MU-NLPC/Calc-aqua_rat huggingface dataset:
Thefactor countof an integer n greater than 1 is the number of distinct prime factors of n. For example, the factor count of 36 is 2, since 2 and 3 are the distinct prime factors of 36 = 2 x 2 x 3 x 3. For which of the following integers is the factor count greatest R?	Choose the correct choice.
A) 60 B) 61 C) 62 D) 63 E) 64

Solution: 60 = 2*2*3*5 factor count =3   61= prime number   62 = 2*31 factor count=2   63=3*3*7 factor count=2   64=2*2*2*2*2*2 factor count=1=R   answer is 60.
Answer: A
If n is an integer, which of the following must be an even integer?
Pick one:	A) n^2-n-1	B) n^2-4n+6	C) n^2-5n+5	D) n^2+3n+8	E) n^2+2n+10

Solution: Check the options by plugging in some values ( Preferably smaller integers like 1 and 2 )   A: n^2-n-1 = -1 { If n = 1 }   B: n^2-4n+6 = 3 { If n = 1 }   C: n^2-5n+5 = 1 { If n = 1 }   n^2+3n+8: n^2+3n+8 = 12 { If n = 1 }n^2+3n+8 = 18 { If n = 2 }   E: n^2+2n+10 = 13 { If n = 1 }   Thus the only possible answer is (n^2+3n+8)
Answer: D
What is the simplified result of following the steps below in order?
(1)	add 5y to 2f
(2)	multiply the sum by 3
(3)	subtract f + y from the product  Choose the most appropriate option
A) 5f + 14y	B) 5x + 16y	C) 5x + 5y	D) 6x + 4y	E) 3x + 12y

Solution: 3(5Y+2F) -F-Y= 14Y+5F   '5f + 14y' is the answer
Answer: A
Martin bought 10 concert tickets, some at the full price of $2.00 per ticket, and some at a discounted price of $1.60 per ticket. If he spent a total of $17.60, how many discounted tickets did he buy?  Answers
A) 3
B) 4
C) 5
D) 6
E) 7

Solution: Let x be the number of tickets he bought at $2 per ticket.   then 2 x + (10-x)1.6 = 17.6   0.4x = 1.6 => x = 4   discounted tickets = 10 -x = 6   Ans : 6
Answer: D
Last year Mrs. Long received $160 in dividends on her shares of Company X stock, all of which she had held for the entire year. If she had had 12 more shares of the stock last year, she would have received $15 more in total annual dividends. How many shares of the stock did she have last year?  Choices: A) 128 B) 140 C) 172 D) 175 E) 200

Solution: A   1. Realize that if there were 12 more shares and 15 more dollars, the shares are worth more than a dollar a share, so there would have to be less than 160. Cancel out c, d, e.   2. Now there are at least three ways of doing it, all of which depend on who you are and how you think. I'll put as many below as I can think of - I think they're all fine and expediant. Remember - if you're spending time looking for the most sophisticated way, you could be just wasting time, especially if you know how to do it algebraically.   Method 1: Algebra   160/x = 175/(x+12)   That's because each stock is worth the same, so if you divide the 160 by the number of shares, or 175 by the number of shares plus 12, you get the same answer. Solve for x = 128.   Method 2: 12 more shares cost $15, so that means each one cost $1.25. So 160/1.25. To do this quickly, convert 1.25 into 5/4(I LOVE FRACTIONS!)Now you've got 160/(5/4) = 160x4/5 = 32x4 = 128.   answer is 128
Answer: A
A & B started a partnership business. A's investment was thrice the investment of B and the period of his investment was two times the period of investments of B. If B received Rs 3000 as profit , what is their total profit?  Select:  A) 21000  B) 30000  C) 32000  D) 34000  E) None of these

Solution: Explanation :   Suppose B's investment = x. Then A's investment= 3x   Suppose Bs period of investment = y, then A's period of investment = 2y   A : B = 3x * 2y : xy   = 6 : 1   Total profit * 1/7 3  * 2= 
3  * 2 = 6
6 : 1   Total profit * 1/7= 3000   => Total profit = 3000*7= 
3000*7 = 21_000
21000. 21000nswer : Option 21000
Answer: A
When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 3 times, what is the probability that it will land once on heads and twice tails?
Choose the correct answer.
A) 1/3	B) 1/6	C) 1/4	D) 1/8	E) 1/5

Solution: Must be once on heads and twice on tails   1/2*1/2*1/2 = 1/8   Answer: 1/8
Answer: D
What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 15%?
Options
A) 20%  B) 27.5%  C) 10%  D) 80%  E) 90%

Solution: SP2 = 2/3 SP1   CP = 100   SP2 = 85   2/3 SP1 = 85   SP1 = 127.5   100 --- 27.5 => 27.5%   Answer: 27.5%
Answer: B
Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Pick one:	A) 1234	B) 2343	C) 4546	D) 3435	E) 5184

Solution: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184   432 12 x 62   5184
Answer: E
Stuart bought a sweater on sale for 30% off the original price and another 25% off the discounted price. If the original price of the sweater was $30, what was the final price of the sweater?
Choose the correct choice from the following answers
A) $15.75	B) $25.75	C) $35.75	D) $45.75	E) $55.75

Solution: The price with 30% off   30 - 30% of 30 = 30 - (30 / 100) ? 30 = 30 - 9= 
30 - 9 = 21
21   The price with another 25% off   21 - 25% of 21= 21 - (25/100) ? 21   = 21 - (525 / 100) = 21 - 5.25= 
21 - 5.25 = 15.75
$15.75   correct answer $15.75
Answer: A
A and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.25000, find their shares?
Choose the correct choice from the following answers.
A) Rs.10000, Rs.15029	B) Rs.10000, Rs.15209	C) Rs.10000, Rs.15129	D) Rs.10000, Rs.15000	E) Rs.10000, Rs.35000

Solution: The ratio of their profits A:B = 8:12 = 2:3   Share of A in the total profit = 2/5 * 25000 = Rs.10000 Share of A in the total profit = 3/5 * 25000 = Rs.15000.Answer:Rs.10000, Rs.15000
Answer: D
By selling an article at Rs.600, a profit of 25% is made. Find its cost price?  Options
A) Rs.350	B) Rs.400	C) Rs.573	D) Rs.480	E) Rs.580

Solution: SP = 600   CP = (SP)*[100/(100+P)]   = 600 * [100/(100+25)]   = 600 * [100/125] = Rs.480   ANSWER:Rs.480
Answer: D
If population of certain city increases at the rate of 5%. If population in 1981 was 138915, then population in 1979 was?
Choose the correct choice from the following options
A) 12,6000 B) 130000 C) 261000 D) 627000 E) 12690

Solution: Explanation:   X * (105/100) * (105/100) = 138915   X = 138915/1.1025= 
138915/1.1025 = 126_000
126000   12,6000nswer: Option 12,6000
Answer: A
The ratio of the number of ladies to gents at a party was 1:4 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?	Options
A) 18  B) 25  C) 29  D) 20  E) 24

Solution: x, 4x   (x-2):(4x-2) = 1:3   3x-6 = 2x-2   x = 4   x+4x = 5x   => 5*4= 
5*4 = 20
20   ANSWER:20
Answer: D
R is the set of positive odd integers less than 10, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?  Select.
A) None  B) One  C) Four  D) Five  E) Two

Solution: squares < 10 {1,4,9 }   S = {1,9}   R = {1,3,.....10}   Hence Two
Answer: E
Today Joelle opened an interest-bearing savings account and deposited $7,000. If the annual interest rate is 5 percent compounded interest, and she neither deposits nor withdraws money for exactly 2 years, how much money will she have in the account? Select the correct option:	A) $7727.50	B) $7717.50	C) $7737.50	D) $7747.50	E) $7757.50

Solution: Interest for 1st year = 7000*5/100= 
7000*5/100 = 350
350   Interest for 2nd year= 7350 *5/100= 
7350 *5/100 = 735/2 = around 367.5
367.50   Total=7000+350+367.50= 
7000+350+367.50 = 7_717.5
7717.50   Answer : $7717.50
Answer: B
In a certain group of 10 members, 5 members teach only French and the rest teach only Spanish or German. If the group is to choose 3-member committee, which must have at least 1 member who teaches French, how many different committee can be chosen ?	Select:
A) 40	B) 50	C) 64	D) 80	E) 110

Solution: Case 1   1french 2either German or Spanish: 5C1 * 5C2 = 50   Case 2   2french 1either German or Spanish: 5C2 * 5C1 = 50   Case 3   3french 5C3 = 10   Answer is 110 = 110
Answer: E
A machine, working at a constant rate, manufactures 18 dies in 25 minutes. How many dies does it make in 1 hr 15 min?	Select the correct option:
A) 55  B) 53  C) 54  D) 52  E) 50

Solution: Change 1 hr 15 min to 75 min. For this, we need to set up a simple proportion of Dies per time   18/25= S/75   The absolutely worst thing you could do at this point in the problem is to cross-multiply. That would be a supremely unstrategic move. We can cancel the common factor of 25 in the two denominators.   18/1 = S/3   S = 3* 18= 
3* 18 = 54
54   The machine would be 54 dies in 1 hr 15 min.   Answer: 54
Answer: C
If it costs d dollars to make the first 100 copies of a poster and e dollars for each poster after that, what is the total cost of 125 posters?  Pick.
A) 25d + 100e
B) 100d + 25e
C) 125de
D) d + 25e
E) 125/(de)

Solution: d + 25eollars needed for first 100 copies = d   d + 25eollars needed for each successive copy = e   Cost of 125 copies = cost of 100 copies + cost of 25 copies = d + 25e   Correct Option: d + 25e
Answer: D
If the sides of a cube are in the ratio 4:3. What is the ratio of their diagonals?	Choose the correct choice: A) 4:3 B) 16:9 C) 64:27 D) 3:4 E) 3:8

Solution: a1:a2 = 4:3   d1:d2 = 4:3   4:3NSWER:4:3
Answer: A
Rodrick mixes a martini that has a volume of 'n' ounces having 38% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 25% Vermouth by volume. How many ounces of Gin must he add?	Choose the correct choice from the following
A) n/6 B) n/3 C) 13n/25 D) 5n/6 E) 8n/5

Solution: total V G   1 ounce 0.38 0.6   n ounce 0.38n 0.6n -------------initial expression   lets say g ounces of gin is added to this mixture   n+g 0.38n 0.6n+g --------------final expression   given that after adding g ounces of gin , V should become 25% of the total volume.   =>Volume of V/total volume = 25/100   => 0.38n /n+g = 1/4   => 1.52n = n+g   => g = 3n/5   Answer is C.   Note that after we add pure Gin, the volume of Vermouth will remain the same. Based on this set the equation:   0.38n=0.25(n+g) --> g=13n/25   Answer: 13n/25.
Answer: C
The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 1250 resolutions?
Choose the most appropriate option: A) 794 m B) 704 m C) 454 m D) 1860 m E) 1760 m

Solution: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 1250 resolutions.   = 1250 * 2 * 22/7 * 22.4= 
1250 * 2 * 22/7 * 22.4 = 176_000
176000 cm= 1760 m   Answer: 1760 m
Answer: E
A man walking at a constant rate of 9 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 15 miles per hour. The woman stops to wait for the man 3 minutes after passing him, while the man continues to walk at his constant rate. How many minutes must the woman wait until the man catches up?  Select:
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: When the woman passes the man, they are aligned (m and w). They are moving in the same direction. After 5 minutes, the woman (W) will be ahead the man (M):   m------M---------------W   w   In the 5 minutes, after passing the man, the woman walks the distance mW = wW, which is 3*15/60 =15/20 miles and the man walks the distance mM, which is 3*9/60 = 9/20 mile.   The difference of 15/20 - 9/20 =3/10 miles (MW) will be covered by the man in (3/10)/9 = 1/30 of an hour, which is 2 minutes.   Answer 2.
Answer: B
Let S be the set of all positive integers n such that n^2 is a multiple of both 24 and 108. Which of the following integers are divisors of every integer n in S ?
Pick:
A) 12 B) 24 C) 120 D) 72 E) 182

Solution: 4 = 2^3*3;   108 = 2^2*3^3.   The smallest perfect square (n^2) which is a multiple of both 24 = 2^3*3 and 108 = 2^2*3^3 is 2^4*3^4, thus the smallest n is 2^2*3^2 = 36. So, only 12 is a divisor of all integers in S.   12nswer: 12.
Answer: A
A certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different arrangements Q of plays can be run, if the same play can’t be run more than once?
Pick one
A) 24
B) 125
C) 243
D) 504
E) 729

Solution: Number of Q ways to choose the first play: 9   Second play: 8   Third:7   9*8*7= 504.504
Answer: D
An express traveled at an average speed of 100 km/hr, stopping for 4 min after every 60 km. How long did it take to reach its destination 600 km from the starting point ?  Pick one:
A) 8 hrs 29 min  B) 6 hrs 28 min  C) 2 hrs 28 min  D) 6 hrs 28 min  E) 6 hrs 36 min

Solution: Explanation:   Time taken to cover 600 km = 600/100= 
600/100 = 6
6 hrs.   Number of stoppages= 600/60 - 1= 
600/60 - 1 = 9
9   Total time of stoppages= 4 x 9 = 36 min   Hence, total time taken = 6 hrs 36 min.   Answer: 6 hrs 36 min
Answer: E
A machine, working at a constant rate, manufactures 20 candles in 40 minutes. How many candles does it make in 1 hr 20 min? Pick one
A) 25  B) 30  C) 40  D) 45  E) 50

Solution: Change 1 hr 20 min to 80 min. For this, we need to set up a simple proportion of staplers per time 20/40= S/80   The absolutely worst thing you could do at this point in the problem is to cross-multiply. That would be a supremely unstrategic move. Instead, cancel before you multiply. For what we can and can’t cancel in a proportion, seethis post. We can cancel the factor of 10 in the 20 and 40.   2/4 = S/80   1/2 = S/80 ; 1/2*2 = S/80*2   1/1=S/40   Now that the fraction is entirely simplified, we can cross-multiply.   S = 1*40= 
1*40 = 40
40   The machine would be 40 candles in 1 hr 20 min.   Answer: 40.
Answer: C
When 52416 is divided by 312, the quotient is 168. what will be the quotient when 52.416 is divided by 0.168? Choose the correct choice from the following answers
A) 5 B) 6 C) 4 D) 3 E) 8

Solution: for the 1st no. there are 2 digits after decimal   for the 2nd no. there are 4 digits after decimal   total no. of decimals = 6   req. no. of digits=(n-1)=(6 -1)= 
(6 -1) = 5
5   5NSWER :5
Answer: A
The average weight of 5 person's increases by 5.5 kg when a new person comes in place of one of them weighing 68 kg. What might be the weight of the new person?  Choose the correct option
A) 60 kg
B) 95.5 kg
C) 80 kg
D) 85 kg
E) 90 kg

Solution: Total weight increased = (5 x 5.5) kg = 27.5 kg.   Weight of new person = (68 + 27.5)= 
(68 + 27.5) = 95.5
95.5 kg   Option 95.5 kg
Answer: B
The ratio of the radius of two circles is 1: 3, and then the ratio of their areas is? Choose the correct choice from the following choices.
A) 1:7	B) 2:9	C) 1:9	D) 3:7	E) 3:4

Solution: r1: r2 = 1: 3   Πr12: Πr22   r12: r22 = 1:9   Answer: 1:9
Answer: C
How many zeros does 50! end with?
Choose the correct answer:
A) 20
B) 24
C) 25
D) 12
E) 32

Solution: According to above 50! has 50/5+50/25=10+2= 
10+2 = 12
12trailing zeros.   Answer: 12.
Answer: D
In a family 4 people eat only vegetarian, 3 people eat only non veg., 2 people eat both veg and non veg.. How many people are in the family?  Choose the most appropriate option.
A) 4  B) 3  C) 10  D) 2  E) 9

Solution: Total number of people in family= veg+non veg+(both veg and non veg)   Total= 4+3+2= 
4+3+2 = 9
9   Answer is 9
Answer: E
A train running at a speed of 36 km/h passes an electric pole in 15 seconds. In how many seconds will the whole train pass a 370-meter long platform?  Choose the correct choice from the following answers.
A) 46  B) 48  C) 50  D) 52  E) 54

Solution: Let the length of the train be x meters.   When a train crosses an electric pole, the distance covered is its own length x.   speed = 36 km/h = 36000 m / 3600 s = 10 m/s   x = 15 * 10= 
15 * 10 = 150
150 m.   The time taken to pass the platform= (150 +370)/ 10= 
(150 +370)/ 10 = 52
52 seconds   The answer is 52.
Answer: D
If q = 25! + 1, which of the following cannot be a prime factor of q?
I. 11
II. 19
III. 23  Choose the correct choice from the following options
A) I​ only
B) III only
C) II and III
D) I and II
E) I​, II, and III

Solution: The numbers 11, 19, and 23 are all factors of 25!   Therefore they can not be factors of 25! + 1.   The answer is I​, II, and III.
Answer: E
A bike covers a certain distance at the speed of 67km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel?  Choose the correct choice from the following answers
A) 89.33 km/h	B) 85.34 km/h	C) 87.67 km/h	D) 90.25 km/h	E) 90.64 km/h

Solution: Ans.(A)   Sol. Total distance = 67 × 8 = 536 km   Now speed = 536/6 = 89.33 km/h
Answer: A
A student committee that must consists of 5 members is to be formed from a pool of 8 candidates. How many different committees are possible	Choose the correct choice from the following answers
A) 5	B) 8	C) 40	D) 56	E) 336

Solution: the committee must consist of 5 members, not at least 5 members. Hence, all you have to do is 8C5 = 56   Answer (56)
Answer: D
4 men&6women finish a job in 8days, while 3men&7women finish it in 10 days. In how many days will 10 women working together finish it ?
Choose the correct choice from the following answers:
A) 50 days
B) 40 days
C) 60 days
D) 70 days
E) 90 days

Solution: Let 1 man's 1 day work = x   and 1 woman's 1 days work = y.   Then, 4x + 6y = 1/8   and 3x+7y = 1/10   solving, we get y = 1/400 [means work done by a woman in 1 day]   10 women 1 day work = 10/400 = 1/40   10 women will finish the work in 40 days   (40 days)
Answer: B
A school currently maintains a fixed number of students per class. If the ratio of students per class were to be increased by 1, 10 fewer classes would be run for a total of 120 students. What is the current ratio W of students per class? Choose the correct choice from the following options:
A) W=3
B) 4
C) 6
D) 8
E) 12

Solution: Another way to look at the problem...   Since the total is 120, RATIO * CLASSES = R*C = 120.....(i)   we are looking where ratio increases by 1 and # of classes decreases by 10 = (R+1)(C-10) = RC+C-10R-10=120....(ii)   (ii)-(i)....   C=10R+10 = 10(R+1).......   so # of classes has to be multiple of 10   AS RC=120.... 10(R+1)*R = 120...................R(R+1) = 12..   so 12 is a multiple of consecutive numbers ONLY 3 *4 fits in..... and R=3   W=3
Answer: A
If you have 6 black socks, 4 blue socks, 8 brown socks, and 2 red socks in your sock drawer, what is the minimum number of socks that you need to pull out in the dark to be sure you had a matching pair?	Choose one:
A) five B) 7 C) 8 D) 9 E) 2

Solution: five   5   fivet least 5, so that at least one color has two socks!
Answer: A
Kamal started a business with Rs.25000 and after 4 months, Kiran joined him with Rs.60000. Kamal received Rs.58000 including 10% of profit as commission for managing the business. What amount did Kiran receive?  Choose the correct choice.
A) 75000
B) 70000
C) 72000
D) 78000
E) 80000

Solution: Ratio 25000 * 12:60000*8   = 25*12 : 60*18   5*3 : 12*2   5:8   let tot prof = x   then kamal received 10x/100 = x/10 as commission for managing the business   remaining profit = x = x/10 = 9x/10 =>5:8   total amt by kamal = x/10+9x/10*5/13   =>58000   x=130000   kiran shrae = 130000-58000= 
130000-58000 = 72_000
72000   ANSWER 72000
Answer: C
The true discount on Rs. 2562 due 4 months hence is Rs. 122. The rate percent is:	Select
A) 18%  B) 12%  C) 15%  D) 25%  E) 14%

Solution: Explanation:   Ans. C. 15%   The true discount on Rs. 2562 due 4 months hence is Rs. 122.   Therefore Present Worth is = 2562 – 122 = 2440.   It means that Rs. 122 is interest on Rs. 2440 for 4 months.   Therefore rate percent is = (122 × 100 × 12)/(2440 × 4) = 15%   Answer: 15%
Answer: C
A part of certain sum of money is invested at 9% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?  Pick.
A) 4:8	B) 4:2	C) 4:3	D) 4:4	E) 4:1

Solution: 12:9   = 4:3   Answer:4:3
Answer: C
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 48 years now, the son's age five years back was? Choose the correct choice from the following:
A) 18years B) 19years C) 20years D) 21years E) 22years

Solution: Let the son's present age be x years. Then, (48 - x) = x   2x = 48.   x = 24.   Son's age 5 years back (24 - 5)= 
(24 - 5) = 19
19 years.   19years)
Answer: B
What will be the result of 12/2 + 4/2 -3^5 +8 all this multiplied by 5? Choices.
A) 18 B) 98 C) 5 D) 9 E) 0

Solution: The division(e.g. 6/2) is done first and then the sum(e.g. 6+2) and   subtraction (e.g. 2-15), at the end you multiply the expression by 5, and the answer is 5, option 5.
Answer: C
The total of the ages of Amar, Akbar and Anthony is 80 years. What was the total of their ages three years ago ? Answers:
A) 71
B) 44
C) 66
D) 16
E) 18

Solution: Explanation:   Required sum = (80 - 3 x 3) years = (80 - 9)= 
(80 - 9) = 71
71 years.   71nswer: 71
Answer: A
Train X departs from station A at 11 a.m. for station B, which is 180 km so far. Train Y departs from station B at 11 a.m. for station A. Train X travels at an average speed of 70 km/hr and does not stop anywhere until it arrives at station B. Train Y travels at an average speed of 50 km/hr, but has to stop for 15 min at station C, which is 60 km away from station B enroute to station A. Ignoring the lengths of the trains, what is the distance, to the nearest kilometre, from station A to the point where the trains cross each other? Choose the correct choice from the following choices:
A) 112 km
B) 118 km
C) 120 km
D) None of these
E) Cannot be determined

Solution: Explanation :   Total time taken by B to cover 60 km   60/50 hr i.e 6/5 hr.   It stops at station C for 1/4 hr   Now , in (6/5 + 1/4) hr , train X travels 70 x (29/20) = 101.5 km.   This means they do not cross each other by the time train Y finishes it stops at station C.   Let they meet after t hour.   Then, 70t + 50(t- 1/4) = 180.   t = 192.5/120 hr.   Distance from A will be 70 x 192.5/120 km i.e 112 km approximately.   112 kmnswer : 112 km
Answer: A
If 0 < p < 1 < q< 3, which of the following must be less than 1?
I.	p/q
II.	pq
III.	q - p  Select
A) I,II only
B) I only
C) II only
D) III only
E) II,III only

Solution: q > 1. So, option II, III is not possible.   So, Option I is correct.   Answer : I only
Answer: B
A train , 800 meter long is running with a speed of 78 km/hr. It crosses a tunnel in 1 minute. What is the length of the tunnel (in meters)?  Choose the correct choice from the following answers.
A) 500
B) 400
C) 300
D) 200
E) 250

Solution: Distance = 800+x meter where x is the length of the tunnel   Time = 1 minute = 60 seconds   Speed = 78 km/hr = 78×10/36 m/s = 130/6 = 65/3 m/s   Distance/time = speed   (800+x)/60 = 65/3   => 800+x = 20×65 = 1300   => x = 1300 - 800= 
1300 - 800 = 500
500 meter   500nswer is 500.
Answer: A
For a bake sale, Simon baked 2n more pies than Theresa. Theresa baked half as many pies as Roger, who baked 1313n pies. No other pies were baked for the sale. What fraction of the total pies for sale did Roger bake? Options.
A) 1/16	B) 1/8	C) 3/16	D) 3/8	E) 13/16

Solution: S : Simon   T : Theresa   R : Roger   Let Theresa baked A.   As per question, we have S = A + 2= 
+ 2 = 2
2A= n/3 or A = n/6   Now, Total = A + (A+2n) + 2A = 8n/3   Fraction, (n/3) / (8n/3) = 1/8   ANSWER:1/8
Answer: B
In assembling a Bluetooth device, a factory uses one of two kinds of modules. One module costs $15 and the other one, that is cheaper, costs $10. The factory holds a $140 worth stock of 13 modules. How many of the modules in the stock are of the cheaper kind?	Pick one:
A) 20	B) 25	C) 30	D) 11	E) 35

Solution: So the number of $10 modules must be 11 so that the leftover 2 modules are of $15 which will give a total value $140. 11*10+2*15 = 110+30= 
110+30 = 140
140   Answer : 11
Answer: D
A contractor undertakes to built a walls in 50 days. He employs 30 peoples for the same. However after 25 days he finds that only 40% of the work is complete. How many more man need to be employed to complete the work in time?
Options.
A) 25
B) 30
C) 45
D) 20
E) None of these

Solution: 30 men complete 0.4 work in 25 days.   Applying the work rule, m1 × d1 × w2 = m2 × d2 × w1   we have,   30 × 25 × 0.6 = m2 × 25 × 0.4   or m2 = 30×25×0.6/25×0.4 = 45 men   Answer45
Answer: C