MU-NLPC/Calc-aqua_rat huggingface dataset:
If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 16?  Choose the correct answer:
A) 1/4
B) 3/8
C) 1/2
D) 9/16
E) 3/4

Solution: I get 5/8 as well   1 to 96 inclusive means we have 48 odd and 48 even integers   E O E / 16 = Integer, therefore we have 48 / 96 numbers divisible by 8   O E O / 16 = Not Integer   We cannot forget multiples of 16 from 1 to 96   We have 6 numbers that are multiple of 16   Therefore, 48/96 + 6/96 = 54/96 = 9/16   answer : 9/16
Answer: D
Out of three consecutive odd numbers eleven times the first number is equal to addition of thrice the third number and adding 8 to five times the second . What is the first number?	Answers:
A) 10
B) 6
C) 11
D) 8
E) 9

Solution: Description :   => 11x=5(x+2)+8+3(x+4)   => 11x=8x+30   => 3x=30   X=10   10nswer 10
Answer: A
In a game, one player throws two fair, six-sided die at the same time. If the player receives at least a three or a one on either die, that player wins. What is the probability that a player wins after playing the game once?	Choose the correct choice.
A) 1/3
B) 4/9
C) 5/9
D) 2/3
E) 3/4

Solution: We're looking for the number of outcomes that include AT LEAST a 1 or a 3.   #getting a one in 1st die = {(1,1), (1,2), ...(1,6) }= 6   #getting a one in 2nd die {(2,1), ...(5,1),(6,1) } = 4 [exclude 1,1 and 3,1] since it will be counted twice   #getting a three in 1st die {(3,1), (3,2), ...(3,6) }= 6   #getting a three in 1st die {(2,3), (4,3), ...(6,3) } = 4 [exclude 1,3 and 3,3] since it will be counted twice   Total possibities = 20   Probability of rolling at least a 1 or a 3 on two dice: 20/36 = 5/9   5/9
Answer: C
What will come in place of the question mark (?) in the following questions?
18.2% of 890 = ? Choose the most appropriate option:	A) 161.98	B) 234.98	C) 642.98	D) 141.98	E) 211.98

Solution: 161.98   161.98   ? = (890 * 18.2)/100= 
(890 * 18.2)/100 = 161.98
161.98
Answer: A
Two employees X and Y are paid a total of Rs. 506 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? Choices.
A) s.250  B) s.280  C) s.290  D) s.299  E) s.230

Solution: Let the amount paid to X per week = x   and the amount paid to Y per week = y   Then x + y = 506   But x = 120% of y = 120y/100 = 12y/10   ∴12y/10 + y = 506   ⇒ y[12/10 + 1] = 506   ⇒ 22y/10 = 506   ⇒ 22y = 5060   ⇒ y = 5060/22 = 460/2 = Rs.230   s.230
Answer: E
In a hockey championship, there are 153 matches played. Every two team played one match with each other. The number of teams participating in the championship is: Select the correct option:
A) 16  B) 17  C) 18  D) 19  E) 14

Solution: Let there were x teams participating in the games, then total number of matches,   nC2 = 153.   On solving we get,   => n =−17 and n =18.   It cannot be negative so,   n = 18 is the answer.   OPTION:18
Answer: C
Narendra started a business, investing 30000. Six months later, Chandan joined him with 15000. If they make a profit of 10000 at the end of the year, what should be the share of Narendra? Choose the most appropriate option
A) Rs.7000	B) Rs.8000	C) Rs.8500	D) Rs.8600	E) Rs.8700

Solution: The ratio of their investments = 30000 × 12 : 15000 × 6 = 4 : 1.   :. Narendra’s share on profit of Rs.10000 = 10000 × 4/5 = Rs.8000.   Rs.8000)
Answer: B
In a certain circle there are 10 points. What is the number of the triangles connecting 4 points of the 10 points? Pick one.
A) 80
B) 96
C) 108
D) 120
E) 210

Solution: IMO : E   HERE we have to select 4 points out of 10 points. Order is not important   So the answer will be 10c4 = 210
Answer: E
Jim and Reneey will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Reneey have an equal chance of choosing any one of the hand signs, what is the probability that Jim will win?  Choose the correct choice from the following choices:
A) 5/6
B) 2/3
C) 1/2
D) 5/12
E) 1/3

Solution: 1/3   probability of jim winning is basically the sum of three probabilities:   probability of jim picking rock and reneey picking scissors = 1/3*1/3 = 1/9   probability of jim picking scissors and reneey picking paper = 1/3*1/3=1/9   probability of jim picking paper and reneey picking rock = 1/3*1/3=1/9   1/9 + 1/9 + 1/9 = 3/9 = 1/3=1/3
Answer: E
John distributes his pencil among his 4 friends Rose, Mary, Ranjan, and Rohit in the ratio 1/5 : 1/3 :1/4:1/5 . What is the minimum no. of pencils that the person should have?	Choices:
A) 59  B) 65  C) 70  D) 77  E) 98

Solution: Rakesh : Rahul : Ranjan : Rohit = 1 / 5 : 1 / 3 : 1 / 4 : 1 / 5   Step 1: At First we need to do is LCM of 2,3,4 and 5 is 60.   Step 2: Then pencil are distributed in ratio among friends,   Rakesh = ( 1 / 5 x 60 ) = 12   Rahul = ( 1 / 3 x 60 ) = 20.   Ranjan = ( 1 / 4 x 60 ) = 15.   Rohit = ( 1 / 5 x 60 ) = 12.   Step 3: Total number of pencils are ( 12 x + 20 x + 15 x + 12 x) = 59 x.   For minimum number of pencils x = 1 .   The person should have at least 59 pencils.   59)
Answer: A
A research team is to consist of 3 scientists from Company A and 3 scientists from Company B. If the pool of available scientists from Company A is 5 and the pool of available scientists from Company B is 4 scientists, how many different research teams are possible? Choose the correct choice from the following options: A) 84 B) 40 C) 30 D) 20 E) 12

Solution: C35∗C34=40   Answer: 40.
Answer: B
The product of all the prime numbers less than 22 is closest to which of the following powers of 10?	Choose the correct choice from the following:
A) 10^9 B) 10^8 C) 1*10^7 D) 10^6 E) 10^5

Solution: Quickly approximate   2, 3, 5, 7, 11, 13, 17, 19   =2.1x10^2*1.3*1.7*1.9   =9.69* 10^6   =1*10^7   1*10^7
Answer: C
Tough and Tricky questions: Exponents.
If a and b are positive integers and x = 4^a and y = 3^b, which of the following is a possible units digit of xy? Choices.
A) 1 B) 8 C) 5 D) 7 E) 9

Solution: Only Units digit of X and Y contribute to the Units digit of XY.   Finding all values ofXfor positive values ofa   When,   a=1; X=4   a=2; X=16   a=3; X=64........ Units digit repeat in a cycle of 4,6,4,6......   Similarly, Finding all values of Y for positive values ofb   b=1; Y=3   b=2; Y= 9   b=3; Y= 27   b=4; Y=81   b=5; Y=243....... Units digit repeat in cycle of 3,9,7,1,3,9....   So, possible value of Units digit of XY can be found by considering all possibilities of Units digit of X and Y   When X=4 and Y=3: Units digit of XY = 12   When X=4 and Y=9: Units digit of XY = 36   When X=4 and Y=7: Units digit of XY = 28   When X=4 and Y=1: Units digit of XY = 4   Only four possibilities for Units digit of XY i.e. 4, 2, 8 and 6.   Only 8 is given in answer choices, therefore answer is 8
Answer: B
What is the remainder if 7^12 is divided by 100?  Select: A) 1 B) 2 C) 3 D) 4 E) 5

Solution: 7^16 can be written as (7^4)^3   If we divide 7^4 by 100 the reminder is 1   So, (7^4)^3 by 100, the reminder is 1^3 = 1   1nswer : 1
Answer: A
A retail item is offered at a discount of d percent (where d > 10), with a 5% state sales tax assessed on the discounted purchase price. If the state sales tax were not assessed, what percent discount from the item’s original retail price, in terms of d, would result in the same final price?	Pick one
A) d+5/1.05	B) d/1.05 +5	C) 1.05d-5	D) d-5/1.05	E) 1.05(p – 5)

Solution: Let x be the price of the item.   Final price after discount and sales tax = x * (1 - d/100) * 1.05   Let e be the percent discount which would result in the same final price.   Then,   x * (1 - d/100) * 1.05 = x * (1 - e/100)   => 1.05 - 1.05d/100 = 1 - e/100   => e/100 = 1.05d/100 - .05   => e = 1.05d - 5   Hence ,option 1.05d-5 is correct.
Answer: C
If a fair die is rolled once, what is the probability that a 3 occurs on at least one roll?
Choose the correct answer
A) 25/36	B) 125/216	C) 1/6	D) 1/36	E) 5/6

Solution: Questions such as these that talk aboutat leastormaximumorminimumin probability questions should make sure realize that probability of any event (N) to occur = 1- P(Not N)   Thus, the probability of at least 1 roll = 1- Probability of NO 3s = 1- (5/6) = 1-5/6 = 1/6   5/6 is the probability of NOT getting a 3 in any 1 roll with 5 allowed numbers (=1,2,4,5,6) out of a total of 6 possibilities.   1/6 is thus the correct answer.
Answer: C
When Usha was thrice as old as Nisha, her sister Asha was 25, When Nisha was half as old as Asha, then sister Usha was 34. their ages add to 100. How old is Usha?  Answers:  A) 40  B) 41  C) 42  D) 43  E) 45

Solution: Let the age of Usha is 3x then Nisha is x and Asha is 25   Also Usha 34, Nisha y, and Asha 2y.   We know that 3x - 34 = x - 2y = 25 - 2y   Solving above three equations we get x = 9, y = 16   Their ages are 34, 16, 32. whose sum = 82. So after 18 years their ages will be equal to 100. So Usha age is  34 + 6= 
 34 + 6 = 40
40   40nswer:40
Answer: A
For every positive integer n, the nth term of a sequence is the total sum of three consecutive integers starting at n. What is the total sum of terms 1 through 80 of this series?
Choose the correct choice from the following.
A) 8990
B) 9380
C) 9630
D) 9960
E) 10,240

Solution: Each term of the series has the form (n+n+1+n+2) = 3n+3   Since the series goes from 1 to 80, the sum of the series is:   3(1+2+...+80) + 80(3) ( + +1+ +2)= 
( + +1+ +2) = 3
3n+3   Since the series goes from 1 to 80, the sum of the series is:   3(1+2+...+80) + 80(3)=   3(80)(81)/2 + 80(3) =   120*81 + 240= 
120*81 + 240 = 9_960
9960   The answer is 9960.
Answer: D
A certain board game is played by rolling a pair of fair six-sided dice and then moving one's piece forward the number of spaces indicated by the sum showing on the dice. A player is "frozen" if her opponent's piece comes to rest in the space already occupied by her piece. If player A is about to roll and is currently six spaces behind player B, what is the probability that player B will be frozen after player A rolls?
Answers:
A) 1/12	B) 5/36	C) 1/6	D) 1/3	E) 17/36

Solution: no. of possible outcomes = 6*6= 
6*6 = 36
36   no. of outcomes that result a total of 6 (as A is 6 spaces behind 5/36)= 5 ( (1,5), (2,4), (3,3), (4,2), (5,1) )   So, the probability = 5/36 (Option 5/36)
Answer: B
Two spherical balls lie on the ground touching. If one of the balls has a radius of 6 cm, and the point of contact is 8 cm above the ground, what is the radius of the other ball?  Select.
A) 12 cm	B) 16 cm	C) 18 cm	D) 20 cm	E) none of the these

Solution: similar triangle properties..   2/r+6 = 6/r-6   giving r = 12.   12 cmnswer: 12 cm
Answer: A
What is the difference between the place value and the face value of 9 in the numeral 296827? Choose the most appropriate option:
A) None of these  B) 89993  C) 89991  D) 89994  E) 89995

Solution: Explanation:   Place value of 9 = 90000   Face value of 9 = 9   Difference = 9000 - 9 = 89991   Answer: 89991
Answer: C
A whale goes on a feeding frenzy that lasts for 5 hours. For the first hour he catches and eats x kilos of plankton. In every hour after the first, it consumes 3 kilos of plankton more than it consumed in the previous hour. If by the end of the frenzy the whale will have consumed a whopping accumulated total 450 kilos of plankton, how many kilos did he consume on the third hour? Choose the correct choice from the following choices:
A) 38
B) 47
C) 50
D) 53
E) 93

Solution: If you list the amount eaten each hour, you'll get an equally spaced list, increasing by 3 each hour. In any equally spaced list, the median equals the mean. Here, the mean is  450/5= 
 450/5 = 90
90, so the median is also 90, and that is the amount eaten in the 2nd hour. We need to add 3 to find the total eaten in the next hour, so the answer is 93   option 93
Answer: E
A man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 20%, he is only able to save Rs. 250 per month. What is his monthly salary?
Options: A) 5000 B) 2999 C) 2878 D) 6250 E) 2771

Solution: Income = Rs. 100   Expenditure = Rs. 80   Savings = Rs. 20   Present Expenditure 80*(20/100) = Rs. 96   Present Savings = 100 â€“ 96 =Rs. 4   100 ------ 4   ? --------- 250 => 6250   Answer: 6250
Answer: D
If the average (arithmetic mean) of seven consecutive integers is k - 2, then the product of the greatest and least integer is  Choose the correct choice from the following options
A) k2 - 9  B) k2 - 2k + 1  C) k2 - 4k - 5  D) k2 + 6k + 9  E) k2 + 4k - 12

Solution: n = smallest number   n+6 = largest number   (n + n + 6)/2 = k - 2   => (2n+6)/2 = k - 2   => n + 3 = k - 2   => n = k - 5   So Product of n and n+6 = (k-5)(k+1)   = k^2 - 5k + k - 5   = k^2 - 4k - 5   Answer - k2 - 4k - 5
Answer: C
Johnson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.7. The probability that vice-president Baker will approve the proposal is 0.5. The probability that vice-president Corfu will approve the proposal is 0.4. The approvals of the three (vice presidents)/VPs are entirely independent of one another.
Suppose the Johnson must get VP Adam’s approval, as well as the approval of at least one of the other VPs, Baker or Corfu, to win funding. What is the probability that Johnson’s proposal is funded? Choose one
A) 0.5  B) 0.6  C) 0.7  D) 0.49  E) 0.8

Solution: probability of adams approval = 0.7   baker approval =0.5   corfu approval=0.4   proabability of approval is must adam approval and atleast one approval   = adam approval*baker approval*corfu approval(approval of both remaining)+adam approval*baker approval*corfu not approval(atleast one remaining approval)+   adam approval*baker not approval*coffu approval( atleast one remaining approval   = 0.7*0.5*0.4+0.7*0.5*0.6+0.7*0.5*0.4   =0.14+0.21+0.14= 
0.14+0.21+0.14 = 0.49
0.49   0.49
Answer: D
A train 130 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
Choose the correct choice from the following answers.
A) 4 B) 7 C) 5 D) 9 E) 8

Solution: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr   [66 * 5/18] m/sec = [55/3] m/sec.   Time taken to pass the man = [130* 3/55] sec = 7 sec   ANSWER:7
Answer: B
An auction house charges a commission of 25% on the first $50,000 of the sale price of an item, plus 10% on the amount of of the sale price in excess of $50,000. What was the price of a painting for which the house charged a total commission of $24,000? Choose the correct choice:
A) $115,000	B) $165,000	C) $215,000	D) $240,000	E) $365,000

Solution: Say the price of the house was $x, then 0.25*50,000+0.1*(x-50,000)=24,000 --> x=$165,000 (25% of $50,000 plus 10% of the amount in excess of $50,000, which is x-50,000, should equal to total commission of $24,000).   Answer: $165,000.
Answer: B
A 250 m long train is running at a speed of 55 Km/hr. It crossed a platform of length 520 m in ? Choose the correct choice from the following choices:
A) 40.4 sec
B) 40.5 sec
C) 50.4 sec
D) 50.5 sec
E) 60.4

Solution: Speed = 55 Km/hr   (to convert km/hr in to M/s)   = 55 x 5/18 M/s   Distance = 250 m + 520 m ( If questions is about train crossing a post you need to consider only the length of Train, )   = 770 m   Time = Distance / Speed   = 770 x 18 / (5 x 55)   = 50.4 sec   correct 40.4 secnswer: option a
Answer: A
A hall 36m long and 15m broad is to be paved with stones, each measuring 2dm by 5 dm. The number of stones required is: Choose the correct answer:
A) 180
B) 1800
C) 5400
D) 18000
E) 1.8

Solution: Area of the hall= 3600*1500   Area of each stone= (20*50)   Therefore, number of stones= (3600*1500/ 20*50)= 5400   ANSWER:5400
Answer: C
A boy has seven trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?  Choose the correct choice
A) 88
B) 98
C) 106
D) 108
E) 84

Solution: Explanation:   The boy can select one trouser in seven ways.   The boy can select one shirt in 12 ways.   The number of ways in which he can select one trouser and one shirt is   7 * 12= 
  7 * 12 = 84
84 ways   84)
Answer: E
A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
Answers:  A) 1:2  B) 1:5  C) 1:9  D) 1:3  E) 1:1

Solution: T = 192/32= 
192/32 = 6
6 h   T= 6 - 3= 
6 - 3 = 3
3   Time Ratio= 6:3 = 2:1   Speed Ratio = 1:2   1:2nswer: 1:2
Answer: A
On a certain transatlantic crossing, 20 percent of a ship's passengers held round-trip tickets and also took their cars abroad the ship. If 40 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship's passengers held round-trip tickets?	Pick one:  A) 33.3%  B) 40%  C) 50%  D) 60%  E) 66.6%

Solution: 0.20P = RT + C   0.4(RT) = no C   => 0.60(RT) had C   0.20P = 0.60(RT)   RT/P = 1/3=33%   33.3%nswer - 33.3%
Answer: A
Car Q and Car Y traveled the same 80-mile route. If Car Q took 2 hours and Car Y traveled at an average speed that was 50 percent faster than the average speed of Car Q, how many hours did it take Car Y to travel the route?  Choose the correct option:
A) 2/3	B) 1	C) 4/3	D) 8/5	E) 3

Solution: The speed of car Q is (distance)/(time) = 80/2= 
80/2 = 40
40 miles per hour.   The speed of car Y= 3/2*40= 
3/2*40 = 60
60 miles per hour --> (time)= (distance)/(speed) = 80/60 = 4/3 hours.   Answer: C.   Or: to cover the same distance at 3/2 as fast rate 2/3 as much time is needed --> (time)*2/3 = 2*2/3 = 4/3 hours.   Answer: 4/3.
Answer: C
The price of stock increased by 8% last year and decreased by 6% this year. What is the net percentage change in the price of the stock? Select: A) 0.2% B) 0.8% C) 1.2% D) 1.52% E) 2%

Solution: (100% + 8%) * (100% - 6%) = 1.08 * 0.94= 
1.08 * 0.94 = 1.0152
1.0152= 101.52%.   The net percentage change in the price of the stock is (+) 1.52%   The answer is 1.52%
Answer: D
A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 15 per metre of cloth. What is the cost price of one metre of cloth? Select the correct option
A) 22  B) 28  C) 90  D) 27  E) 23

Solution: SP of 1m of cloth = 8925/85 = Rs. 105   CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth   = Rs. 105 - Rs. 15   = Rs.90.   Answer:90
Answer: C
The distance between Delhi and Mathura is 110 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?
Choose the correct choice from the following.
A) 11  B) 77  C) 16  D) 10  E) 98

Solution: D = 110 – 20 = 90   RS = 20 + 25= 
20 + 25 = 45
45   T= 90/45= 
90/45 = 2
2 hours   8 a.m. + 2= 10 a.m..Answer: 10
Answer: D
Three is the largest number that can be divided evenly into 27 and the positive integer x, while 10 is the largest number that can be divided evenly into both 100 and x. Which of the following is the largest possible number that could be divided into x and 1500  Choose the most appropriate option.
A) 30
B) 70
C) 210
D) 300
E) 150

Solution: 27 = 3*3*3, and its GCF with x is 3, which implies that x has ONE factor of 3, but not TWO factors of 3.   100 and x have a GCF of 10, which implies that x has ONE factor of 10, but not TWO factors of 10.   Then we want to know what is the largest possible GCF of x and 2100.   Well 1500 = 3 *5 * 10 * 10   We want x to include as many factors in common with 2100 as possible, to make the GCF with 2100 as big as possible.   We know x has one factor of 3, but not two factors --- that takes the 3.   We know x has one factor of 10, but not two factors --- we can take one of those 10's, but we have to leave the other   No other restrictions, so we can also grab that factor of 7 --- nothing saying that we can't, and it's there for the taking.   3*5*10= 
3*5*10 = 150
150   If we allow x to include as many factors as possible, within the constraints given, that is the most x could have in common with 2100.   150
Answer: E
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?	Choose the correct answer.
A) 3/6  B) 3/2  C) 3/4  D) 3/1  E) 3/6

Solution: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train   = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y   = 23 x + 23 y   ==> 4 x = 6 y ==> x/y   = 3/2.   Answer: 3/2
Answer: B
The H.C.F of two numbers is 23 and the other two factors of their L.C.M are 14 and 15. The larger of the two numbers is:
Pick one:
A) 338	B) 278	C) 345	D) 231	E) 121

Solution: Clearly, the numbers are (23 * 14) and (23 * 15). Larger number   = (23 * 15)= 
(23 * 15) = 345
345.   Answer: 345
Answer: C
If the ratio of the sum of the first 6 terms of a G.P. to the sum of the first 3 terms of the G.P. is 126, what is the common ratio of the G.P?
Select the correct option: A) 3 B) 1/3 C) 2 D) 5 E) 1/5

Solution: 126=(a1+a2+a3+a4+a5+a6)/(a1+a2+a3)   Factorize the same terms   126=1+(a4+a5+a6)/(a1+a2+a3)   Write every term with respect to r   a1=a1   a2=a1*r^1   a3=a1*r^2   .........   126=1+(a1(r^3+r^4+r^5))/(a1(1+r^1+r^2))   125=(r^3 (1+r^1+r^2))/((1+r^1+r^2))   125=r^3   r=5   5
Answer: D
A company has 50 employees, of which 22 studied accounting, 15 studied finance and 14 studied marketing. Ten employees have done just two courses and only one made ​​the three courses. How many employees have no training? Pick:
A) A)0
B) B)9
C) C)10
D) D)11
E) E)26

Solution: Total employees=50   studied accounting=22   studied finance=15   studied marketing=14   10 employees have been double counted and one employee has been counted thrice.   Therefore employees who have received training=22+15+14-10-(2*1)   =51-12= 
51-12 = 39
39   Employees with no training=50-39= 
50-39 = 11
11   Ans=11
Answer: D
A project manager needs to select a group of 4 people from a total of 4 men and 4 women. How many possible group combinations exist such that no group has all men ?  Choose one.
A) 72 B) 68 C) 74 D) 82 E) 69

Solution: Since the order in which the group is selected does not matter, we are dealing with a combinations problem (and not a permutations problem).   The formula for combinations is:   N!/((N-K)!K!)   Where N = the total number of elements from which we will select, 8 people in this case.   Where K = the total number of elements to select, 4 people in this case.   The total number of combinations is therefore:   8!/((8-4)!4!) = 70   However, one of these combinations are not valid since they have all members of men   The correct answer is  70-1= 
 70-1 = 69
69.Ans 69
Answer: E
A train covers a certain distance at a speed of 320kmph in 6 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of Pick one: A) 1152km/hr B) 1120km/hr C) 1650km/hr D) 1750km/hr E) 1850km/hr

Solution: Explanation:   Distance = 320Ã—6 = 1920km   Required speed = (1920Ã— 3/5) = 1152km/hr   1152km/hrnswer: Option 1152km/hr
Answer: A
Thirty percent of the women in a college class are science majors, and the non-science majors make up 80% of the class. What percentage of the men are non-science majors if 40% of the class are men?	Choose the correct option:
A) 2%
B) 5%
C) 28%
D) 30%
E) 95%

Solution: 3/k + 2/m = 6/t   Assuming total # is 100 :   [Science - Women] will have - 0.3 * 60 = 18   [Non-Science-Women] will have - 42   [Science-Men] will have = 20-18= 
20-18 = 2
2   [Non-Science-men] will have - 38   S0 38/40 * 100= 95%   Answer - 95%
Answer: E
The diameters of two spheres are in the ratio 1:2 what is the ratio of their volumes? Select:
A) 1:7  B) 1:3  C) 1:8  D) 1:1  E) 1:2

Solution: 1:8   Answer: 1:8
Answer: C
How many integers are there between 42 and 97, inclusive?	Choose the correct choice from the following answers.
A) 51
B) 55
C) 56
D) 57
E) 58

Solution: I guess the easiest way to answer this is -   Say you have two positive integers, x and y where y > x   Then the number of integers between x and y is given by - (y - x) + 1   In this case, it's (97 - 42) + 1= 
(97 - 42) + 1 = 56
56   Option 56
Answer: C