MU-NLPC/Calc-aqua_rat huggingface dataset:
A man taking the census walks up to the apartment of a mathematician and asks him if he has any children and how old they are. The mathematician says "I have three daughters and the product of their ages is 72." The man tells the mathematician that he needs more information, so the mathematician tells him "The sum of their ages is equal to our apartment number." The man still needs more information so the mathematician tells him "My oldest daughter has her own bed and the other two share bunk beds."
How old are his daughters?  Choose the correct choice from the following:  A) 5-2-3  B) 6-4-4  C) 9-5-4  D) 8-3-3  E) 7-2-2

Solution: His daughters are 8, 3, and 3. The prime factorization of 72 is 2 * 2 * 2 * 3 * 3, so the possible ages are 2, 3, 4, 6, 8, 9, 12, and 18. Using the prime factorization and these numbers the only combinations of numbers that work for the first clue are:   18, 2 and 2.   9, 4 and 2.   6, 6 and 2.   6, 4 and 3.   8, 3, and 3.   Since he doesn't know the ages after this piece of information the sum of the three numbers must not be unique. The sum of 8, 3, and 3; and 6, 6, and 2 are the same. Now the final clue comes in handy. Since we know that the oldest daughter has her own bed it is likely that she has the bed to herself and is older than the other two so there ages are 8, 3, and 3 rather than 2, 6 and 6.
Answer: D
An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is: Choose the correct choice from the following answers: A) 1.04 B) 2.04 C) 3.04 D) 4.04 E) None of these

Solution: Explanation:   100 cm is read as 102 cm.   A1 =(100 × 100)cm2 and A2= (102 × 102)cm2   (A2 - A1) = [1022 - 1002]   = (102 + 100) x (102 - 100) = 404 cm2 Answer: 4.04
Answer: D
One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill tank in 36 min, then the slower pipe alone will be able to fill the tank in?	Choose the correct choice from the following options: A) 81 min B) 108 min C) 144 min D) 192 min E) 120 min

Solution: Let the slower pipe alone fill the tank in x min.   Then, faster pipe will fill it in x/3 min.   1/x + 3/x = 1/36   4/x = 1/36 => x = 144 min.   ANSWER:144 min
Answer: C
If Finn was 16 months old one year ago, how old was he, in months, x months ago?	Answers.
A) x − 30	B) x − 12	C) 28 − x	D) 24 − x	E) 30 − x

Solution: Age Today = 16 months + 12 months (1year) = 28 months   X months ago- Today's Age - X = 28 - X   Ans- 28 − x
Answer: C
On the xy co-ordinate plane, point C is (5,-2) and point D is (-2,2.5). The point on line segment CD that is twice as far from C as from D is:
Choose the correct choice from the following answers:	A) (1,-1)	B) (1,1)	C) (2,0.25)	D) (3,-0.5)	E) (3,1)

Solution: We want the point on the line that is twice as far from C as it is from D. We can examine the x and y coordinates separately since they are independent.   *It should be noted that there are two solutions to this problem, one point between C and D, and another point with D in the middle of C and the point. We can quickly look at the answer choices and see that all the points are between C and D, therefore we can search for that point using the following method:   Taking the x-coordinate first, the distance between C and D is |(x-coordinate of C) - (x-coordinate of D)|= |5 - (-1)= 
5 - (-1) = 6
6   The x-coordinate that is twice as far from C as it is from D (and in between C and D) will be 4 units from C and 2 units from D. So the x coordinate of the point we're looking for is  5-4= 
 5-4 = 1
1, or  (-1)+2= 
 (-1)+2 = 1
1.   Now looking at the y-coordinate, we do the same thing. The distance between C and D is |(-2) - 2.5|= 4.5   The y-coordinate that is twice as far from C as it is from D (and in between C and D) will be 3 units from C and 1.5 units from D. So the y coordinate of the point we're looking for is  (-2)+3= 
 (-2)+3 = 1
1, or  2.5-1.5= 
 2.5-1.5 = 1
1.   So now we have our coordinates of the point on the line that is twice as far from C as it is from (3,-0.5): (3,-0.5)   Answer: (3,-0.5)
Answer: D
Two bullet train s 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:
Pick.
A) 15.8 sec.  B) 12.8 sec.  C) 11.8 sec.  D) 10.8 sec.  E) 08.8 sec.

Solution: D   10.8 sec.   Relative speed = (60 + 40) km/hr = 100x5/18 = 250/9 m/ sec.   Distance covered in crossing each other = (140 + 160)= 
(140 + 160) = 300
300 m.   Required time= 300x9/250 = 54/5= 
54/5 = 54/5 = around 10.8
10.8 sec.
Answer: D
If the number 241 * 523 is completely divisible by 9, then the smallest whole number in place of * will b  Pick one:
A) 4  B) 5  C) 1  D) 8  E) 9

Solution: Sum of digits = (2 + 4 + 1 + x + 5 + 2 + 3) = (17 + x), which must be divisible by 9.   x = 1.   1)
Answer: C
What is the lowest positive integer that is divisible by each of the odd integers between 17 and 23, inclusive?
Choose the correct choice from the following answers
A) 3×17×19×21	B) 5×17×19×23	C) 23*21*17*19	D) 7×15×19×21	E) 15×17×19×21

Solution: We should find the LCM of 17, 19, 23 and 21 = 3*7 --> LCM = 3*23*7*17*19 = 23*21*17*19.   Answer: 23*21*17*19.
Answer: C
Umesh directly went from P, to Q which is 9 feet distant. Then he turns to the right and walked 4 feet. After this he turned to the right and walked a distance which is equal from P to Q. Finally he turned to the right and walked 3 feet. How far is he now from P? Pick one:	A) 6 feet	B) 5 feet	C) 1 feet	D) 0 feet	E) 10 feet

Solution: 1 feet   ANSWER:1 feet
Answer: C
Income and expenditure of a person are in the ratio 10 : 4. If the income of the person is Rs. 19000, then find his savings?	Choose the correct option:
A) 79754  B) 87689  C) 59875  D) 11400  E) 87648

Solution: Let the income and the expenditure of the person be Rs. 10x and Rs. 4x respectively.   Income, 10x = 19000 => x = 1900   Savings = Income - expenditure = 10x - 4x = 6x 10  - 4= 
10  - 4 = 6
6x= 6(1900)   So, savings = Rs. 11400.   Answer:11400
Answer: D
The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 23hrs. How much distance will the car cover in 4hrs if the speed of the bike is twice speed of the tractor? Choose the correct choice:
A) 340 km
B) 480 km
C) 360 km
D) 450 km
E) None of these

Solution: Sol. Average speed of a tractor = 25 km / h   The speed of a bus in an hour = 25 × 2 = 50 km   The speed of a car in an hour = 9/5 * 50= 
9/5 * 50 = 90
90 km   So, the distance covered by car in 4 h is   90 × 4= 360 km   Ans.(360 km)
Answer: C
There are e members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 55 possible combinations in which Michael is not selected, what is the value of e?  Select
A) 11 B) 12 C) 15 D) 18 E) 22

Solution: Combinations of two persons, in which Michael was not selected = 55   number of ways two persons can be selected from m people = m*(m-1)/2   Let m be the number of people excluding Michael, then m*(m-1) = 110 => m=11   Thus, e = m + 1(Michael) = 12   option 12
Answer: B
there are 15 cars and 16 trucks? which is greater15 or 16?	Pick
A) 15	B) 14	C) 12	D) 17	E) 16

Solution: 16
Answer: E
A rectangular grassy plot 110 m. by 65 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 60 paise per sq. metre
Choose the correct choice from the following answers
A) s510
B) s780
C) s880
D) s480
E) s980

Solution: area of the plot=110m*65m=7150sq.m   area of plot excluding gravel110 *65= 
110 *65 = 7_150
7150sq.m   area of plot excluding gravel=105m*60m=6300sq.m   area of gravel 105 *60= 
105 *60 = 6_300
6300sq.m   area of gravel=7150sq.m-6300sq.m =850sq.m   cost of building it = 850sq.m*60   = 51000p   in Rs =51000/100= 
51000/100 = 510
Rs510   s510NSWER:s510
Answer: A
Which of the following equivalent to (1/64)^2? Choose the correct option
A) (0.05)^3  B) (0.06)^3  C) (0.07)^3  D) (0.08)^3  E) (0.09)^3

Solution: (1/64)^2 = (1/4^3)^2 = (1/4)^6 = (1/16)^3 = (0.06)^3   Answer: Option (0.06)^3
Answer: B
What is the sum of all 3 digit positive integers that can be formed using the digits 1, 4, and 7, if the digits are allowed to repeat within a number?
Pick one
A) 10,655	B) 11,988	C) 12,433	D) 13,766	E) 14,322

Solution: The number of these 3-digit numbers is   3*3*3= 
  3*3*3 = 27
27   Each digit 1, 4, and 7 will appear in the ones, tens, and hundreds place 9 times each.   The sum equals 9(111) + 9(444) + 9(777)= 11,988   The answer is 11,988.
Answer: B
If r and y are integers and (15^r + 15^(r+1))/4^y = 15^y what is the value of r?	Choose the most appropriate option
A) 2  B) 3  C) 4  D) 5  E) Cannot be determined

Solution: \frac{15^r( 1+ 15)}{4^y} = 15^y   (15^r . 4^2 ) / 4^y = 15^y. 4^0   15^r . 4^(2-y) = 15^y. 4^0   Equating the powers, r = y; 2-y = 0; So r = y = 2=2
Answer: A
Find the odd man out:
5, 8, 20, 42, 124, 246
Choose the correct choice from the following choices.
A) 20	B) 99	C) 77	D) 26	E) 81

Solution: Explanation:   The series is followed on the pattern of 2 alternate sequences with common formula being 2n-2 and 3n-2 respectively.   8 = 2*5-2   22 = 3*8-2   42 = 22*2-2   124 = 42*3-2   246 = 124*2-2   Hence, 20 is the odd no.   20NSWER: 20
Answer: A
The length of rectangle is thrice its breadth and its perimeter is 96 m, find the area of the rectangle?  Choose the correct choice from the following options:
A) 432	B) 288	C) 278	D) 269	E) 271

Solution: 2(3x + x) = 96   l = 36 b = 12   lb = 36 * 12= 
36 * 12 = 432
432   432nswer:432
Answer: A
Some pen bought something at loss for Rs 60.He then sold it the price of 81 and his profit was 20% of the loss.At what price did he buy the object Choose the most appropriate option:
A) 77.5
B) 76.5
C) 75.5
D) 74.5
E) 73.5

Solution: lets 77.5ssume loss be Rs x on Rs 60   Cost Price = 60+x   He then sold it the price of 81 and his profit was 20% of the loss   60+x + 20%x = 81   Solving this x will be 17.5   Cost Price = 60 + x = 60 + 17.5= 
60 + 17.5 = 77.5
77.5   77.5NSWER:77.5
Answer: A
In Set T, the average (arithmetic mean) equals the median W. Which of the following must be true?
I. Set T consists of evenly spaced numbers.
II. Set T consists of an odd number of terms.
III. Set T has no mode.
IV. None of the above.	Select the correct option.
A) I only  B) I and II  C) II and III  D) I, II, and III  E) IV only

Solution: This is a very good 'trap question'.   Consider Set A= { 0,0,0,0 } Mean=Median=Mode=0- Eliminates 1,2 and 3 OR   Consider Set B= {1,2,2,3 } Mean=Median=Mode=2- Eliminates 1,2 and 3   If you think that only in 'consecutive integers' the average is equal to the median W you might fall for 'D'.   Ans: IV only
Answer: E
A rectangular swimming pool is 8 feet by 20 feet. A deck that has uniform width surrounds the pool. The total area of the pool and deck is 540 square feet. What is the width of the deck?  Choose the correct choice from the following options: A) 1 B) 2 C) 3 D) 4 E) 5

Solution: Let the width =W   Total Area of the pool and deck= (2W+8)(2W+20)   We can Test the answer choices along with unit digit method   A) 2 feet ...........12*24 has unit digit 8..........5liminate   B) 2.5 feet.........13*25 has unit digit 5..........5liminate   C) 3 feet............14*26 has unit digit 4...........Hold   D) 4 feet............16*28 has unit digit 8...........5liminate   5) 5 feet............18*30 has unit digit 0...........5liminate   Answer: 5 w=5
Answer: E
Exactly 3/7 of the people in the room are under the age of 21, and exactly 5/8 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21?
Choose the most appropriate option:
A) 24 B) 35 C) 39 D) 60 E) 65

Solution: The total number of the people in the room must be a multiple of both 7 and 8 (in order 3/7 and 5/8 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 7 and 8, which is 56.   Since, the total number of the people in the room is greater than 50 and less than 100, then there are 56 people in the room.   Therefore there are   3/7*56= 
  3/7*56 = 24
24 people in the room under the age of 21.   24nswer: 24.
Answer: A
A telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 0, 1, 6, or 7. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most 2 attempts is closest to which of the following? Choose the correct choice from the following options
A) 1/6
B) 1/9
C) 1/18
D) 1/24
E) 1/36

Solution: There are 6*6= 
6*6 = 36
36 possibilities.   Bob has 2 chances so the probability is 2/36= 1/18.   The answer is 1/18.
Answer: C
If in a kindergarten class, there are five children 3 feet 4 inches tall (indicated by notation 3'4"), two children 4'3" tall and thirteen children 2'9" tall, which of the following is the median height of the children?
Choose the correct choice from the following
A) 2'9"
B) 2'6"
C) 3'3"
D) 3'4"
E) 4'3

Solution: Total number of children in class = 20   so median must be between 10th and 11th child when they are arranged in ascending order.   When arranged in ascending order 5th and 6th child will have the height of 3'4"   so required median height = (2'9"+2'9")/2 = 2'6"   2'9"ns:Option 2'9"
Answer: A
A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
Choose the most appropriate option.
A) 2 3/2  B) 2 2/3  C) 2.5  D) 3  E) 3.5

Solution: 100*(20/100)= 
100*(20/100) = 20
20 --- 10   ? --- 1=> Rs.2   100 --- 80   ? --- 2 => Rs.2.5   Answer: 2.5
Answer: C
Change 1/8 = 8-1 to logarithmic notation. Choose the correct answer:
A) log(8)8
B) log7
C) log(5)8
D) log 5
E) None of these

Solution: Solution:   1/8 = 8-1 = log88   log(8)8nswer is log(8)8
Answer: A
Eighteen years ago, a father was three times as old as his son. Now the father is only twice as old his son. Then the sum of the present ages of the son and the father is:
Choose the correct choice from the following options
A) 54	B) 72	C) 105	D) 108	E) 118

Solution: Let the present ages of the father and son be 2x and x years respectively.   Then, (2x - 18) = 3(x - 18) => x = 36   Required sum = (2x + x) = 108 years.   ANSWER:108
Answer: D
One lady has 2 children, one of her child is boy, what is the probability of having both are boys	Choose the most appropriate option
A) 1/2  B) 1/3  C) 1/4  D) 1/5  E) 3/4

Solution: n(S)=one of her child is boy out of 2 children=BB,BG=2   n(E)=both are boys=BB=1   so p=n(E)/n(s)=1/2   1/2NSWER:1/2
Answer: A
If the product 48^64 × 9x2 is divisible by 12, then what is the value of x? Answers
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: 4864 × 9a2 is divisible by 12   => 4864 × 9a2 is divisible by 3   and 4864 × 9a2 is divisible by 4   4864 is divisible by 4 because number formed by the last two digits is 64 which is divisible by 4. Hence 4864 × 9a2 will also be divisible by 4   4864 is not divisible by 3 (because   4 + 8 + 6 + 4= 
  4 + 8 + 6 + 4 = 22
22 which is not divisible by 3). Hence 9a2 must be divisible by 3 because 48^64 × 9x2 is divisible by 3=> 9 + x + 2 is divisible by 3   => 11 + a is divisible by 3   Hence a can be 1 or 4 or 7 such that 11 + a is divisible by 3   So, from the given choices, 1 is the answer.   1
Answer: A
Sterling Silver is 92.5% pure silver. How many grams of Sterling Silver must be mixed to a 90% Silver alloy to obtain a 500g of a 91% Silver alloy?
Choose the correct choice from the following options:
A) 200
B) 300
C) 400
D) 500
E) 600

Solution: Let x and y be the weights, in grams, of sterling silver and of the 90% alloy to make the 500 grams at 91%. Hence   x + y =500   The number of grams of pure silver in x plus the number of grams of pure silver in y is equal to the number of grams of pure silver in the 500 grams. The pure silver is given in percentage forms. Hence   92.5% x + 90% y = 91% 500   Substitute y by 500 - x in the last equation to write   92.5% x + 90% (500 - x) = 91% 500   Simplify and solve   92.5 x + 45000 - 90 x = 45500   x = 200 grams.   200 grams of Sterling Silver is needed to make the 91% alloy.   200nswer 200
Answer: A
Walking with 4/5 of my usual speed, I miss the bus by 6 minutes. What is my usual time?  Answers
A) 16 min B) 26 min C) 34 min D) 24 min E) 12 min

Solution: Speed Ratio = 1:4/5 = 5:4Time Ratio   = 4:5 1 -------- 6 4 --------- ? è 24   Answer: 24 min
Answer: D
A 300 m long train crosses a platform in 33 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
Choose the most appropriate option.
A) 286 m
B) 250 m
C) 277 m
D) 278 m
E) 267 m

Solution: Speed = 300/18 = 50/3 m/sec.   Let the length of the platform be x meters.   Then, (x + 300)/33 = 50/3   => x = 250 m.   Answer:250 m
Answer: B
A train running at the speed of 72 km/hr crosses a pole in 9 seconds. Find the length of the train?	Answers:
A) 150 meter	B) 299 meter	C) 666 meter	D) 155 meter	E) 180 meter

Solution: Speed = 72*(5/18) m/sec = 20 m/sec   Length of Train (Distance) = Speed * Time     (20) * 9= 
  (20) * 9 = 180
180 meter   Answer: 180 meter
Answer: E
A 240 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train? Choose the correct choice from the following options:
A) 230	B) 260	C) 267	D) 256	E) 298

Solution: Relative speed = 120 + 80= 
120 + 80 = 200
200 km/hr.= 200 * 5/18 = 500/9 m/sec.   Let the length of the other train be x m.   Then, (x + 240)/9 = 500/9 => x = 260.   Answer: 260
Answer: B
If an article is sold at 19% profit instead of 12% profit, then the profit would be Rs. 105 more. What is the cost price?	Pick:
A) 2278
B) 388
C) 1500
D) 2776
E) 8811

Solution: Let the cost price of an article be Rs. x.   (19% of x) - (12% of x) = 105   19x/100 - 12x/100 = 105 => 7x = 105 * 100   => x = 1500   Cost price = Rs. 1500   Answer:1500
Answer: C
If 8 men do a work in 80 days, in how many days will 20 men do it?
Options.
A) 18 days
B) 32 days
C) 42 days
D) 48 days
E) 44 days

Solution: 8 * 80 = 20 * x   x = 32 days   ANSWER:32 days
Answer: B
A train 160 m long passes a man,running at 6 kmph in the direction opposite to that of the train,in 6 seconds.The speed of the train is
Choose the correct choice from the following.
A) 54 kmph
B) 60 kmph
C) 66 kmph
D) 72 kmph
E) 90 kmph

Solution: speed of train relative to man: 160/6 * 18/5 km/hr   = 96 km/hr   let speed of train= x   therefore x+6 = 96   x= 96-6= 
96-6 = 90
90 km/hr   ANSW90 kmphR:90 kmph
Answer: E
The angle between the minute hand and the hour hand of a clock when the time is 12.30, is	Choose the correct choice from the following answers:
A) 35°
B) 65°
C) 45°
D) 195°
E) 95°

Solution: Angle between hands of a clock   When the minute hand is behind the hour hand, the angle between the two hands at M minutes past H 'o clock   =30(H−M/5)+M/2 degree   When the minute hand is ahead of the hour hand, the angle between the two hands at M minutes past H 'o clock   =30(M/5−H)−M/2 degree   Here H = 12, M = 30 and minute hand is behind the hour hand.   Hence the angle   =30(H−M/5)+M/2   =30(12−30/5)+30/2   =30(12−6)+15   =30×6+15 =195°   Answer is 195°.
Answer: D
A credit card number has 6 digits (between 1 to 9). The first two digits are 12 in that order, the third digit is bigger than 5, the forth is divisible by 3 and the fifth digit is 3 times the sixth. How many different credit card numbers exist?  Choose the most appropriate option:
A) 27
B) 72
C) 36
D) 112
E) 422

Solution: {1}{2}{greater than 5}{divisible by 3}{3x}{x}:   The third digit can take 4 values:6, 7, 8, or 9.   The fourth digit can take 3 values: 3, 6, or 9.   The fifth and sixth digits can take 3 values: 31, 62, or 93.   Total = 4*3*3= 
4*3*3 = 36
36.   Answer: 36.
Answer: C
The taxi charges in a city comprise of a fixed charge, together with the charge of the distance covered. For a journey of 16 km, the charges paid are Rs. 156 and for a journey of 24 km, the charges paid are Rs. 204. What will a person have to pay for travelling a distance of 30 km? Choose the most appropriate option.
A) Rs. 236  B) Rs. 240  C) Rs. 248  D) Rs. 252  E) Rs. 352

Solution: For a journey of 16 km, the charges paid are Rs. 156 and for a journey of 24 km, the charges paid are Rs. 204.   Additional charges for 8 kms = 204-156= 
204-156 = 48
48 Rs   additional charge/km= 48/8= 
48/8 = 6
Rs 6   additional charge for 6 kms= 6*6= 
6*6 = 36
Rs 36.   total charges for 30 kms= 204 +36= 
204 +36 = 240
Rs 240   ANSWER:Rs. 240
Answer: B
A boatman goes 3 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water? Choose the correct answer:
A) 40 minutes
B) 1 hour 7 min
C) 1 hour 15 min
D) 1 hour 30 min
E) 1 hour 10 min

Solution: speed (upstream) =3/1= 
3/1 = 3
3 kmhr   speed (downstream)=1/(10/60)= 
1/(10/60) = 6
6 kmhr   speed in still water= 1/2 (3+6) = 4.5 kmhr   time taken in stationary = 5/4.5 = 1 hrs 7 min   ANSWER:1 hour 7 min
Answer: B
In a mens hostel, there were 95 students. To accommodate 30 more students the average is decreased by rupees 5. But total expenditure increased by Rs.500. Find the total expenditure of the hostel now ?
Choose the correct choice from the following.
A) Rs.4680  B) Rs.4287  C) Rs.4129  D) Rs.4112  E) Rs.4101

Solution: Explanation:   Let the expenditure on the 95 students be 'x'   Then,   95x + 500 = 120(x â€“ 5)   95x + 500 = 120x - 600   120x - 95x = 1100   25x = 1100   => x = 44   Therefore, total expenditure of the hostel becomes   95 x 44 + 500 = 4680.   Rs.4680nswer: Rs.4680
Answer: A
For the set {2, 2, 3, 3, 4, 4, 5, 5,7,7 x}, which of the following values of x will most increase the standard deviation? Choose the correct choice from the following options
A) 1	B) 2	C) 3	D) (-3.2)^2	E) 5

Solution: Standard Deviation Step 1, as pointed out by others, is to find out the mean = 4.2   Step 2, For each number: subtract the Mean and square the result =   (1-4.2)^2=(-3.2)^2   (2-4.2)^2=(-2.2)^2   (3-4.2)^2 =(-1.2)^2   (4-4.2)^2=(.2)^2   (5-4.2)^2=(.8)^2   Clearly (1-3.5)^2=(-3.2)^2 will give you the greatest value among all the other options.   Hence (-3.2)^2
Answer: D
The population of a town is 186800. If it increase at the rate of 7% per annum. What will be its population for 2years hence?	Choices:
A) 200000
B) 215600
C) 194582
D) 213867
E) 215460

Solution: population after 2years = 186800*(1+ 7/100)^2 = 213867   Answer is 213867
Answer: D
In the city of San Durango, 60 people own cats, dogs, or rabbits. If 30 people owned cats, 40 owned dogs, 14 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three?  Choose the most appropriate option.
A) 2
B) 4
C) 6
D) 12
E) 32

Solution: You are considering a case when cat dogs and rabbit are not exactly equal to 12 .   The solution shall be 60=30+40+14-12-2x   and hence x shall be 6.   Answer 6
Answer: C
If the area of a square with sides of length 3 centimeters is equal to the area of a rectangle with a width of 4 centimeters, what is the length of the rectangle, in centimeters?
Choose the correct option: A) 4 B) 8 C) 12 D) 3 E) 18

Solution: Let length of rectangle = L   3^2 = L*4   => L = 9/4 = 3   Answer 3
Answer: D
In a hostel there were 100 students. To accommodate 20 more students the average is decreased by rupees 5. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?
Pick one:
A) 5429
B) 2897
C) 5400
D) 2689
E) 2781

Solution: 100x + 400 = 12(x – 5)   x = 50   100 * 50 + 400= 
100 * 50 + 400 = 5_400
5400   Answer:5400
Answer: C
The digital sum of a number is the sum of its digits. For how many of the positive integers 24-80 inclusive is the digital sum a multiple of 7?
Choose the correct choice from the following options.
A) 7 B) 9 C) 14 D) 16 E) 20

Solution: is there other way than just listing?   25   34   43   52   59   61   68   70   77   9 ways..   9
Answer: B