MU-NLPC/Calc-aqua_rat huggingface dataset:
What is the sum of the integers 45 through 175 inclusive? Choose the correct choice from the following options.
A) 12,295
B) 13,000
C) 14,300
D) 14,410
E) 28,820

Solution: sum of n consecutive positive integers=n(n+1)/2..   in one case n=44 and other 175... subtract the sum to get the answer   sum of first 175 +ive numbers=175*176/2=15400..   sum of first 45 +i've numbers=45*44/2=990..   answer=15400-990= 
15400-990 = 14_410
14410   ANSWER:14,410
Answer: D
which of the following options must be accurate if given the equation below: h=-e^7
I. h is positive.
II. If e is negative then h is negative.
III. e is non-negative. Choose one:
A) I only
B) II and III only
C) I and III only
D) II only
E) III only

Solution: I. h is positive --> not true;   II. If h is negative then e is negative. h is negative means that e is not zero. ;   III. e is non-negative.   Answer: II only (I only).
Answer: D
The side of a square has the length of 9. What is the area of the region shaded?  Select:
A) 48-8π  B) 48-6 π  C) 24+6π  D) 16+8π  E) 64-9π

Solution: The area of a square whose side is 9 – (the area of a square whose side is 4 + the area of the semi-circle whose side is 4) = the area of the region shaded   The correct answer is 64-9π.
Answer: E
2 students appeared at an examination. 1 of them secured 9 marks more than the other one and hismarks was 56% of the sum of their marks. Find the marks obtained by them are?	Choose the correct choice
A) 39 and 31
B) 40 and 33
C) 42 and 33
D) 37 and 31
E) 35 and 32

Solution: Let their marks be (x+9) and x.   Then, x+9 = 56/100(x + 9 +x)   => 25(x+9)   => 14 (2x + 9)   => 3x = 99   => x = 33.   So, their marks are 42 and 33   42 and 33
Answer: C
a^2*b^2+a^2+b^2=259
b^2*c^2+b^2+c^2=1299
c^2*a^2+c^2+a^2=499
then find b=?	Choose the correct option:  A) 2  B) 3  C) 4  D) 5  E) 6

Solution: adding 1 to all equqtions.,we get them modified to the following form   (a^2+1)(b^2+1)=260   (b^2+1)(c^2+1)=1300   (c^2+1)(a^2+1)=500   by corresponding mul and div we get a=3,b=5,c=7   ANSWER:5
Answer: D
John and Jane went out for a dinner and they ordered the same dish. Both used a 10% discount coupon. John paid a 15% tip over the original price of the dish, while Jane paid the tip over the discounted price for the coupon. If John paid $0.36 more than Jane, what was the original price of the dish?
Choose the correct answer:
A) 24
B) 34.8
C) 37.8
D) 42
E) 84

Solution: The difference between the amounts John paid and Jane paid is the deference between 15% of p and 15% of 0.9p:   0.15p - 0.15*0.9p = 0.36 --> 15p - 13.5p = 36 --> p = 24.   24nswer: 24.
Answer: A
If a population of women in a town is 50% of men . What is the population of men as a percentage of population of women ? Choose the correct choice from the following.
A) 100%
B) 120%
C) 200%
D) 150%
E) 180%

Solution: We're told that the number of Women in a town is equal to 50% of the number of Men in that town.   Men = 10   Women = 5   We're asked for the number of Men, as a percentage of the number of Women.   M/W %= 10/5 = 200%   Answer is 200%
Answer: C
A sum of money is divided among A, B, C & D in the ratio 3:5:8:9 respectively. If the share of D Rs.1872 more than the share of A, then what is the total amount of money of B & C together?	Choose the most appropriate option:	A) Rs. 4000	B) Rs. 4056	C) Rs. 4060	D) Rs. 4100	E) Rs. 4150

Solution: Sol. Share of B + C = -3 x (5 + 8) = Rs. 4056   Rs. 4056
Answer: B
Train X and train Y pass one another traveling in opposite directions. Twenty minutes later they are 100 miles apart. If train X’s constant speed is 30 miles per hour greater than train Y’s, how far does train X travel during that time?  Choose the correct choice from the following answers.
A) 28  B) 40  C) 55  D) 72  E) 80

Solution: Let the rate of the Train Y be R   Then the rate of the Train X will be R+30 (given)   As per relative rate concept, the rate at which they are increasing the distance between them is R+(R+30) [add the rates] i.e. 2R+30   d=100 and t = 20 min i.e 20/60 hr   using RTD table, (2R+30) * 20/60 = 100 ==> R= 135 miles/hr   So the rate of train X is 165 miles/hr (since R+30)   The distance traveled by Train X in 20 min is R*T = 165 * 20/60= 
165 * 20/60 = 55
55 miles (55)
Answer: C
The speed of a boat in still water in 42 km/hr and the rate of current is 7 km/hr. The distance travelled downstream in 44 minutes is:	Choose the correct choice.
A) 86.6 km  B) 46.6 km  C) 35.9 km  D) 35.6 km  E) 26.6 km

Solution: Speed downstream = (42 + 7)= 
(42 + 7) = 49
49 kmph   Time= 44 minutes =44/60 hour = 11/15 hour   Distance travelled = Time × speed =11/15×49 = 35.9 km   ANSWER:35.9 km
Answer: C
A man buys 60 pens at marked price of 46 pens from a whole seller. If he sells these pens giving a discount of 1% , what is the profit percent?  Choose one: A) 7.6 % B) 7.7 % C) 29.13 % D) 33.6 % E) 37.82 %

Solution: Explanation:   Let Marked price be Re. 1 each   C.P. of 60 pens = Rs. 46   S.P. of 60 pens = 99% of Rs. 60 = Rs. 59.4   Profit % = (Profit /29.13 %.P.) x 100   Profit% = (13.4/46) x 100 = 29.13%   ANSWER: 29.13 %
Answer: C
What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years?  Choose the correct option
A) 64.98
B) 64.29
C) 53.98
D) 64.1
E) 22.13

Solution: n:   S.I. = (1000 * 10 * 4)/100 = Rs. 400   C.I. = [1000 * (1 + 10/100)4 - 1000]   = Rs. 464.10 Difference   = (464.10 - 400)   = Rs. 64.10   Answer:64.1
Answer: D
Two faces of a fair die are Yellow, two faces red and one blue.The die is tossed three
times. The probability that the colours, yellow, red and blue appear in the first, second and
third tosses respectively is Choose one: A) 1/36 B) 1/18 C) 1/32 D) 1/54 E) None of these

Solution: Probability of getting yellow color = P(Y) = 2/6 = 1/3   Probability of getting red color = P(R) = 2/6 = 1/3   Probability of getting blue color = P(B) = 1/6   So, the probability that the colors yellow, red and blue appear in first, second and third toss respectively= P(Y ∩ R ∩ B) = P(Y) x P(R) x P(B) = 1/3 x 1/3 x 1/6 = 1/54   ANSWER:1/54
Answer: D
A big container is 30% full with water. If 36 liters of water is added, the container becomes 3/4 full. What is the capacity of the big container? Choose the most appropriate option:
A) 36 liters B) 40 liters C) 45 liters D) 54 liters E) 80 liters

Solution: A big container is 30% full with water and after 36 liters of water is added, the container becomes 75% full. Hence these 36 liters account for 45% of the container, which means that the capacity of it is  36/0.45= 
 36/0.45 = 80
80 liters.   OR: if the capacity of the container is x liters then: 0.3x+36=0.75x --> x=80 liters.   Answer: 80 liters.
Answer: E
Find the middle one when The sum of three consecutive even numbers is 36? Choose the correct answer:
A) 10  B) 12  C) 13  D) 15  E) 16

Solution: 3 consecutive numbers can be a - 1, a, a + 1   So sum of numbers = 3a = 36.   Hence a = 12.   12
Answer: B
10 men can complete a work in 7 days. But 10 women need 14 days to complete the same work. How many days will 5 men and 10 women need to complete the work? Pick:
A) 5
B) 6
C) 7
D) 8
E) 10

Solution: Work done by 10 men in 1 day = 1/7   Work done by 1 man in 1 day = (1/7)/10 = 1/70   Work done by 10 women in 1 day = 1/14   Work done by 1 woman in 1 day = 1/140   Work done by 5 men and 10 women in 1 day = 5 × (1/70) + 10 × (1/140)   = 5/70 + 10/140 = 1/7   = 5 men and 10 women can complete the work in 7 days Answer : Option 7
Answer: C
A couple decides to have 3 children. If they succeed in having 3 children and each child is equally likely to be a boy or a girl, What is the probability that they will have exactly 1 girl and 2 boys? Select: A) 3/4 B) 1/2 C) 5/8 D) 1 E) 1/4

Solution: Sample space = 2^3 = 8   Favourable events = {bgg}, {bgb}, {bbb}, {ggg}, {gbg},   Probability = 5/8 = 5/8.   Ans (5/8).
Answer: C
The average of first five multiples of 3 is
Choices:
A) 3	B) 6	C) 9	D) 12	E) 15

Solution: Solution   Average	= 3(1+2+3+4+5) / 5   = 45 / 5.= 
45 / 5. = 9
9.   Answer 9
Answer: C
In how many years, Rs. 200 will produce the same interest @ 5 % as Rs. 900 produce in 2 years @ 3 ½ %?
Choose one.
A) 6.3 years B) 8.2 years C) 9 years D) 12 years E) None of these

Solution: Explanation:   P = Rs 900, R = 3 ½ % = 7/2 %, T = 2 years.   Therefore,   S.I. = PRT/100   S.I. = Rs. (900 x 7/2 x 2/100) = Rs. 63   Now, P = Rs. 200, S.I. = Rs. 63, R = 5 %   Time = ((100 x 63) / (200 x 5) ) years = 6.3 years   6.3 yearsNSWER 6.3 years
Answer: A
In the new budget the price of Petrol rose by 20%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase? Choose the correct option.
A) 16.67%  B) 25%  C) 20.45%  D) 31.56%  E) 40%

Solution: Reduce in consumption = R/(100+R) *100% = 20/120 *100 = 16.67%   16.67%nswer is 16.67%
Answer: A
At what price must an article costing Rs.57 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
Choose one.
A) 62.5
B) 69.5
C) 62.3
D) 62.1
E) 75

Solution: CP = 57   SP = 57*(125/100)= 
57*(125/100) = 285/4 = around 71.25
71.25   MP*(95/100)= 71.25   MP = 75   Answer:75
Answer: E
If the diameter of circle R is 20% of the diameter of circle S, the area of circle R is what percent of the area of circle S?	Pick one:  A) 5%  B) 10%  C) 15%  D) 14%  E) 4%

Solution: Let diameter of circle R , dr = 20   and diameter of circle S , ds = 100   Radius of circle R , Rr = 10   Radius of circle S , Rs = 50   Area of circle R/ Area of circle S = (pi * Rr ^2 ) /( pi * Rs^2 )   = (10/50)^2 = (2/10)^2   =4%   Answer :4%
Answer: E
If 3^e- 3^(e-1) = 162 then e(e-1) =
Choose the correct answer
A) 12
B) 16
C) 20
D) 30
E) 81

Solution: It seems like you were really close but you solved for e - 1 instead. I am curious - how did you reason through the question? Perhaps you figured the answer has to be in the form of e(e -1), e.g. (3)(4) = 12. Even then, had you figured e has to be a little bigger (plugging in 4 for e gives you 81 which is too low), So when you reasoned the answer to be 4 you may have plugged the 4 in the (e - 1) exponent place.   Again, a quick plugging in should get you (20) 20 as the only other answer with consecutive integers as factors is far too big.
Answer: C
The average age of 15 students of a class is 15 years. Out of these, the average age of 6 students is 14 years and that of the other 9 students is 16 years, The age of the 15th student is Answers:
A) 11
B) 12
C) 13
D) 14
E) 15

Solution: Explanation:   Age of the 15th student = [15 * 15 - (14 * 6 + 16 * 8)= 
15 * 15 - (14 * 6 + 16 * 8) = 13
13 years. Answer: 13
Answer: C
The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?	Choose the correct choice from the following:  A) 40, 68 kmph  B) 40, 30 kmph  C) 90, 60 kmph  D) 40, 60 kmph  E) 20, 60 kmph

Solution: Speed downstream = 60 + 20= 
60 + 20 = 80
80 kmph   Speed upstream= 60 - 20= 
60 - 20 = 40
40 kmph   Answer: 40, 60 kmph
Answer: D
A woman has three blouses of different colors, two skirts of different colors, and two different pairs of shoes. She refuses to wear her pink blouse with her green skirt. How many different blouseskirt-shoe combinations could she wear?	Choose the correct choice from the following answers
A) 8
B) 12
C) 16
D) 10
E) 18

Solution: total ways = 3*2*2=12..   now its better to find the ways in which the pink blose and green skirty are together and subtract from total to get the answer..   the ways in which the pink blose and green skirty are together=1*1*2=2..   total ways =12-2=10..   10
Answer: D
How many halves are there in one-fourth? Options: A) 0.02 B) 12 C) 32 D) 0.7 E) 0.5

Solution: divide 1/4 by 1/2   =1/4÷1/2   =1/4*2/1   =2/4   =0.5.   Answer is 0.5.
Answer: E
A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have? Choose the correct option:  A) 50  B) 88  C) 77  D) 66  E) 51

Solution: 50+B+C = 500   50+C = 200   B+C = 350   --------------   50+B+2C = 550   50+B+C = 500   ----------------   C = 50   50nswer:50
Answer: A
What will be the percentage increase in the area of the cube's surface if each of the cube's edges grows by 10%? Choose the correct choice from the following options:
A) 25%  B) 28%  C) 21%  D) 30%  E) 32%

Solution: The question is very easy. My logic is the following:   A surface = 6*a^2   After 10% increase A surface = 6* ((1.1a)^2) = 6*1.21*a^2   The increase in the surface area = (6*1.21*a^2 - 6*a^2)/6*a^2 = (6*a^2(1.21-1))/(6*a^2) = 1.21-1= 
1.21-1 = 0.21
0.21= 21%   Answer : 21%
Answer: C
In a colony of 50 residents, the ratio of the number of men and women is 3:2. Among the women, the ratio of the educated to the uneducated is 1:3. If the ratio of the number of education to uneducated persons is 4:6, then find the ratio of the number of educated and uneducated men in the colony?  Pick
A) 1:1 B) 3:2 C) 1:3 D) 2:5 E) 5:7

Solution: Number of men in the colony = 3/5 (50) = 30   Number of women in the colony = 2/5 (50) = 20   Number of educated women in the colony = 1/4 (20) = 5   Number of uneducated women in the colony = 3/4 (20) = 15   Number of educated persons in the colony = 4/10 (50) = 20   As 5 females are educated, remaining 15 educated persons must be men.   Number of uneducated men in the colony = 30 - 15= 
30 - 15 = 15
15   Number of educated men and uneducated men are in the ratio 15:15=> 1:1   1:1nswer:1:1
Answer: A
Two dice are tossed. The probability that the total score is a prime number is: Options:
A) 5/5  B) 5/9  C) 5/1  D) 5/7  E) 5/12

Solution: n(S) = (6 x 6) = 36.   Let E = Event that the sum is a prime number.   Then E	= { (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3),   (5, 2), (5, 6), (6, 1), (6, 5) }   n(E) = 15   The total cases are   6 * 6 * 6= 
  6 * 6 * 6 = 216
216.   The probability= 15/36 = 5/12.   Answer: 5/12
Answer: E
If x and y are positive integers such that x < y and z=x/y, which of the following must be true?
I. z<(x − 1)/y
II. z<(x − 1)/(y − 1)
III. z>(x + 1)/(y + 1)
Answers:
A) I only	B) I and II	C) II and III	D) II only	E) None of these

Solution: x < y --> Let x = 2 and y = 3 --> z = 2/3   I. z<(x − 1)/y --> 2/3 < 1/3 --> False   II. z<(x − 1)/(y − 1) --> 2/3 < 1/2 --> False   III. z>(x + 1)/(y + 1) --> 2/3 > 3/4 --> False   Answer: None of these
Answer: E
Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is? Choose the correct choice from the following choices:
A) 638	B) 738	C) 375	D) 98	E) 8303

Solution: A+B+375 = 1500   A = 1/3(B+375); B = 2/3(A+375)   A/(B+375) = 1/3   A = 1/4 * 1500= 
1/4 * 1500 = 375
> 375   Answer:375
Answer: C
Ten stickers numbered 1 to 10 are placed in a bowl, mixed up thoroughly and then one sticker is drawn
randomly. If it is known that the number on the drawn sticker is more than 3, what is the probability
that it is an even number? Choose the correct choice from the following answers:
A) 3/7  B) 4/7  C) 5/7  D) 7/11  E) 9/11

Solution: Let A be the event ‘the number on the card drawn is even’ and B be the   event ‘the number on the card drawn is greater than 3’. We have to find P(A|B).   Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}   Then A = {2, 4, 6, 8, 10}, 4/7 = {4, 5, 6, 7, 8, 9, 10}   and A n 4/7 = {4, 6, 8, 10}   Also P(A) = 5/2, P(4/7) = 7/10 and P(A n 4/7) = 4/10   Then P(A|4/7) = P(A n 4/7)/P(4/7) = (4/10)/(7/10)	= 4/7   4/7)
Answer: B
In a renowned city, the average birth rate is 10 people every two seconds and the death rate is 2 people every two seconds. Estimate the size of the population net increase that occurs in one day. Pick:
A) 32,300  B) 172,800  C) 345,600  D) 338,200  E) 259,200

Solution: Every 2 seconds, 8 persons are added (10-2). Every second 4 persons are added.   In a day 24hrs = 24 * 60 Minutes = 24 * 60 * 60= 
24 * 60 * 60 = 86_400
86400 seconds.   86400 * 4= 
86400 * 4 = 345_600
345600   Option 345,600
Answer: C
A man can row his boat with the stream at 6 km/h and against the stream in 3 km/h. The man's rate is?	Answers.
A) 1.5 kmph B) 3 kmph C) 8 kmph D) 7 kmph E) 5 kmph

Solution: DS = 6   US = 3   S = ?   S = (6 - 3)/2= 
(6 - 3)/2 = 3/2 = around 1.5
1.5 kmph   1.5 kmphnswer: 1.5 kmph
Answer: A
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The sum of the first 53 positive even integers is 2550. What is the sum of the even integers from 96 to 200 inclusive?	Pick one
A) 5,100  B) 7,844  C) 10,100  D) 15,500  E) 20,100

Solution: even numbers from 96 to 200=104/2+1= 
104/2+1 = 53
53   Sum= (200+96)x53/2=7844   So 7,844 is the ans.
Answer: B
Carmelo and LeBron participate in a five-person footrace on the basketball court during All-Star Weekend. If all five contestants finish (including Charles Barkley) and there are no ties, how many different arrangements of finishes are there in which Carmelo defeats LeBron? Choose the correct choice from the following:
A) 5040	B) 2520	C) 720	D) 120	E) 60

Solution: 5! = 120   120/2= 
120/2 = 60
60 half the time carmelo is in front, vice versa   Answer:   (60) 60
Answer: E
Given the equation 7^p-3^(-p)=6.7, which of the following options is the correct value of p?	Pick one:
A) 1	B) 2	C) 3	D) 5	E) 0

Solution: Plugging in the various option into the equation to find out which is correct:   7^p-3^(-p)=6.7   7^1-3^(-1)=6.7 Ans. 1
Answer: A
There is a 50 cm line marked at each centimeter and an insect is placed at every centimeter. 9 frogs are trained to jump a constant distance. The first one jumps 2 cm in every leap, the second one jumps 3 cm and so on until the 9th one jumps 10 cm in every leap and they eat any insect that is available at that spot. If all of them start from start line and finish the entire 50 cm, how many insects were still left after the race was over?	Pick one:
A) 0
B) 4
C) 6
D) 8
E) 11

Solution: Only the prime numbers greater than 10 and less than 50 were left.   That is 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47.   The total is 11.   The answer is 11.
Answer: E
If each digit in the set A = {1, 2, 3, 4, 5, 6} is used exactly once, in how many ways can the digits be arranged?
Pick:  A) 720  B) 830  C) 940  D) 1050  E) 1160

Solution: 6! = 720   The answer is 720.
Answer: A
One half of a two digit number exceeds its one third by 6. What is the sum of the digits of the number?
Choose the correct choice from the following options.
A) 7	B) 9	C) 11	D) 12	E) 15

Solution: Explanation:   x/2 – x/3 = 6 => x =6   3 + 6= 
3 + 6 = 9
9   9)
Answer: B
For any non-zero a and b that satisfy |ab| = ab and |a| = -a, |b-3| + |ab-b| =
Pick one:  A) ab-4+b  B) 2b-ab-4  C) ab+4  D) ab-2b+5  E) 4-ab

Solution: Given: |ab| = ab and |a| = -a   Question: |b-3| + |ab-b| = ?   **** Looking at |ab| = ab tells us that a and b are either both positive or negative   **** Looking at |a| = -a tells us that a must be negative   **** ab+4ombine two observations: a and b are both negative values   Let a=-1 and b=-1   |b-4| + |ab-b| = |-1-3| + |1-(-1)| = 5   Test a) ab-4 = (-1)(-1)-4 = -5   Test b) 2b-ab-4 = (2)(-1) - (1) - 4 = -7   Test c) ab+4 = 1 + 4= 
1 + 4 = 5
5   Answer: ab+4
Answer: C
There are 9 cities numbered 1 to 9.From how many cities the flight can start so as to reach the city 8 either directly or indirectly such that the path formed is divisible by 3.	Select the correct option:
A) 7	B) 8	C) 9	D) 10	E) 11

Solution: Start from 1: 1368, Start from 2: 2358, Start from 3: 378, Start from 4: 48, Start from 5: 528, Start from 6: 678, Start from 7: 78, Why start from 8???, Start from 9: 918. So flights can start from all 8 other cities.   ANSWER:8
Answer: B
One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in Select: A) 144 mins B) 140 mins C) 136 mins D) 132 mins E) None of these

Solution: Explanation:   Let the slower pipe alone fill the tank in x minutes   then faster will fill in x/3 minutes.   Part filled by slower pipe in 1 minute = 1/x   Part filled by faster pipe in 1 minute = 3/x   Part filled by both in 1 minute =   1/x+3/x=1/36   =>4/x=1/36   x=36∗4=144mins   144 minsnswer: Option 144 mins
Answer: A
A bag contains 18 purple jellybeans, 14 green jellybeans, and 12 yellow jellybeans; these jellybeans are the only items in the bag. If a person picks a jellybean at random out of the bag, what is the probability that the jellybean will be green?
Choose the correct choice from the following
A) 15%  B) 20%  C) 32%  D) 30%  E) 35%

Solution: Probability of green beans = 14 / (18 + 14 + 12) = 14/44 = 32%   Answer is 32%
Answer: C
In what time will a railway train 52 m long moving at the rate of 24 kmph pass a telegraph post on its way?	Choose the correct choice from the following
A) 3 sec
B) 4 sec
C) 8 sec
D) 6 sec
E) 7 sec

Solution: T = 52/24 * 18/5 = 8 sec   ANSWER:8 sec
Answer: C
The weights of three boys are in the ratio 4 : 5 : 6. If the sum of the weights of the heaviest and the lightest boy is 45 kg more than the weight of the third boy, what is the weight of the lightest boy?	Choose the most appropriate option:
A) 87 kg	B) 36 kg	C) 98 kg	D) 65 kg	E) 87 kg

Solution: Let the weights of the three boys be 4k, 5k and 6k respectively.   4k + 6k = 5k + 45   => 5k = 45 => k = 9   Therefore the weight of the lightest boy   = 4k = 4(9) = 36 kg.   Answer:36 kg
Answer: B
A club with a total membership of 25 has formed 3 committees, M, S and R, which have 8, 12 and 5 members respectively. If no members of committee M is on either of the other 2 committees, what is the greatest possible number of members in the club who are on none of the committees? Choose the most appropriate option.
A) 5  B) 7  C) 8  D) 10  E) 12

Solution: As no member of committee M is on either of the other 2 committees then 25-M=25-8= 
25-8 = 17
17 people are on committee S, committee R or on none of the committee. We want to maximize the last group: members in the club who are on none of the committees   General rule for such kind of problems:   to maximize one quantity, minimize the others;   to minimize one quantity, maximize the others.   So we should minimize total # of people who are on committee S and committee R. Now if ALL 5 people who are the members of committee R are also the members of committee S (if R is subset of S) then total # members of committee S and committee R would be minimized and equal to 12. Which means that 17-12= 
17-12 = 5
5 is the greatest possible number of members in the club who are on none of the committees.   5nswer: 5.
Answer: A
Solve the equation for x : 19(x + y) + 17 = 19(-x + y) - 21 Answers:
A) 1  B) 2  C) -1  D) -3  E) -4

Solution: -1   -1   19x + 19y + 17 = -19x + 19y - 21   38x = -38 => x = -1
Answer: C
A is half good a work man as B and together they finish a job in 13 days. In how many days working alone B finish the job? Choose the correct choice from the following options:
A) 23
B) 22
C) 39/2
D) 36
E) 48

Solution: 39/2   39/2   W39/2 = 1:2   2x + x = 1/13 => x = 1/39   2x = 2/39 => 39/2 days
Answer: C
How many diagonals does a 58-sided convex polygon have?
Pick:  A) 870  B) 1125  C) 1595  D) 2560  E) 3190

Solution: A 58-sided convex polygon has 58 vertices.   If we examine a single vertex, we can see that we can connect it with 55 other vertices to create a diagonal. Note that we can't connect the vertex to itself and we can't connect it to its adjacent vertices, since this would not create a diagonal.   If each of the 58 vertices can be connected with 55 vertices to create a diagonal then the total number of diagonals would be (58)(55) = 3190   However, we must recognize that we have counted every diagonal twice.   To account for counting each diagonal twice, we must divide 3190 by 2 to get 1595.   The answer is 1595.
Answer: C