400/1000=.40 (OR) 40%
ANSWER:C
Answer: (C) .40
Question: The calendar of the year 2024 can be used again in the year?
(A) 2288
(B) 2052
(C) 2778
(D) 2719
(E) 1711
Rationale: Explanation:
Given year 2024 when divided by 4, leaves a remainder 0.
NOTE: When remainder is 0, 28 is added to the given year to get the result.
So, 2024 + 28 = 2052
Answer: B) 2052
Answer: (B) 2052
Question: The area of a square garden is Q square feet and the perimeter is P feet. If Q=2P+20, what is the perimeter of the garden in feet?
(A) 32
(B) 36
(C) 40
(D) 44
(E) 48
Rationale: Let x be the length of one side of the square garden.
x^2 = 8x + 20
x^2 - 8x - 20 = 0
(x-10)(x+2) = 0
x = 10, -2
P = 4(10) = 40
The answer is C.
Answer: (C) 40
Question: The average of 65 numbers is 40. If two numbers, 50 and 60 are discarded, then the average of the remaining numbers is nearly
(A) 28.32
(B) 39.52
(C) 38.78
(D) 29
(E) 30
Rationale: Explanation :
Total sum of 63 numbers = (65 * 40) - (50+60) = 2600 - 110= 2490
Average = 2457/63 = 39.52
Answer : B
Answer: (B) 39.52
Question: A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
(A) 60 km
(B) 87 km
(C) 89 km
(D) 67 km
(E) 20 km
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 4.5
=> x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2 => x
= 20 km.
Answer:E
Answer: (E) 20 km
Question: A football field is 9600 square yards. If 1200 pounds of fertilizer are spread evenly across the entire field, how many pounds of fertilizer were spread over an area of the field totaling 5600 square yards?
(A) 450
(B) 600
(C) 700
(D) 2400
(E) 3200
Rationale: Answer C) 9600 yards need 1200 lbs
1 Yard will need 1200/9600 = 1/8 lbs
3600 Yards will need 1/8* 5600 Yards = 700lbs
Answer: (C) 700
Question: When a merchant imported a certain item, he paid a 9 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that the merchant paid was $85.50, what was the total value of the item?
(A) $1,150
(B) $1,350
(C) $1,550
(D) $1,750
(E) $1,950
Rationale: Let x be the value in excess of $1,000.
0.09x = 85.5
x = $950
The total value was $950 + $1,000 = $1,950.
The answer is E.
Answer: (E) $1,950
Question: There are 7000 people in the particular village , among them 30% are educated and out of these 28% are doing agriculture and out of them 50% are woman's. Then find out the number of woman's who are educated and doing agriculture?
(A) 294
(B) 235
(C) 350
(D) 288
(E) 580
Rationale: Total number of people in the village = 7000; out of them 30% educated = 2100; out of them 28% doing agriculture = 588; out of them 50% are woman's = 294.
Answer: (A) 294
Question: What sum of money will produce Rs.80 as simple interest in 2 years at 16 percent?
(A) 400
(B) 250
(C) 300
(D) 350
(E) 200
Rationale: 80 = (P*2*16)/100
P = 250
Answer: B
Answer: (B) 250
Question: In a class of 20 students, 2 students did not borrow any books from the library, 8 students each borrowed 1 book, 3 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: The total number of books the students borrowed is 20*2=40.
The students who borrowed zero, one, or two books borrowed 8*1+3*2=14 books.
The 7 students who borrowed at least three books borrowed 40-14=26 books.
If 6 of these students borrowed exactly 3 books, then the maximum that one student could have borrowed is 26-18= 8 books.
The answer is A.
Answer: (A) 8
Question: The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 15 percent, what was the annual interest rate last year?
(A) 1%
(B) 1.1%
(C) 9.1%
(D) 10%
(E) 13.63%
Rationale: 15=1.1*x
X=13.63%
Answer E)
Answer: (E) 13.63%
Question: In a group of ducks and cows, the total number of legs are 24 more than twice the no. of heads. Find the total no.of buffaloes.
(A) 10
(B) 12
(C) 14
(D) 16
(E) 17
Rationale: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 24
=> 2x = 24 => x = 12
B
Answer: (B) 12
Question: A box has exactly 100 balls, and each ball is either red, blue, or white. If the box has 5 more blue balls than white balls, and thrice as many red balls as blue balls, how many white balls does The box has ?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: x = the number of red balls
y = the number of blue balls
z = the number of white balls
From the first sentence we have
Equation #1: x + y + z = 100
...the box has 5 more blue balls than white balls...
Equation #2: y = 5 + z
...thrice as many red balls as blue balls...
Equation #3: x = 3y
Solve equation #2 for z: z = y - 5
Now, we can replace both x and z with y in Equation #1
3y + y + (y - 5) = 100
5y - 5 = 100
5y = 105
y = 21
There are 21 blue balls. This is 5 more than the number of white balls, so z = 16. That's the answer. Just as a check, x = 63, and 63 + 21 + 16 = 100.
Answer = 16,(E)
Answer: (E) 16