MU-NLPC/Calc-aqua_rat huggingface dataset:
A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 10km?	Choose the correct choice.
A) 3  B) 5  C) 8  D) 9  E) 6

Solution: M = 4   S = 2   US = 4 - 2= 
4 - 2 = 2
2   D= 10   T = 10/2= 
10/2 = 5
5   Answer:5
Answer: B
A librarian has a set of seven books, including four different books about Abraham Lincoln. The librarian wants to put the seven books on a shelf with the four Lincoln books next to each other, somewhere on the shelf among the other three books. How many different arrangements of the seven books are possible?
Pick one
A) (7!)/(4!) B) (4!)(3!) C) (4!)(4!) D) (4!)(7!) E) (4!)(3!)(7!)

Solution: You can club the four Lincoln books as one, which leaves us with three other books plus this one to think about. So, these four items can be arranged in 4! ways, and since the four books can be moved around among themselves with each combination giving us a new overall combination, we have an additional 4! ways. Therefore, the answer would be 4!*4!, which is (4!)(4!).
Answer: C
A committee of 3 people is to be chosen from four married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?	Pick
A) 16  B) 24  C) 26  D) 30  E) 32

Solution: Each couple can send only one "representative" to the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) out of 4 to send only one "representatives" to the committee: 4C3=4.   But each of these 3 couples can send two persons (husband or wife): 2*2*2=2^3=8.   Total # of ways: 4C3*2^3=32.   Answer: 32.
Answer: E
A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
Pick one:
A) 100 m  B) 350 m  C) 25 m  D) 30 m  E) 35 m

Solution: Explanation:   Speed = 300/18 = 50/3 m/sec.   Let the length of the platform be x meters.   Then, (x + 300)/39 = 50/3   3x + 900 = 1950 => x = 350 m.   Answer:350 m
Answer: B
Can you find the missing number in the sequence given below?
11 14 17 12 15 ? 13 16 19 14 17 20 Pick.
A) 20 B) 21 C) 18 D) 23 E) 24

Solution: Solution:   18   Explanation :   The sequence is given in the puzzle is :   11 14 17 12 15 ? 13 16 19 14 17 20   Let's break the given series as below:   11 14 17   12 15 ?   13 16 19   14 17 20   Now read the number from left hand side from top to bottom as :   So the number that will replace '?' is 18.   Answer 18
Answer: C
In a drawer there is a number of pair of socks, out of which 1/5 are white pairs, 1/10 are black pairs, and the remaining 7 pairs are red. How many white socks are in the drawer?
Choose the correct choice from the following answers
A) 10  B) 2  C) 1  D) 7  E) 4

Solution: Let x be the total number of pairs of socks.   x(1/5+1/10)=3x/10 the number of pairs white and black.   x-3x/10=7x/10 is the number of red pairs of socks   7x/10=7 implies x=10.   There are 10 pairs of socks out of which 1/5 are white, that is, 1/5*10=2.   Thus, the total number of white socks is 2*2= 
2*2 = 4
4.   Answer 4 4.
Answer: E
How many of the following numbers are divisible by 3 but not by 9.
4320, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276  Select the correct option:	A) 5	B) 6	C) 7	D) 8	E) 9

Solution: Taking the sum of the digits, we have :   S1 = 9, S2 = 12, S3 = 18, S4 = 9, S5 = 21, S6 = 12, S7 = 18, S8 = 21, S9 = 15, S10 = 24.   Clearly, S2, S5, S6, S8, S9, S10 are all divisible by 3 but not by 9.   So, the number of required numbers = 6.   ANSWER:6
Answer: B
A committee has 5 men and 6 women. What are the number of ways of selecting 3 men and 2 women from the given committee?	Choose the correct choice:
A) 150
B) 200
C) 250
D) 300
E) 350

Solution: The number of ways to select three men and two women = 5C3 * 6C2 = 10 * 15= 
10 * 15 = 150
150   The answer is 150.
Answer: A
After decreasing 24% in the price of an article costs Rs.836. Find the actual cost of an article?  Pick one.
A) 1218	B) 2777	C) 1100	D) 2688	E) 1991

Solution: 1100P* (76/100) = 836   1100P1100 * (76/100)= 
1100 * (76/100) = 836
836   1100P= 11 * 100= 
11 * 100 = 1_100
> 1100P= 1100   Answer: 1100
Answer: C
Harkamal purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 75 per kg. How much amount did he pay to the shopkeeper? Select
A) A)1235  B) B)1055  C) C)1065  D) D)1075  E) E)1080

Solution: Cost of 8 kg grapes = 70 × 8 = 560.   Cost of 9 kg of mangoes = 75 × 9 = 675.   Total cost he has to pay = 560 + 675= 
560 + 675 = 1_235
1235.   1235)
Answer: A
A Winson's company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?
Choose the correct choice from the following choices
A) 1:2
B) 4:5
C) 1:1
D) 3:2
E) 5:3

Solution: 1:2 Winson's company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996.1996- x----- y------- x+y   1997- x1---- y1-- x1+y1   x1= a*x .....(P)   y1= 1.07*y...(Q)   x1+y1/x+y = 1.01   solve using P and Q and find x/y
Answer: A
Find the average of all the numbers between 6 and 36 which are divisible by 5. Choose the correct choice from the following answers:
A) 18	B) 20	C) 24	D) 30	E) 22.5

Solution: Solution   Average	= (10+15+20+25+30+35)/6)   = 135 / 6= 
135 / 6 = 45/2 = around 22.5
22.5   Answer 22.5
Answer: E
The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8091 for a computer table, then what was the cost price of the computer table?  Select the correct option.
A) 7297
B) 2977
C) 2871
D) 6725
E) 6525

Solution: Explanation:   CP = SP * (100/(100 + profit%))   = 8091(100/124) = Rs. 6525.   Answer: 6525
Answer: E
One week, a certain truck rental lot had a total of 20 trucks, all of which were on the lot Monday morning. If 50% of the trucks that were rented out during the week were returned to the lot on or before Saturday morning of that week, and if there were at least 10 trucks on the lot that Saturday morning, what is the greatest number of different trucks that could have been rented out during the week?  Choose the correct choice.
A) 18  B) 20  C) 12  D) 8  E) 4

Solution: N - Not rented trucks; R - Rented trucks   N + R = 20   N + R/2 = 10   R = 20   20
Answer: B
2x + y = 20
|y| <= 20
For how many ordered pairs (x , y) that are solutions of the system above are x and y both integers?
Options:
A) 15
B) 17
C) 19
D) 21
E) 25

Solution: Hi - The questions says |y| <=20 so the values of y will range from 0 to 20. So the values of y will be 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20. So 21 (d) is the answer. remember sign doesn't matter for y as y will always be positive.21
Answer: D
998 x 998 = ?
Options:  A) 996000  B) 1000000  C) 996004  D) 4000  E) 996008

Solution: 998 x 998= (998)2   = (1000 - 2)2   = (1000)2 + (2)2 - (2 x 1000 x 2)   = 1000000+ 4 - 4000   = 1000004 - 4000= 
1000004 - 4000 = 996_004
996004.   996004)
Answer: C
Solve for x: 2x – y = (3/4)x + 6.  Choose the most appropriate option:
A) (y + 6)/5	B) 4(y + 6)/5	C) (y + 6)	D) 4(y - 6)/5	E) 2(y - 6)/5

Solution: Solution:   2x – y = (3/4)x + 6.   or, 2x - (3/4)x = y + 6.   or, (8x -3x)/4 = y + 6.   or, 5x/4 = y + 6.   or, 5x = 4(y + 6).   or, 5x = 4y + 24.   or, x = (4y + 24)/5.   Therefore, x = 4(y + 6)/5.   Answer: (4(y + 6)/5).
Answer: B
If 0 < x < 1 < y, which of the following must be true? Choose the correct choice from the following options:
A) 1 < 1/x < 1/y B) 1/x < 1 < 1/y C) 1/x < 1/y < 1 D) 1/y < 1 < 1/x E) 1/y < 1/x < 1

Solution: Soln:   0<x<1<y. Let x=1/2 and y =2   Substituting values:   A. 1<2<1/2 --- Wrong   B. 2<1< 1/2 --- Wrong   C. 2<1/2<1 --- Wrong   D. 1/2<1<2 --- Correct   E. 1/2<2<1 --- Wrong   Hence answer is 1/y < 1 < 1/x
Answer: D
A certain sum of money is divided among A, B and C so that for each Rs. A has, B has 65 paisa and C 40 paisa. If C's share is Rs.40, find the sum of money? Choose the most appropriate option:
A) Rs.201 B) Rs.220 C) Rs.228 D) Rs.205 E) Rs.202

Solution: A:B:C = 100:65:40   = 20:13:8   8 ---- 40   41 ---- ? => Rs.205   Answer: Rs.205
Answer: D
40 is subtracted from 60% of a number, the result is 50. Find the number?  Select the correct option.
A) 150
B) 140
C) 130
D) 120
E) 110

Solution: (60/100) * X – 40 = 50   6X = 900   X = 150   150NSWER:150
Answer: A
Zayn, Mark, David ,Peter, Harry and Paula line up at a ticket window. In how many ways can they arrange themselves so that David is second in line from the window?  Select:  A) a 100  B) b 112  C) c 90  D) d 120  E) e 30

Solution: D   David's position is fixed. Now we need to arrange all others around David.   There are 5x4x3x2x1= 120 ways to arrange five people.
Answer: D
If m / p is an integer, which of the following statements must be true?
Choose the correct choice from the following answers:
A) m / p is an integer
B) p is an integer
C) both m and p are integers
D) either m or p is negative
E) m = np where n is an integer

Solution: Let m = 1/4; p = 1/8 -->m/p = 2   m= np where n is an integer --> 1/4 = 2*(1/8) --> Correct   Answer: m = np where n is an integer
Answer: E
A box contain 12 chocolates and 10 biscuit packets .What is the probability that one chocolate is selected is:	Choose the correct answer.
A) 12/22
B) 10/22
C) 21
D) 5/22
E) 6/11

Solution: Total number of chocolates and biscuit packets = 12+10= 
12+10 = 22
22   no.of chocolates in a box= 12   probability of one chocolate is selected = 12/22= 6/11   Answer is 6/11
Answer: E
Look at this series: 2.2, 2.5, 2.8, 3.1, ... What number should come next?
Choose the correct answer
A) 3.2
B) 3.3
C) 3.4
D) 3.5
E) 3.6

Solution: 3.4   3.4   In this simple addition series, each number increases by 0.3.
Answer: C
For a positive integer n, let Pn denote the product of the digits of nn and Sn denote the sum of the digits of nn. The number of integers between 10 and 100 for which Pn+Sn=n
Choose the correct choice from the following options
A) 2
B) 3
C) 9
D) 12
E) None

Solution: Explanation:   Let the two digit number be 'ab'   Given, a × b + a + b = 10a + b   a × b = 9a   b = 9   Therefore, for b = 9, the above condition satisfies. So all the two digit numbers for which units digit is 9 are our solutions. They range from 19 to 99. Total 9 numbers.   9orrect option: c
Answer: C
2 friends X & Y walk from A to B at a distance of 39 miles at 3 miles/hr and 3.5 miles/hr respectively. Y reaches B, returns immediately and meets X at ‘C’ . find distance from A to C.	Choose the most appropriate option.
A) 38 km
B) 39 km
C) 35 km
D) 36 km
E) 34 km

Solution: Since the time of meeting will be same. Set the equation for time as equal.   ---------------39---------------   A*...................C*...........*B   -----(39-x)-------|----x------   At C,   T(A)=T(B)   ((39-x)/3)=((39+x)/3.5)   Solve for x. and subtract x from 39 to get the answer.   answer is  39-3= 
 39-3 = 36
36km.   ANSWER:36 km
Answer: D
Company KW is being sold, and both Company A and Company B were considering the purchase. The price of Company KW is 90% more than Company A has in assets, and this same price is also 100% more than Company B has in assets. If Companies A and B were to merge and combine their assets, the price of Company KW would be approximately what percent of these combined assets?  Choose the most appropriate option: A) 66% B) 75% C) 86% D) 97% E) 150%

Solution: Let the price of Company A's assets be 100   Price of assets of KW is 90% more than company A's assets which is 190   Price of assets of KW is 100% more than company B's assets which means price of Company B's assets is half the price of KW = 95   A+B = 195   KW = 190   KW/(A+B)*100 = 190/195*100 = 97.43% or 97%97%
Answer: D
Finch has s pairs of shoes, which is 1/6 as many as Guptil and twice as many as S.Smith. In terms of s, how many pairs of shoes do the three of them have combined?  Choose the correct choice:	A) 5s	B) 15/2*s	C) 14s	D) 3s	E) 13/2*s

Solution: == s +6s + s/2 ==> 7s + 1/2 s = 15/2*s   Ans .15/2*s
Answer: B
What is the sum of all the multiples of 10 between 0 and 120? Choose one:
A) 500
B) 620
C) 450
D) 340
E) 780

Solution: The multiples of 10 between 0 and 120 are 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110 and 120. If these are all added together, the result is 780.   Final Answer:   780
Answer: E
If n=5p where p is a prime number greater than 1, how many different positive even divisors does n have, WITHOUT N VALUE?
Choose the correct choice from the following options:  A) 1  B) 2  C) 3  D) 45  E) 5

Solution: N = 5P and that P is a prime number greater than 1. Let's TEST P = 2; so N = 10   The question now asks how many DIFFERENT positive EVEN divisors does 10 have, including 10?   10:   1,10   5,2   How many of these divisors are EVEN? 2 …..1 even divisors.   1NSWER:1
Answer: A
In a sports club with 35 members, 15 play badminton and 18 play tennis and 5 do not play either. How many members play both badminton and tennis? Choose the correct choice from the following answers.
A) 3  B) 5  C) 6  D) 7  E) 8

Solution: 15+18= 
15+18 = 33
33   but where as total number is   35-5= 
  35-5 = 30
30   therefore answer is   33-30= 
  33-30 = 3
3   Hence 3nswer is 3
Answer: A
If 6th March, 2013 is Wednesday, what was the day of the week on 6th March, 2012?  Answers
A) Sunday  B) Saturday  C) Tuesday  D) Wednesday  E) None of these

Solution: Solution   The year 2012 is a leap year. So, it has 2 odd days.   But, Feb 2012 not included because we are calculating from March 2012 to March 2013. So it has 1 odd day only.   The day on 6th March, 2013 will be 1 day beyond the day on 6th March, 2012. Given that, 6th March, 2013 is Wednesday.   6th March, 2012 is Tuesday (1 day before to 6th March, 2013)   Answer Tuesday
Answer: C
In Winchard's company 60% of the employees earn less than $50,000 a year, 60% of the employees earn more than $40,000 a year, 11% of the employees earn $43,000 a year and 5% of the employees earn $49,000 a year. What is the median salary for the company?
Choose the correct choice from the following answers.
A) 43.0	B) 45.5	C) 46.0	D) 49.0	E) 50.0

Solution: In Winchard's company 60% of the employees earn less than $50,000 a year, 50 and 51 employee will be each 43K. hence median = (43K+43k)/2=43.0(43 +43 )/2= 
(43 +43 )/2 = 43
43.0
Answer: A
Jason flips a coin three times. What is the probability E that the coin will land on the same side in all three tosses?	Pick one:
A) 1/16  B) 1/8  C) 1/4  D) 1/3  E) 1/2

Solution: Total outcome is 2^3=8   Favorable cases HHH or TTT   Therefore, probability E is 2/8 or 1/4.1/4
Answer: C
Two numbers when divided by a divisor leave remainders of 218 and 342 respectively. The remainder obtained when the sum of the numbers is divided by the same divisor is 68. Find the divisor.
Choose one.
A) 387  B) 423  C) 492  D) 512  E) 602

Solution: Let x be the divisor.   N1 = xa + 218   N2 = xb + 342   N1 + N2 = x(a+b) + 560 = xc + 68   x(c-a-b) = 492 but we know that x > 342, thus (c-a-b) must equal 1.   The answer is 492.
Answer: C
Find the middle one when The sum of three consecutive even numbers is 36?  Choose the correct choice from the following answers:
A) 10
B) 12
C) 14
D) 16
E) 17

Solution: 3 consecutive numbers can be a - 1, a, a + 1   So sum of numbers = 3a = 36.   Hence a = 12.   12
Answer: B
If Packard reads at a constant rate of 4 pages every 5 minutes, how many seconds will it take him to read N pages?	Choose the correct choice:
A) 75  B) 2N  C) 5/2*N  D) 24N  E) 150

Solution: Packard would read 1 page in 5/4 min   Packard would read N page in (5/4)*N min i.e. (5/4)*N*60 Seconds = 75N Seconds.   Option 75 is the correct 75nswer.
Answer: A
Four friends built a colony for themselves. They built their own houses at different distances from each other.
Chris lived 60 km away from Alex.
Darren lived 40 km away from Bill.
Chris lived 10 km nearer to Darren than he lived to Bill.
Can you find out how far was Darren's house from Alex?  Choose the most appropriate option.
A) 55 km. B) 65 km. C) 75 km. D) 85 km. E) 95 km.

Solution: Solution:   75km   Explanation:   Distance between Bill and Darren = 40 km   Distance between Bill and Chris + Distance between Chris and Darren = 40 km   Distance between Bill and Chris + (Distance between Bill and Chris - 10) = 40 km   2 * Distance between Bill and Chris = 50 km   Distance between Bill and Chris = 25   Distance between Chris and Darren = 15 km   Therefore, distance between Darren's house and Alex's house = 60 + 15= 
60 + 15 = 75
75 km.   Answer 75 km.
Answer: C
A 700-level question for the GMAT committed souls studying over the weekend.
If a and b are distinct integers and a^b=b^a, how many solutions does the ordered pair (a, b) have? Choose one:
A) None
B) 1
C) 2
D) 4
E) Infinite

Solution: (2,4) and (4,2)   a=1 b=1 and a=2 b=2 also has the solution. But we need distinct. Now when we will increase a>4, b^a increase more rapidly than a^b.   ANSWER:1
Answer: B
If a man crosses a 400 m long street in 5 minutes. What is his speed?  Choices:  A) 7 km/hr  B) 7.1 km/hr  C) 7.2 km/hr  D) 4.8 km/hr  E) 8.5 km/hr

Solution: distance = 400 meter   time = 5 minutes = 5 x 60 seconds = 300 seconds   Speed = distance/time=400/300=1.33m/s=1.33×18/5 km/hr=4.8 km/hr   4.8 km/hr
Answer: D
If x + y = 8 and y − 3x = 7, then what is the value of y-x? Choose the correct choice:
A) 1/7 B) 3 C) 15 D) 15/2 E) 60/7

Solution: x+y=8 ...equation 1   -3x+y=7 ...equation 2   adding both the equations   -2x+2y=15=>y-x=15/2   correct answer option 15/2
Answer: D
The length and breadth of a rectangle is increased by 5% and 15% respectively. What is the increase in the area?  Select the correct option
A) 21.25	B) 22.75	C) 19.25	D) 20.75	E) 22.25

Solution: 100*100= 
100*100 = 10_000
10000   105*115= 
105*115 = 12_075
12075   -----------   2075   10000------2075   100-----?=>20.75   Answer 20.75
Answer: D
The average of five numbers is 30. If one number is excluded, the average becomes 28. The excluded number is?
Answers
A) 8
B) 6
C) 38
D) 35
E) 96

Solution: Excluded number   = (30 * 5) - (28 * 4)   = 150 - 112= 
150 - 112 = 38
38   Answer:38
Answer: C
If the price of a book is first decreased by 50% and then increased by 60%, then the net change in the price will be?
Choose the correct choice from the following answers
A) 20% decrease
B) 10% increase
C) 10% decrease
D) 15% increase
E) 25% decrease

Solution: Let the original price be $100   New final price = 160% of (50% of $100)   = 160/100 * 50/100 *100= 
160/100 * 50/100 *100 = 80
$80   Decrease is 20%   20% decreasenswer is 20% decrease
Answer: A
Superman flied 200 miles in 1 hour 1 minute. What was the average speed of Superman?	Answers
A) 180 miles / hour B) 170.3 miles / hour C) 196.72 miles / hour D) 160 miles / hour E) 150 miles / hour

Solution: We first convert the time of 1 hours 1 minutes in minutes   1 hours 1 minutes = 1 * 60 + 1= 
1 * 60 + 1 = 61
61 minutes   Average speed S is given by distance / time. Hence   S= 200 miles / 61 minutes = 3.27 mile / minute   = 196.72 miles / hour   correct answer 196.72 miles / hour
Answer: C
Two circular blocks are placed one above the other. Block A at the bottom has a diameter of 24 cm. Block B at the top has a diameter of 16 cm. What fraction of Block A's surface is not covered by Block B? Choose the correct choice from the following answers:	A) 5/6	B) 2/3	C) 2/9	D) 18/20	E) 4/5

Solution: The questions asks us to find the surface which is not covered by the Block B i.e., area of the surface not covered.   Where as circumference is the length along the edge of the circle,   2*pi*r implies the length of the curve   pi*r^2 implies area enclosed by that curve..hence Area of the circle is considered for this problem   Area of the Block B=pi* r^2, where r=8   =>pi*64   Area of the Block A=pi*144   Surface not covered by the Block B=pi*144-pi*64=Pi*80   fraction of Block A surface is not covered by a Block B= Pi*80/total area of the Block A   =>Pi*80/Pi*144=2/9   Answer 2/9
Answer: C
Liam is pulled over for speeding just as he is arriving at work.He explains to the police officer that he could not afford to be late today, and has arrived at work only four minutes before he is to start. The officer explains that if Liam had driven 5mph slower for his whole commute, he would have arrived at work exactly on time. If Liam's commute is 40 miles long,how fast was he actually driving?(Assume that Liam drove at a constant speed for the duration of his commute.)  Choose the correct choice from the following options.
A) 50 mph B) 45 mph C) 48 mph D) 52 mph E) 60 mph

Solution: Let t be the number of hours he would need to reach office on time.   when he is driving with over speed, he reached office 4 min earlier! so the equation for this is s(t - 4/60) = 40   where s is the speed and 30 is the distance.   if he decreases his speed by 5mph then he would have reached his office on time: (s-5)t = 40   if you solve above equations, you will arrive at t = 2/3 hr and s = 60mph   therefore answer is 60 mph
Answer: E
Salesperson A's compensation for any week is $240 plus 6 percent of the portion of A's total sales above $1,000 for that week. Salesperson B's compensation for any week is 8 percent of B's total sales for that week. For what amount of total weekly sales would both salespeople earn the same compensation? Choose the correct answer:  A) $7000  B) $9000  C) $11,000  D) $13,000  E) $15,000

Solution: 240+0.06(x-1000) = 0.08x   0.02x = 180   x = $9,000   The answer is $9000.
Answer: B
A train passes a station platform in 21 seconds and a man standing on the platform in 15 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? Choose the correct choice from the following choices
A) 299	B) 277	C) 90	D) 88	E) 112

Solution: Speed = [54 * 5/18] m/sec = 15 m/sec.   Length of the train = (15 * 15)= 
(15 * 15) = 225
225 m.   Let the length of the platform be x meters.   Then, x + 225 / 21= 15   x + 225 = 315   x = 90 m.   Answer:90
Answer: C
Evaluate combination
11C3  Select.
A) 10000	B) 1000	C) 165	D) 1	E) 0

Solution: Explanation:   n165n=1   n165r=n!/r!(n-r)!   111653=11!/3!(11-3)!=165   Option 165
Answer: C
The present ratio of students to teachers at a certain school is 40 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?  Choose the correct choice from the following choices
A) 5	B) 8	C) 10	D) 12	E) 15

Solution: We are given that the ratio of students to teacher is 40 to 1. We can rewrite this using variable multipliers.   students : teachers = 40x : x   We are next given that student enrollment increases by 50 and the number of teachers increases by 5. With this change the new ratio becomes 25 to 1. We can put all this into an equation:   Students/Teachers  25/1 = (40x + 50)/(x + 5)   If we cross multiply we have:   25(x + 5) = 40x + 50   25x + 125 = 40x + 50   5 = x   Since x is the present number of teachers, currently there are 5 teachers.   5nswer 5.
Answer: A
There are 15 points in a given plane, no three of which are on the same line. If one of the points is represented as 'L', then how many triangles can be determined with the 15 points that contain the point L?	Choose the correct choice from the following choices:
A) 91
B) 105
C) 182
D) 210
E) 455

Solution: Fist point is L which is fixed so can be selected in 1 way   Second point can be selected in 14 ways   Third point can be selected in 13 ways   so total ways = 1x14x13 = 182   but answer is 91 which is 182/2=182
Answer: C
Choose the number pair/group which is different from others?	Select the correct option:
A) 8 : 39 B) 8 : 38 C) 8 : 33 D) 8 : 32 E) 8 : 31

Solution: Explanation:   In all other pairs, 2nd number = (1st number × 3) + 1.   Answer: 8 : 33) 8 : 33
Answer: C