MU-NLPC/Calc-aqua_rat huggingface dataset:
A foreign language club at Washington Middle School consists of n students, 3/5 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?  Choose the correct choice from the following.
A) 2n/5
B) n/3
C) 4n/75
D) 2n/15
E) n/15

Solution: 3/5 of the students are boys, thus 2/5 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 2/5 of the students, then 2/5*2/15=4/75 are girls who study German.   The answer is 4n/75.
Answer: C
A telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 0, 1, 2, 7, or 8. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most 2 attempts is closest to which of the following ? Answers:
A) 1/625 B) 2/625 C) 50/625 D) 75/625 E) 90/625

Solution: I think most of the answers are missing a point. Let me try to put it across:   Total number of possible numbers are : 5x5 = 25   Correct number =1   Case 1: When he gets it right in first attempt: P(E1) = 1/25   Case 2: He gets 1st attempt wrong and second right:   When he gets it wrong then the probability of getting wrong is 24/25.   Now there are 24 cases with him and he chooses the right one this time.   Probability of right case is 1/24   Thus, P(E2) = 24/25 x 1/24   =1/25   Probability of getting it right in at most two cases = P(E1) + P(E2)   = 1/25 + 1/25   = 2/25   = 50/625   Option (50/625) is therefore right as most of you mentioned but the method employed was wrong.
Answer: C
The value of a stock is X dollars. On Sunday the stock's value grew by half of its value, but on Monday its value dropped to a third of its new value. What is the stock's value at the end of Monday?  Choose the correct choice from the following options.
A) X.  B) X/2.  C) 2X/3  D) X/3  E) X/4.

Solution: Given the value of stock is X dollars.   Then on Sunday the stock's value is increased by half i.e. X + X/2 = 3X/2 ( this is the new value)   Then on Monday its value dropped by 1/3 of new value = 1/3(3X/2) = 3X/6   Then 3X/2 - 3X/6 = 6X/6 = 6. (new value - 1/3 value)   X.ns: X. is correct option..
Answer: A
Jim travels the first 3 hours of his journey at 60 mph speed and the remaining 5 hours at 24 mph speed. What is the average speed of Jim's travel in mph?	Choose the correct choice from the following
A) 35.5mph B) 37.5mph C) 38.5mph D) 39.5mph E) 36.5mph

Solution: 3 hours of his journey at 60 mph means 180 miles in 3 hours   5 hours at 24 mph speed means 120 miles in 5 hours. In total 300 miles in 8 hours.   Average Speed is   ((3*60)+(5*24))/8= 
  ((3*60)+(5*24))/8 = 75/2 = around 37.5
37.5mph   ANSWER:37.5mph
Answer: B
If p is a positive integer and 10p/96 is an integer, then the minimum number ofuniqueprime factors p could have is H: Answers:  A) H=1  B) H=2  C) H=3  D) H=4  E) H=5

Solution: 10p/96 should resolve to a integer => 5p/48 should resolve to an integer.   Hence p/48 should resolve to a integer.   48 -- > 2^4 * 3.   Hence p should have atleast 2^4*3 for p/48 to resolve to a int.   The unique prime factors in 2^4 * 3 is 2, 3 and hence the answer is H=2(2).
Answer: B
5358 x 51 = ? Select:
A) 273258 B) 273158 C) 273268 D) 283258 E) 262268

Solution: 5358 x 51	= 5358 x (50 + 1)   = 5358 x 50 + 5358 x 1   = 267900 + 5358= 
267900 + 5358 = 273_258
273258   273258nswer is 273258.
Answer: A
How many possible integer values are there for x if |4x - 3| < 6 ?  Select:
A) One
B) Two
C) Three
D) Four
E) Five

Solution: Solution: |4x-3| < 6   let 4x=a therefore we have |a-3| < 6 ==> read this as origin is at +3 and we have to move +6 to the right and -6 to the left   (the less than sign represents that the a must be within boundaries )   (3-6)----------3----------(3+6)   now, we have -3<a<9   but a =4x ==> -3<4x<9   dividing all values by +4 we have -0.75 <x < 2.24   Now question says Integer values (not rational ) therefore we have 0,1,2   ANSWER:Three
Answer: C
what is the distance between two parallel chords of length 32 cm and 24 cm in a circle of radius 20 cm ?	Choose the correct choice from the following
A) 1 or 7
B) 3 or 21
C) 4 or 28
D) 2 or 14
E) 5 or 14

Solution: since the chord length=2sqrrt(r^2-d^2)   chord length=32,r=20 then we get d=12   chord length=24,r=20 then we get d=16   then we add/subtract we get option c) 4 or 28   ANSWER:4 or 28
Answer: C
0.0006688/0.0000150 x 19.85 = ?	Answers:
A) 850	B) 900	C) 950	D) 1000	E) 2000

Solution: Explanation :   ? = 6688/150 x 19.85 = 45 x 20 = 900   Answer : Option 900
Answer: B
Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?	Pick one
A) 16 a.m B) 10 a.m C) 17 a.m D) 76 a.m E) 11 a.m

Solution: Suppose they meet x hours after 7 a.m.   Distance covered by A in x hours = 20x km.   Distance covered by B in (x - 1) hours = 25(x - 1) km.   Therefore 20x + 25(x - 1) = 110   45x = 135   x = 3.   So, they meet at 10 a.m.   Answer:10 a.m
Answer: B
The velocity of a falling object in a vacuum is directly proportional to the amount of time the object has been falling. If after 7 seconds an object is falling at a speed of 90 miles per hour, how fast will it be falling after 12 seconds?	Choose the correct choice from the following answers
A) 18 miles per hour  B) 156 miles per hour  C) 216 miles per hour  D) 1080 miles per hour  E) 5400 miles per hour

Solution: Since Velocity is proportional to Time   Velocity =k*Timewhere k is the constant of proportionality   Time= 7 seconds   Velocity = 7k = 90 miles per Hour   i.e. k = 13   i.e. The relation between Velocity and Time becomes   Velocity =13*Time   Time= 12 seconds   Velocity = 13*12= 
13*12 = 156
156 miles per hour   Answer: Option 156 miles per hour
Answer: B
In a recent election, Geoff received 1 percent of the 6,000 votes cast. To win the election, a candidate needed to receive more than x% of the vote. If Geoff needed exactly 3000 more votes to win the election, what is the value of x ?  Select the correct option.
A) 50 B) 54 C) 56 D) 51 E) 63

Solution: Word problems are tricky in somehow more than other problem because you have the additional step to translate.   Breaking the problem: Geoff how many votes he receives ?? 60 votes   he needs 3571 more votes so :   60+3000= 
  60+3000 = 3_060
3060   Now what's the problem wants ?? a x %........3060 is what % of total votes 6000........translating: 3060= x/100 * 6000 ---   x= 51 %..........51
Answer: D
When you multiply a number by 4 and
then subtract 7, the result is the same as
if you first subtracted 7 from the same
number and then multiplied by 11. What
is the number?	Choose the correct choice from the following answers:  A) 23  B) 13  C) 19  D) 31  E) 10

Solution: Let x equal the number and then change the words into an equation and solve for x:   4x – 7 = 11(x – 7)   4x – 7 = 11x – 77   70 = 7x   10 = x   correct answer 10)10
Answer: E
As a treat for her two crying children, a mother runs to the freezer in which she has five cherry ice pops, three orange ice pops, and four lemon-lime ice pops. If she chooses two at random to bring outside to the children, but realizes as she runs out the door that she cannot bring them different flavors without one invariably being jealous of the other and getting even more upset, what is the probability that she has to return to the freezer to make sure that they each receive the same flavor? Options:
A) 1/9
B) 1/6
C) 5/18
D) 1/999
E) 5/6

Solution: Probability of not getting the same flavor ->   Favourable -> Cherry - orange [ 5C1 * 3C1 [or simply 5*3 ] or Cherry - lemon [ 5*4] or orange - lemon [3*4]   Prob = (5*3 + 5*4 + 3*4 ) / 9C2 = 47/47520 = 1/999   Answer -> 1/999
Answer: D
How many integerskgreater than 100 and less than 1200 are there such that if the hundreds and the units digits ofkare reversed, the resulting integer is k+99? Pick one
A) 50
B) 60
C) 70
D) 80
E) 100

Solution: Numbers will be like 102 => 201 = 102 + 99   203 => 302 = 103 + 99   so the hundereth digit and units digit are consecutive where unit digit is bigger than hundred digit.   There will be ten pairs of such numbers   for every pair there will 10 numbers like for 12 => 102, 112,132,142,152, 162,172,182,192.   Total = 10 *10= 
10 *10 = 100
100 hence 100
Answer: E
A mall charges 50 cents for the first hour of parking and $4 for each additional hour until the customer reaches 4 hours, after that the parking fee is $2 per hour. If a Rahul parked his car in the mall for 7 hours and 30 minutes, how much is he going to pay?
Pick.
A) $25  B) $12.  C) $23.5  D) $24.5.  E) $25.5

Solution: 0.50+4*4+2*4+0.50= 
0.50+4*4+2*4+0.50 = 25
$25   $25nswer: $25
Answer: A
Tom and John traveled in the same direction along the equal route at their constant speed rates of 15 km per hour and 10 km per hour, respectively. After 15 minutes Tom passed John, Tom reaches a certain Gas station, how many L minutes it takes John to reach the station?  Choose the correct choice from the following options.
A) 5 min
B) 6 min
C) 7 and 1/2 min
D) 8 min
E) 10 min

Solution: Since the question states “after 15 minutes”, we can say Tom traveled 15/4km for 15 minutes as he can travel 15km per hour. Hence, using the same logic, we can say John traveled 10/4km as he travels 10km per hour. So, John has to travel (15/4)-(10/4)km=5/4km more. Since John’s speed is 10km/hour, which means 1km/6minutes. As he has to travel 5/4km more, it is going to take him 6(5/4) minutes. Hence,L 6(5/4)=15/2 minutes. The correct answer is 7 and 1/2 min.
Answer: C
A train traveling at 180 kmph crosses a platform in 30 seconds and a man standing on the platform in 12 seconds. What is the length of the platform in meters?  Select the correct option.
A) 240 meters  B) 360 meters  C) 420 meters  D) 600 meters  E) Cannot be determined

Solution: Answer   Distance covered by the train when crossing a man and when crossing a platform   When a train crosses a man standing on a platform, the distance covered by the train is equal to the length of the train.   However, when the same train crosses a platform, the distance covered by the train is equal to the length of the train plus the length of the platform.   The extra time that the train takes when crossing the platform is on account of the extra distance that it has to cover. i.e., length of the platform.   Compute length of platform   Length of the platform = speed of train * extra time taken to cross the platform.   Length of platform = 180 kmph * 12 seconds   Convert 180 kmph into m/sec   1 kmph = 5/18 m/s (This can be easily derived. But if you can remember this conversion, it saves a good 30 seconds).   ∴ 180 kmph = 5/18∗180 = 50 m/sec   Therefore, length of the platform = 50 m/s * 12 sec = 600 meters.   Choice 600 meters
Answer: D
A certain gallery is hanging a series of 8 paintings. All the paintings will be exhibited in a row along a single wall. Exactly 2 of the paintings are on panel, the remainder are on canvas. In how many ways can the paintings be exhibited if the works on panel must be the second and sixth in the row?
OE
Choose the most appropriate option
A) 1440
B) 200
C) 122
D) 80
E) 16

Solution: We need to consider them separately because the question specifies:   1. Panel paintings have to be placed only at 2nd and 6th place.   2. Implies that Canvas has to be placed 1,3,4,5,7, 8th place.   So we have two separatebucketsto consider.   So panels can be ordered in 2!   Canvas can be ordered in 6!   since relative position of panels to canvas is fixed (Panels 2nd and 6th) the answer is 2! x 6!=1440   1440
Answer: A
Perimeter of the backwheel =9 feet,front wheel=7 feet on a certain distance ,the front wheel gets 10 revolution more than the back wheel.what is the distance  Choose the correct choice from the following
A) 315
B) 2888
C) 270
D) 18191
E) 112

Solution: Let the backwheel made x revolutions then front wheel makes x + 10   x x 9 = (x + 10) x 7   x = 35   So distance traveled = 35 x 9 = 315   315nswer:315
Answer: A
In how many ways can 5 apples (identical) be distributed among 4 children? (Some children may get no apples.)
Select the correct option
A) 56 B) 144 C) 200 D) 256 E) 312

Solution: Let's just represent apple by the letter A and assume that in order to distribute these apples to different people, we just need to partition them in to 4 baskets.   In order to partition the apples in to 4 baskets, we would need three Partition bars , as shown below:   56 | 56 | 5656 | 56   Child 1 Child 2 Child 3 Child 4   So basically we have 3 identical partition bars and 5 identical apples, how many ways can we arrange these?   8!/5!3! = 56   56NS:56
Answer: A
A box contains seven bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good.	Choose the correct choice from the following answers
A) 34/35  B) 125/186  C) 125/126  D) 125/186  E) 125/128

Solution: Required probability   = 1 - 1/35   = 34/35   34/35nswer: 34/35
Answer: A
When a certain number X is divided by 143, the remainder is 45. Which of the following numbers, if added to X, would result in a number divisible by 12? Pick:
A) 7
B) 21
C) 34
D) 47
E) 6

Solution: So the number given is N = 143Q + 45   If this number is divided by 13, the remainder would be R[(143Q + 45)/13]   Since 143 is divisible by 13 , the product 143Q gives no remainder   This means the remainder of 45/13 should be the remainder of the entire number N   which is 6   To make it divisible by 13 , the smallest number that can be added = 12 - 6= 
12 - 6 = 6
6   Correct Option : 6
Answer: E
In a family 13 people eat only vegetarian, 8 people eat only non veg., 6 people eat both veg and non veg.. How many people eat veg in the family?	Choose the correct choice from the following answers.
A) 20
B) 11
C) 19
D) 31
E) 21

Solution: Total people eat veg = only veg + both veg and non veg   Total= 13+6= 
13+6 = 19
19   Answer= 19
Answer: C
A certain fraction has the same ratio to 1/33, as 3/4 does to 7/11. What is this certain fraction?	Answers:
A) 1/14 B) 1/18 C) 1/21 D) 1/25 E) 1/28

Solution: x / (1/33) = (3/4) / (7/11)   x = 3*11*1 / 33*4*7 = 1/28   The answer is 1/28.
Answer: E
A bookshop had science and art books in the ratio of 2:5. By the end of the week, 20% of both type of books were sold and 2240 books were unsold. How many science books were there at the starting?
Choose one
A) 650  B) 670  C) 700  D) 800  E) 890

Solution: science books sold = 2x × 0.2 = 0.4x   science books unsold = 2x – 0.4x = 1.6x   art books sold = 5x × 0.2 = x   art books unsold = 5x – x = 4x   total books unsold = 1.6x + 4x = 5.6x   5.6x 1.6  + 4= 
1.6  + 4 = 5.6
5.6x   5.6x= 2240   x = 400   2x science = 800   800
Answer: D
In how many ways can 5 boys be allotted four different HOSTEL ROOMS such that none of the rooms are empty and all the 5 boys are accommodated?	Options:	A) 260	B) 240	C) 280	D) 290	E) 300

Solution: 4 boys can be selected from 5 boys in 5C4 ways = 5   4 boys can be arranged in 4 rooms in 4! ways   and since 1 boy has to share a room with one of the 4 boys, therefore total ways = 2! = 2   Hence total number of ways in which allocation can be done = 5C4 * 4! * 2! = 5*2*4! =240   240
Answer: B
A person travels from X to Y and vice versa. How long will it take to travel both the ways by bus?
(A) It takes 15 hours in travelling from X to Y by train and returning by bus.
(B) The distance between two places is 360 km.
(C) He can save 3 hrs if he travels both the ways by train.  Choose the most appropriate option.
A) A and B together B) B and C together C) A and C together D) Any two of them E) All statements are required

Solution: from x to y and y to x it takes 15hrs   let time taken by train be a and by bus be b   so a+b=15   train takes 3 hrs less i.e,   a+a=12   2a=12   a=6   6+b=15   b=9   2b=18hrs   ANSWER:A and C together
Answer: C
what is the remainder when 788863203 is divided by 990	Choices:
A) 693  B) 369  C) 769  D) 639  E) 469

Solution: 788863203 / 990   788863203 / 9*110   87651467 / 110 => rem = 77   we have cancelled it by 9   reqd remainder = 9*77= 
9*77 = 693
693   693NSWER:693
Answer: A
A man purchased 5 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets? Choose the correct choice:
A) A)250	B) B)350	C) C)450	D) D)470	E) E)500

Solution: Explanation:   10 * 150= 
10 * 150 = 1_500
1500   5 * 100 + 5 * 150= 
5 * 100 + 5 * 150 = 1_250
1250   1500 – 1250= 250   250
Answer: A
The standard serial numbers for a temporary ID card in a institution are 2 letters followed by 5 digits. How many different ID cards are possible if letters and digits can be repeated?  Pick:
A) 26 × 3 × 10 × 4  B) 26 × 25 × 24 × 10 × 9 × 8 × 7  C) 26³ × 9 × 9 × 9 × 9  D) 26 × 25 × 24 × 10 000  E) 26 x 26 x 100 000

Solution: OFFICIAL SOLUTION:   (E) The formula for permutations of events is the product of the number of ways each event can occur. There are 26 letters and 10 digits. So there are 26 × 26 options for the two letters, and 10 × 10 × 10 × 10 x 10 for the five digits. The number of different license plates is 26 × 26 × 10 × 10 × 10 × 10 x 10 = 26 x 26 × 100 000.   The correct answer is choice (26 x 26 x 100 000).
Answer: E
A number when divided by 20 leaves 6 as a remainder. What will be the remainder if the number is divided by 19? Choose the correct option:
A) 7
B) 6
C) 5
D) 11
E) 13

Solution: Let the minimum whole number be 20+6= 
20+6 = 26
26 where 6 is the remainder.   26 when divided by 19 then leaves 7.   Correct answer 7.
Answer: A
If p and q are positive integers each greater than 1, and 15(p+1)=29(q+1), what is the least possible value of p+q?
Choose the most appropriate option:
A) 36
B) 42
C) 44
D) 46
E) none

Solution: 17(p+1)=29(q+1) --> (p+1)/(q+1) = 29/17 --> the least positive value of p+1 is 29, so the least value of p is 28 and the least positive value of q+1 is 15, so the least value of q is 14 --> the least value of p+q is   28+14= 
  28+14 = 42
42.   Answer: 42.
Answer: B
A circle is inscribed in a Triangle of side 6cm. And a square is inscribed in the Circle. What is the area of square?  Pick one
A) 4 cm^2	B) 6 cm^2	C) 5 cm^2	D) 7 cm^2	E) 8 cm^2

Solution: the radius of the incircle in a equilateral triangle is a/2(sqrt)3 where a=side of triangle=6 cm   so the diameter of the circle would be the diagonal of square   so diagonal=2*a/2(sqrt)3=a/(sqrt)3   so area of square=1/2*(diagonal)^2=6*6/2*3=6 cm^2   ANSWER:6 cm^2
Answer: B
For any numbers a and b, a#b = ab(7 − b). If a and a#b both represent positive numbers, which of the following could be a value of b?
Choose the correct choice from the following options.
A) 6,5,	B) 6,5,4,	C) 6,5,4,3,	D) 6,5,4,3,2	E) 6,5,4,3,2,1

Solution: a#b positive then b may be positive or negative. if positive then b< 7 may be 6,5,4,3,2 or 1 and if negative then it is more than or equal to - 1 negative . ab will be -ve which is not possible as a and a#b should be positive.   ans 6,5,4,3,2,1   6,5,4,3,2,1
Answer: E
Mr. Thomas invested an amount of 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be 3508, what was the amount invested in Scheme B?	Choose the correct choice from the following answers:
A) 6400  B) 6500  C) 7200  D) 7500  E) None

Solution: Explanation: Let the sum invested in Scheme A be x and that in Scheme B be (13900 - x).   Then, (x x 14 x 2)/100 + ((13900 - x) x 11 x 2)/100 = 3508   28x - 22x = 350800 - (13900 x 22)   6x = 45000   x = 7500.   So, sum invested in Scheme B = (13900 - 7500)= 
(13900 - 7500) = 6_400
6400.   6400nswer: Option 6400
Answer: A
4 different airplanes owned by a rock band will be refueling today at the same airport. There are 2 larger planes carrying people and 2 smaller planes carrying equipment. All tanks are empty and will need to be filled completely. The 2 smaller tanks hold 60 liters each and the larger tanks are 50% bigger. Fuel is .50 cents a liter and there is a charge of $100 service for each plane. How much will it cost to fill all 4 planes?	Choices
A) $475
B) $500
C) $525
D) $550
E) $575

Solution: Lots of calculations.   100*4 + 2*60*.50+ 60*(3/2)*2*.50= 
100*4 + 2*60*.50+ 60*(3/2)*2*.50 = 550
$550   The correct option is $550
Answer: D
The ratio between the length and the breadth of a rectangular plot is 7 : 5. If the perimeter of the plot is 432 metres, what is its area?
Choose the correct choice from the following.
A) 11320 sq.metres
B) 11260 sq.metres
C) 11280 sq.metres
D) 11340 sq.metres
E) None of these

Solution: Let the length and breadth be 7x and 5x respectively.   Then, P = 2(7x + 5x) = 432â‡’ x = 18   Area = 7 Ã— 18 Ã— 5 Ã— 18 = 11340 sq.m.   Answer 11340 sq.metres
Answer: D
A train 280 m long, running with a speed of 63 km/hr will pass a tree in? Choose the correct choice from the following.
A) 28 sec
B) 16 sec
C) 21 sec
D) 11 sec
E) 18 sec

Solution: Speed = 63 * 5/18 = 35/2 m/sec   Time taken = 280 * 2/35= 
280 * 2/35 = 16
16 sec   Answer:16 sec
Answer: B
The number of boxes in a warehouse can be divided evenly into 9 equal shipments by boat or 24 equal shipments by truck. What is the smallest number of boxes that could be in the warehouse? Choices
A) 27  B) 33  C) 72  D) 81  E) 162

Solution: Answer is the L72M of 9 and 24   = 72   Answer 72
Answer: C
The length of a room is 5.5 m and width is 3.75 m. Find the cost of paying the floor by slabs at the rate of Rs. 800 per sq.metre	Answers:
A) 22488 B) 16500 C) 27889 D) 23778 E) 29982

Solution: Explanation:   Area = 5.5 × 3.75 sq. metre.   Cost for 1 sq. metre. = Rs. 800   Hence total cost = 5.5 × 3.75 × 800 = 5.5 × 3000 = Rs. 16500   Answer: 16500) Rs.16500
Answer: B
By selling a house for Rs.45000, it was found that 1/4 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c? Choose the correct answer.
A) 38020
B) 38000
C) 38028
D) 38019
E) 34200

Solution: CP + CP/4 = 45000   CP = 36000   SP = 36000*(95/100)= 
36000*(95/100) = 34_200
34200   Answer: 34200
Answer: E
9 friends bought a building together for 1 million dollars. If the each person in the entire group has to pay the same amount and none of them have bills smaller than $1, how much money would they each have to pay?  Choose the correct option:	A) $1,000,000	B) $1,000,001	C) $1,000,004	D) $1,000,007	E) $1,000,009

Solution: In order to divide the sum in 9 parts, the amount must be divisible by 9   Divisibility rule of 9: The sum of the digits must be divisible by 9   Sum of digits of 1,000,000 = 1 and 9 is divisible by 9.   Hence, we need to add 9 to this number for it to be divisible by 9   Correct Option: $1,000,009
Answer: E
Of the 55 cars on a car lot, 40 have air-conditioning, 25 have power windows, and 12 have both air-conditioning and power windows. How many of the cars on the lot have neither air-conditioning nor power windows? Pick one:
A) 15 B) 8 C) 10 D) 2 E) 18

Solution: Total -Neither = All Air Conditioning + All Power Windows - Both   or 55 - Neither = 40 + 25 -12= 
40 + 25 -12 = 53
53.=> Neither = 2, hence D.   Answer : 2
Answer: D
In a tree, 3/5 of the birds are parrots while the rest are toucans. If 1/3 of the parrots are female and 3/4 of the toucans are female, what fraction of the birds in the tree are male?
Select
A) 1/2 B) 2/5 C) 3/5 D) 3/10 E) 7/10

Solution: The fraction of birds that are male parrots is (2/3)(3/5)=2/5.   The fraction of birds that are male toucans is (1/4)(2/5)=1/10.   The total fraction of male birds is 2/5 + 1/10 = 1/2.   The answer is 1/2.
Answer: A