MU-NLPC/Calc-aqua_rat huggingface dataset:
If x and y are perfect squares, then which two of the following is not necessarily a perfect square?  Choose the correct choice from the following choices:	A) x^2	B) xy	C) 4x	D) x+y	E) x^5

Solution: If x=y=1^2=1, then each option but C is a perfect square, therefore C is NOT necessarily a perfect square.   Answer: 4x.
Answer: C
A farm has chickens, cows and sheep. There are six times the number of chickens and cows than sheep. If there are more cows than chickens or sheep, and together, cows and chickens have a total of 100 feet and heads, how many sheep live at the farm?
Pick one:
A) 5 B) 8 C) 10 D) 4 E) 17

Solution: Chicken - ch   Cows - C   Sheep -S   ch+C=6S   C> ch and c>s   Each cow has 4 legs and 1 head   Each chicken has 2 legs and 1 head   So 5c+3ch=100 (sum of legs and head)   There are 2 possible solutions to this equation   c=11 and ch=9 or   c=14 and ch=10   Since from first equation where ch+c=6s   The sum of ch and c should be divisbile by 6. 20 is not so the only possible solution is c=14 and ch=10. So s=4   Answer : 4
Answer: D
The length of a rectangle is increased by 25% and its breadth is decreased by 20%. What is the effect on its area? Choose one
A) 10000
B) 10020
C) 10208
D) 10029
E) 10182

Solution: 100 * 100= 
100 * 100 = 10_000
10000   125 * 80= 
125 * 80 = 10_000
10000   10000nswer:10000
Answer: A
Solve This
6 + 7 = 12
8 + 9 = 16
5 + 6 = 10
7 + 8 = 14
Then, 9 + 10 = ??  Choices
A) 11
B) 12
C) 13
D) 14
E) 18

Solution: 18   ANSW18R:18
Answer: E
9.009/1.001	Pick.
A) 0.009  B) 0.09  C) 0.9  D) 9  E) 90

Solution: Answer is 9, move the decimal forward three places for both numerator and denominator or just multiply both by a thousand. The result is 9009/1001= 
9009/1001 = 9
9   Answer 9
Answer: D
If t>0.9, which of the following options can be the value of t? Choose the correct answer:
A) 0.9^2  B) √(0.9)  C) 0.09  D) 0.9  E) 0.9^3

Solution: Lets take a few examples   When .2 is squared it gives .04   when .5 is squared it gives .25   When .9 is squared it gives .81   So raising a fraction to its power of 2 or 3 only reduces the value of the fraction   This is because   .2 = 2/10   .2^2= 4/100   .2^3=8/1000   Since the denominator gets an extra 0 each time u increase the power , it is going to drag the value down   √(0.9)ut if you just think about the opposite case :   Then we can see , if squaring a fraction diminish its value, then taking the square root of it will again increase its value   that is √(0.04) will give you back 0.2   so √(0.04) > 0.04   so obviously diminishing the power will appreciate the value   So t √(0.9) > 0.9   Hence Correct Answer is (√(0.9))
Answer: B
Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 160 sandwiches were made, how many bologna sandwiches
were made? Choose the correct choice from the following.
A) 15  B) 30  C) 38  D) 42  E) 56

Solution: For deciding such task we should calculate all parts 5 + 7 + 8= 
5 + 7 + 8 = 20
20 parts   and we should calculate how many sandwiches holds 1 part:   160 / 20= 
160 / 20 = 8
8 sandwiches in one part   For bologna we have 8 parts so:    7 * 8= 
 7 * 8 = 56
56   Answer is 56
Answer: E
A store has 10 bottles of juice, including 5 bottles of apple juice. In the evening, 6 bottles of juice are sold one by one. What is the probability of selling 3 bottles of apple juice among the 6 bottles? Assume that every bottle has an equal chance of being bought. Choose the correct option:
A) 4/9  B) 6/11  C) 8/15  D) 10/21  E) 12/25

Solution: The total number of ways to sell 6 bottles from 10 is 10C6 = 210.   The number of ways to sell 3 bottles of apple juice is 5C3*5C3 = 10*10= 
10*10 = 100
100   P(selling 3 bottles of apple juice)= 100/210 = 10/21   The answer is 10/21.
Answer: D
The length of the bridge, which a train 140 meters long and travelling at 45 km/hr can cross in 30 seconds, is?  Choose one.
A) 388  B) 267  C) 235  D) 288  E) 261

Solution: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (140 + X)/30 = 25/2 ==> X = 235 m.   Answer: 235
Answer: C
For any positive integer n, the sum of the first n positive integers equals [n(n+1)]/2.
What is the sum of all the even integers between 99 and 201?	Pick: A) 6540 B) 7650 C) 8760 D) 9870 E) 10,980

Solution: 100 + 102 +...+ 200 = 51*100 + (2+4...+100) = 51*100 + 2(1+2+...+50) =   51*100 + 2(50)(51)/2 = 150*51= 
150*51 = 7_650
7650   The answer is 7650.
Answer: B
What is the solution of the equations x - y = 0.9 and 11(x + y)-1 = 2 ?	Choices.
A) x = 3.2, y = 2.3  B) x = 1, y = 0.1  C) x = 2, y = 1.1  D) x = 1.2, y = 0.3  E) None

Solution: x = 3.2, y = 2.3nswer   x - y = 0.9 ...(i)   and 11(x + y)-1=2   ⇒ 11/ (x + y) = 2   ⇒ 2(x + y) =11   ⇒ x + y = 11/2 ...(ii)   On solving Eqs.(i) and (ii),we get   x = 3.2   and y = 2.3   Correct Option: x = 3.2, y = 2.3
Answer: A
Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made?	Select:
A) Rs. 13.50	B) Rs. 14.50	C) Rs. 15.50	D) Rs. 16.50	E) None of these

Solution: Let the quantities of A and B mixed be 3x kg and 7x kg.   Cost of 3x kg of A = 9(3x) = Rs. 27x   Cost of 7x kg of B = 15(7x) = Rs. 105x   Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x   Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66   Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50   ANSWER:Rs. 16.50
Answer: D
A certain college's enrollment at the beginning of 1992 was 20 percent greater than it was at the beginning of 1991, and its enrollment at the beginning of 1993 was 10 percent greater than it was at the beginning of 1992. The college's enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ?	Answers
A) 17.5%
B) 24%
C) 30%
D) 32%
E) 38%

Solution: Suppose enrollment in 1991 was 100   Then enrollment in 1992 will be 120   And enrollment in 1993 will be 120*1.10= 
120*1.10 = 132
132   Increase in 1993 from 1991= 132-100= 
132-100 = 32
32   Answer : 32%
Answer: D
At what rate of annual simple interest,a certain sum will amount to four times in 15 year?
Choose the correct choice from the following options.
A) 15% B) 17.5% C) 20% D) 25% E) 35%

Solution: r=?   t=15 yrs   SI=p*r*t/100   Amount = SI+p = 4p   (p*r*15/100)+p = 4p   p(15r/100 + 1) = 4p   15r + 100 = 400   15r = 300   r = 20%   ANSWER:20%
Answer: C
At what angle the hands of a clock are inclined at 15 minutes past 5?
Choose the correct option: A) 67.9 B) 67.5 C) 67.2 D) 67.1 E) 67.92

Solution: Answer: 67.5) 67.5 degrees
Answer: B
The area of a parallelogram is 147 sq m and its base is thrice the corresponding height. Then the length of the base is?  Choose the correct choice from the following answers:
A) 14m
B) 29m
C) 49m
D) 7
E) none

Solution: b*h=147 b*h=147=>b^2=49m.b=7 Answer: (7)
Answer: D
Albert buys 4 horses and 9 goats for $ 13,400. If he sells the horses at 10% profit and the goats at 20% profit, then he earns a total profit of $ 1880. The cost of a horse is:  Options
A) $ 3000	B) $ 6000	C) $ 2000	D) $ 8000	E) $ 7000

Solution: C   $ 2000   Let C.P. of each horse be $ x and C.P. of each cow be $ y.   Then, 4x + 9y = 13400 -- (i)   And, 10% of 4x + 20% of 9y = 1880   2/5 x + 9/5 y = 1880 => 2x + 9y = 9400 -- (ii)   Solving (i) and (ii), we get : x = 2000 and y = 600.   $ 2000ost price of each horse = $ 2000.
Answer: C
Free notebooks were distributed in a class among all the students. Each student got notebooks which were one-eighth of the number of student. If number of student been half, then each child would have received 16 notebooks in total. Find the total number of books distributed among students?
Choose the most appropriate option.
A) 456  B) 480  C) 499  D) 501  E) 512

Solution: Let suppose total number of students in class are X.   Then from the question we can conclude it that,   X∗18X=X2∗16=>X=64Total notebooks,=18X2=(18∗64∗64)=512   512
Answer: E
The sum of three numbers is 98. If the ratio of the first to the second is 2:3. And that of the second to the third is 5:8, then the second number is: Answers:
A) 17
B) 30
C) 87
D) 27
E) 82

Solution: Let the three parts A, B, C.   Then, A:B = 2:3 and B:C = 5:8   = (5 * 3/5) : (8 * 3/5) = 3:24/5   A:B:C = 2:3:24/5   = 10:15:24 => B = 98 * 15/49= 
98 * 15/49 = 30
30.   Answer:30
Answer: B
When tossing two coins once, what is the probability of heads on both the coins?  Choose the correct choice:
A) 2/7
B) 3/5
C) 2/6
D) 1/4
E) 1/47

Solution: Explanation :   Total number of outcomes possible when a coin is tossed = 2   Hence, total number of outcomes possible when two coins are tossed, n(S) = 2 × 2 = 4   E = event of getting heads on both the coins = {HH}   Hence, n(E) = 1   P(E)=n(E)/n(S)=1/4   1/4
Answer: D
A train is 360 meter long is running at a speed of 60 km/hour. In what time will it pass a bridge of 140 meter length?
Choose the correct answer:
A) 87  B) 69  C) 30  D) 72  E) 21

Solution: Speed = 60 Km/hr = 60*(5/18) m/sec = 50/3 m/sec   Total distance = 360+140= 
360+140 = 500
500 meter   Time= Distance/speed   = 500 * (3/50)= 
500 * (3/50) = 30
30 seconds   Answer: 30
Answer: C
The average of 13 numbers is 60. Average of the first 7 of them is 56 and that of the last 7 is 61. Find the 8th number?
Select.
A) 39
B) 83
C) 45
D) 53
E) 64

Solution: Sum of all the 13 numbers = 13 * 60= 
13 * 60 = 780
780   Sum of the first 7 of them= 7 * 56= 
7 * 56 = 392
392   Sum of the last 7 of them= 7 * 61= 
7 * 61 = 427
427   So, the 8th number= 427 + 392 - 780= 
427 + 392 - 780 = 39
39.   39nswer:39
Answer: A
five children, Arya, Betsy, Chen, Daniel, Emily, are to be seated in a single row of six chairs. If Betsy cannot sit next to Emily, how many different arrangements of the six children are possible?  Choose one
A) 240  B) 480  C) 540  D) 72  E) 840

Solution: Since it is more time consuming and error prone to find ways Betsy and E not sitting together, It is better we find ways in which they will be together and then subtract from total ways..   total ways = 5!..   ways B and E will be sitting together..   take both B and E as one, then these two together with other 3 can sit in 4! ways ...   Also B and E can sit within themselves in 2! ways..   so the answer required = 5!-2*4!=72..   72
Answer: D
A standard Veggiematik machine can chop 36 carrots in 4 minutes. How many carrots can 6 standard Veggiematik machines chop in 3 minutes?
Select the correct option:
A) 36	B) 54	C) 162	D) 216	E) 324

Solution: Direct Relationship:-   1 standard Veggiematik machine - 36 162arrots - 4 minutes,   1 standard Veggiematik machine - 9 162arrots - 1 minute,   Now   6 standard Veggiematik machine - ? 162arrots - 3 minutes,   Hence = 9X6X3 =324 162arrots   Answer 162
Answer: C
The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?  Pick one:  A) 9  B) 4  C) 8  D) 5  E) 3

Solution: S = 4   M = x   DS = x + 4   US = x - 4   6/(x + 4) + 6/(x - 4) = 2   x = 8   Answer:8
Answer: C
If A is thrice as fast as B and together can do a work in 15 days. In how many days A alone can do the work? Pick:
A) 36	B) 20	C) 28	D) 54	E) 45

Solution: A’s one day’s work= 1/X   20’s one day’s work= 1/3x   A + 20’s one day’s work= 1/x + 1/3x = 1/15   = 3+1/3x = 4/3x = 1/15   x = 15*4/3= 
15*4/3 = 20
20   ANSWER:20
Answer: B
a, b, c, d, and e are five consecutive numbers in increasing order of size. Deleting one of the five
numbers from the set decreased the sum of the remaining numbers in the set by 20%. Which one of
the following numbers Q was deleted?  Pick one.
A) a B) b C) c D) d E) e

Solution: a+b+c+d+e => 1+2+3+4+5= 
1+2+3+4+5 = 15
15   Q=20%*15= 3 =>c
Answer: C
A sells a Cricket Bat to B at a profit of 20%. B sells it to C at a profit of 25%. If C pays $222 for it, the cost price of the Cricket Bat for A is:  Pick one
A) 150  B) 148  C) 130  D) 160  E) 210

Solution: 125% of 120% of A = 222   125/100 * 120/100 * A = 222   A = 222 * 2/3= 
222 * 2/3 = 148
148.   ANSWER 148
Answer: B
Sally has a gold credit card with a certain spending limit, and a platinum card with twice the spending limit of the gold card. Currently, she has a balance on her gold card that is 1/3 of the spending limit on that card, and she has a balance on her platinum card that is 1/9 of the spending limit on that card. If Sally transfers the entire balance on her gold card to her platinum card, what portion of her limit on the platinum card will remain unspent?	Pick
A) 11/30 B) 29/60 C) 17/30 D) 13/18 E) 11/15

Solution: Let s assume the platinum card spending limit =x   Gold card spending limit will be =x/2   balance on gold card is =x/2*1/3=x/6   Platinum card unspent limit is= x-1/9x=8/9x   So if gold card balance is transferred then the rest unspent will be   8/9x-x/6=13/18x   So the ans is 13/18
Answer: D
The membership of a committee consists of 3 English teachers, 4 Mathematics teachers, and 2 Social Studies teachers. If 2 committee members are to be selected at random to write the committee’s report, what is the probability that the two members selected will both be social teachers?  Choose the correct choice from the following choices.
A) 2/3  B) 1/12  C) 2/9  D) 1/2  E) 1/24

Solution: Probability of first member an English teacher = 3/9   Probability of second member an English teacher = 2/8   Probability of both being english teacher = 3/9 x 2/8 =1/12 (1/12)
Answer: B
If 4 men can colour 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in Pick one.
A) 1 day B) 2 days C) 4 days D) 3 days E) None

Solution: The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m   No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 6 = 1 day.   Option '1 day'
Answer: A
A cyclist covers a distnce of 750 m in 2 min 30 sec. What is the speed in km/hr of the cyclist? Pick
A) 28 km/hr  B) 18 km/hr  C) 20 km/hr  D) 22 km/hr  E) 24 km/hr

Solution: Speed = { 750 } m/sec =5 m/sec = { 5 * 18 } km/hr =18km/hr   ANSWER 18 km/hr
Answer: B
A person sold a horse at a gain of 15%. Had he bought it for 25% less and sold it for Rs. 600 less, he would have made a profit of 32%. The cost price of the horse was:  Answers.
A) Rs. 3,750 B) Rs. 3,250 C) Rs. 2,750 D) Rs. 2,250 E) None

Solution: Solution: Let the original CP = Rs. X.   Hence, SP= X + 15% of X = 115X/100 = Rs. 23X/20.   New, CP = X - 25% of X = 75X/100 = 3X/4.   New SP = 3X/4 + 32% of 3X/4 = Rs. 99X/100.   According to the question,   (23x/20)-(99x/100)= 600   Or, (115x-99x)/100 = 600   16x = 600*100   X = 600*100/16 = Rs. 3750.   Rs. 3,750nswer: Option Rs. 3,750
Answer: A
pipes P and Q would fill a cistern 18 and 24 minutes respectively. Both pipes being opened, find when the first pipe must be turned off so that the cistern may be just filled in 12 minutes? Pick
A) 8 B) 9 C) 2 D) 7 E) 5

Solution: x/18 + 12/24 = 1   x = 9   Answer: 9
Answer: B
A Ship going at the speed of 18 km/hr crosses a light house in 20 seconds. What is the length of the train? Select:	A) 120	B) 150	C) 100	D) 240	E) 200

Solution: Speed=(18x5/18)=5 m/sec.   Length of the train=(Speed x Time).   Length of the train=5x20m = 100 m.   Answer: 100
Answer: C
The ratio of the incomes of X and Y is 6:4 and the ratio of their expenditure is 5:3. If at the end of the year, each saves $2000 then the income of X is? Choose the correct choice from the following choices.
A) $11000
B) $10000
C) $12000
D) $10500
E) $10600

Solution: Let the income of X and Y be $6x and $4x   Let their expenditures be $5y and $3y   6x-5y = 2000-------1)   4x-3y = 2000-------2)   From 1) and 2)   2x-2y = 0 2 -2= 
2 -2 = 0
0=> x = y   x = 2000   Income of X 5 * 2000= 
5 * 2000 = 10_000
$10000   Answer : $10000
Answer: B
There is a square of side 6cm . A circle is inscribed inside the square. Find the ratio of the area of circle to square.  Answers:
A) 11/14	B) 1/14	C) 13/14	D) 12/14	E) 5/14

Solution: Let the side of square = a unit   so 11/14rea of Square = a^2   Diameter of inscribed circle = side of square = a   Radius of circle = a/2   11/14rea of circle = (22/7)(a/2)^2   Ratio of area of circle to square = {(22/7)(a/2)^2}/a^2 = 11/14   11/14NSWER:11/14
Answer: A
The length of a room is 8 m and width is 4.75 m. What is the cost of paying the floor by slabs at the rate of Rs. 900 per sq. metre.  Select:
A) 25650 B) 25750 C) 26550 D) 26750 E) 34200

Solution: Area = 8 × 4.75 sq. metre.   Cost for 1 sq. metre. = Rs. 900   Hence total cost = 8 × 4.75 × 900   = 8 × 4275 = Rs. 34200   Answer is 34200.
Answer: E
If the height of an equilateral triangle TBC is equal in length to the hypotenuse of an isosceles right triangle DEF, a side of ΔTBC is how many times as long as a leg of the right triangle DEF?	Choose the correct choice
A) (√2)/(√3)	B) (√3)/(√2)	C) √2	D) (2√2)/(√3)	E) 2/(√3)

Solution: Side of the equilateral triangle TBC = 2m ----> height = m * sqtr(2)   Hipotenuse of the right triangle TBC = m * sqrt(3) ----> side = m * sqtr(3) / sqtr(2)   Question is 2m/m * sqtr(3) / sqtr(2) = 2*sqrt(2)/sqrt(3)=(2√2)/(√3)
Answer: D
A certain pilot flew 400 miles to City K at an average speed of 350 miles per hour with the wind and made the trip back at an average speed of 450 miles per hour against the wind. Which of the following is closest to the pilot’s average speed, in miles per hour, for the round-trip? Choose the correct choice from the following choices
A) 390	B) 290	C) 300	D) 310	E) 320

Solution: 390vg speed = total distance/ total time   total distance = 800   total time = 400/350 + 400/450 = 128/63   => avg speed = (800*63)/128 = 390(approx)   ans is 390
Answer: A
Ramu rides his bike at an average speed of 45 km/hr and reaches his desitination in four hours. Somu covers the same distance in six hours. If Ramu covered his journey at an average speed which was 9 km/hr less and Somu covered his journey at an average speed which was 10 km/hr more, then the difference in their times taken to reach the destination would be (in minutes)? Choose the correct choice from the following answers:
A) 12
B) 30
C) 27
D) 12
E) 13

Solution: Distance travelled by Ramu = 45 * 4= 
45 * 4 = 180
180 km   Somu travelled the same distance in 6 hours.   His speed= 180/6= 
180/6 = 30
30 km/hr   Hence in the conditional case, Ramu's speed= 45 - 9= 
45 - 9 = 36
36 km/hr and Somu's speed= 30 + 10= 
30 + 10 = 40
40km/hr.   Therefore travel time of Ramu and Somu would be 5 hours and 4.5 hours respectively. Hence difference in the time taken= 0.5 hours = 30 minutes.   Answer: 30
Answer: B
A woman named Vaisali started a business investing Rs. 30,000. Roja joined him after six months with an amount of Rs. 90,000 and Sachin joined them with Rs. 60,000 after another six months. The amount of profit earned should be distributed in what ratio among Vaisali, Roja and Sachin respectively, 3 years after A woman started the business ?	Choose the correct option:
A) 7:6:10
B) 6 : 15 : 8
C) 14:15:16
D) 12:15:16
E) 42:45:56

Solution: Explanation :   Akash : Roja : Sachin = (30,000 x 36) : (90,000 x 30) : (60,000 x 24)   = 36 : 90 : 48 = > 6 : 15 : 8   Answer : 6 : 15 : 8
Answer: B
A rope of which a calf is tied is increased from 10 m to 23 m, how much additional grassy ground shall it graze?  Select:
A) 1217	B) 1348.2	C) 1210	D) 1212	E) 1312

Solution: π (232 – 102) = 1348.2   Answer:1348.2
Answer: B
Katie has 9 employees that she must assign to 3 different projects. If 3 employees are assigned to each project and no one is assigned to multiple projects, how many different combinations B of project assignments are possible?
Choose the most appropriate option.
A) 252  B) 1,680  C) 2,340  D) 362,880  E) 592,704

Solution: The ways to select three employees out of 9 for first project = 9C3   The ways to select three employees out of Remaining 6 for Second project = 6C3   Third Project already has the group of three to be assigned to it so need to select that   So total ways to assign 3 employees to each of 3 projects 1,680 = 9C3 * 6C3 * 1 = 1,680   Answer: Option 1,680
Answer: B
Jane sold N boxes of cookies. Each cookie costs M dollars to make, and Jane always makes a profit of P dollars per cookie.
If each box of cookies contains Q cookies, what was the selling price for all the cookies? Choose the correct choice from the following answers: A) NP+QM B) NM-PQ C) NQ+PM D) (PQ+MQ)N E) NQ(P-M)

Solution: The selling price= the cost price+ profit   The cost price= NQM   The profit made=NQP   And the total selling price=NQM+NQP   =NQ(M+P)   The answer is (PQ+MQ)N!!!
Answer: D
A boat can move upstream at 15 kmph and downstream at 23 kmph, then the speed of the current is?
Choose the correct choice from the following answers:
A) 5 kmph  B) 7 kmph  C) 8 kmph  D) 9 kmph  E) 4 kmph

Solution: US = 15   DS = 23   M = (23 - 15)/2= 
(23 - 15)/2 = 4
4   Answer:4 kmph
Answer: E
Train X crosses a stationary train Y in 60 seconds and a pole in 25 seconds with the same speed. The length of the train X is 300 m. What is the length of the stationary train Y?
Select the correct option.
A) 277 m B) 420 m C) 617 m D) 868 m E) 651 m

Solution: Let the length of the stationary train Y be LY   Given that length of train X, LX = 300 m   Let the speed of Train X be V.   Since the train X crosses train Y and a pole in 60 seconds and 25 seconds respectively.   => 300/V = 25 ---> ( 1 )   (300 + LY) / V = 60 ---> ( 2 )   From (1) V = 300/25= 
300/25 = 12
12 m/sec.   From (2) (300 + LY)/12= 60   => 300 + LY = 60 (12) = 720   => LY = 720 - 300= 
720 - 300 = 420
420 m   Length of the stationary train= 420 m   Answer:420 m
Answer: B
In a rectangular coordinate system, points O (2,0), P (2,6), and Q (6,0) represent the sites of three proposed housing developments. If a fire station can be built at any point in the coordinate system, at which point would it be equidistant from all three developments?  Choose the correct choice from the following.
A) (4,3)
B) (5,2)
C) (3,3)
D) (3,4)
E) (4,2)

Solution: All points equidistant from O and Q lie on the line x = 4, so the fire station should lie on this line.   All points equidistant from O and P lie on the line y = 3, so the fire station should lie on this line.   These two intersect at (4,3) and that will be the point equidistant from all 3 points.   The answer is (4,3).
Answer: A
By selling 11 pencils for a rupee a man loses 30%. How many for a rupee should he sell in order to gain 30%?
Choose the correct choice from the following
A) 8	B) 7	C) 6	D) 11	E) 9

Solution: 70% --- 12   130% --- ?   70/130 * 11   = 6   Answer:11
Answer: D
If x and y are integers and |x - y| = 11, what is the minimum possible value of xy? Choose the correct choice from the following choices:
A) -10 B) -18 C) -28 D) -30 E) -32

Solution: Sometimes the answer choices to a given question provide a big 'hint' as to how you can go about solving it. This prompt can also be solved without any complex math ideas - you just need to do a bit of 'brute force' math and you'll have the answer relatively quickly.   We're told that X and Y are INTEGERS and |X - Y| = 11. We're asked for the MINIMUM possible value of (X)(Y).   Since all of the answer choices are NEGATIVE, this tells us that ONE of the two variables MUST be negative (and the other must be positive), so we should restrict our work to those options.   IF...   X = 10, Y = -1, then XY = -10   X = 9, Y = -2, then XY = -18   X = 8, Y = -3, then XY = -24   X = 7, Y = -4, then XY = -28   X = 6, Y = -5, then XY = -30   X = 5, Y = -6, then XY = -30   X = 4, Y = -7, then XY = -28   From this, we can conclude the XY will start to get bigger as X continues to decrease down to 1, so there's no need to do any additional work.   Final Answer:   -30
Answer: D
In the coordinate plane, points (x, 8) and (20, y) are on line k. If line k passes through the origin and has slope 1/4, then x * y =
Answers:
A) 120
B) 100
C) 135
D) 140
E) 160

Solution: Line k passes through the origin and has slope 1/4 means that its equation is y=1/4*x.   Thus: (x, 8)=(32, 8) and (20, y) = (20,5) --> x*y=32*5= 
32*5 = 160
160.   Answer: 160
Answer: E